diff options
227 files changed, 8760 insertions, 8221 deletions
diff --git a/.gitattributes b/.gitattributes index db179c8d2..e087e1737 100644 --- a/.gitattributes +++ b/.gitattributes @@ -19,6 +19,7 @@ tools/CoqMakefile.in whitespace=trailing-space *.css whitespace=trailing-space,tab-in-indent *.dtd whitespace=trailing-space,tab-in-indent *.el whitespace=trailing-space,tab-in-indent +*.g whitespace=trailing-space,tab-in-indent *.h whitespace=trailing-space,tab-in-indent *.html whitespace=trailing-space,tab-in-indent *.hva whitespace=trailing-space,tab-in-indent @@ -37,9 +38,11 @@ tools/CoqMakefile.in whitespace=trailing-space *.nsh whitespace=trailing-space,tab-in-indent *.nsi whitespace=trailing-space,tab-in-indent *.py whitespace=trailing-space,tab-in-indent +*.rst whitespace=trailing-space,tab-in-indent *.sh whitespace=trailing-space,tab-in-indent *.sty whitespace=trailing-space,tab-in-indent *.tex whitespace=trailing-space,tab-in-indent +*.tokens whitespace=trailing-space,tab-in-indent *.txt whitespace=trailing-space,tab-in-indent *.v whitespace=trailing-space,tab-in-indent *.xml whitespace=trailing-space,tab-in-indent diff --git a/.github/CODEOWNERS b/.github/CODEOWNERS index fea50c58c..2d8fc791b 100644 --- a/.github/CODEOWNERS +++ b/.github/CODEOWNERS @@ -37,6 +37,10 @@ /dev/doc/ @Zimmi48 # Secondary maintainer @maximedenes +/dev/doc/changes.md @ghost +# Trick to avoid getting review requests +# each time someone modifies the dev changelog + /doc/ @maximedenes # Secondary maintainer @silene @@ -56,6 +60,9 @@ /lib/ @ejgallego # Secondary maintainer @ppedrot +/lib/cWarnings.* @maximedenes +# Secondary maintainer @ejgallego + ########## Proof engine ########## /engine/ @ppedrot @@ -104,8 +111,8 @@ /plugins/btauto/ @ppedrot # Secondary maintainer @herbelin -# I don't know Pierre Corbineau's GitHub nickname -/plugins/cc/ @herbelin +/plugins/cc/ @PierreCorbineau +# Secondary maintainer @herbelin /plugins/derive/ @aspiwack # Secondary maintainer @ppedrot @@ -113,8 +120,8 @@ /plugins/extraction/ @letouzey # Secondary maintainer @maximedenes -# I don't know Pierre Corbineau's GitHub nickname -/plugins/firstorder/ @herbelin +/plugins/firstorder/ @PierreCorbineau +# Secondary maintainer @herbelin /plugins/fourier/ @herbelin # Secondary maintainer @gares @@ -149,8 +156,8 @@ /plugins/quote/ @herbelin -# Should be Pierre Corbineau too -/plugins/rtauto/ @herbelin +/plugins/rtauto/ @PierreCorbineau +# Secondary maintainer @herbelin ########## Pretyper ########## @@ -294,6 +301,9 @@ /META.coq @ejgallego # Secondary maintainer @letouzey +/dev/build/windows @MSoegtropIMC +# Secondary maintainer @maximedenes + ########## Developer tools ########## diff --git a/.gitlab-ci.yml b/.gitlab-ci.yml index 03e001f4a..f0d7463fc 100644 --- a/.gitlab-ci.yml +++ b/.gitlab-ci.yml @@ -85,10 +85,6 @@ before_script: - echo 'end:coq.install' - set +e - variables: &build-variables - EXTRA_CONF: "-native-compiler yes -coqide opt" - EXTRA_PACKAGES: "$COQIDE_PACKAGES" - EXTRA_OPAM: "$COQIDE_OPAM" .warnings-template: &warnings-template # keep warnings in test stage so we can test things even when warnings occur @@ -151,9 +147,9 @@ before_script: build: <<: *build-template variables: - EXTRA_CONF: "-with-doc yes" - EXTRA_PACKAGES: "$COQDOC_PACKAGES" - EXTRA_OPAM: "$COQDOC_OPAM" + EXTRA_CONF: "-native-compiler yes -coqide opt -with-doc yes" + EXTRA_PACKAGES: "$COQIDE_PACKAGES $COQDOC_PACKAGES" + EXTRA_OPAM: "$COQIDE_OPAM $COQDOC_OPAM" PIP_PACKAGES: "$SPHINX_PACKAGES" # no coqide for 32bit: libgtk installation problems @@ -167,9 +163,10 @@ build:32bit: build:bleeding-edge: <<: *build-template variables: - <<: *build-variables + EXTRA_CONF: "-native-compiler yes -coqide opt" COMPILER: "$COMPILER_BLEEDING_EDGE" CAMLP5_VER: "$CAMLP5_VER_BLEEDING_EDGE" + EXTRA_PACKAGES: "$COQIDE_PACKAGES" EXTRA_OPAM: "$COQIDE_OPAM_BE" warnings: diff --git a/.travis.yml b/.travis.yml index 41814e954..e56204b0e 100644 --- a/.travis.yml +++ b/.travis.yml @@ -235,6 +235,7 @@ matrix: - COQ_DEST="-local" before_install: - brew update + - brew unlink python - brew install opam gnu-time - if: NOT (type = pull_request) @@ -6,6 +6,27 @@ Tools - Coq_makefile lets one override or extend the following variables from the command line: COQFLAGS, COQCHKFLAGS, COQDOCFLAGS. +Vernacular Commands + +- Removed deprecated commands Arguments Scope and Implicit Arguments + (not the option). Use the Arguments command instead. + +Tactic language + +- Support for fix/cofix added in Ltac "match" and "lazymatch". + +- Ltac backtraces now contain include trace information about tactics + called by OCaml-defined tactics. + +Changes from 8.8+beta1 to 8.8.0 +=============================== + +Tools + +- Asynchronous proof delegation policy was fixed. Since version 8.7 + Coq was ignoring previous runs and the -async-proofs-delegation-threshold + option did not have the expected behavior. + Changes from 8.7.2 to 8.8+beta1 =============================== diff --git a/CONTRIBUTING.md b/CONTRIBUTING.md index 213b87735..1a3c99369 100644 --- a/CONTRIBUTING.md +++ b/CONTRIBUTING.md @@ -38,13 +38,11 @@ Whitespace discipline (do not indent using tabs, no trailing spaces, text files Here are a few tags Coq developers may add to your PR and what they mean. In general feedback and requests for you as the pull request author will be in the comments and tags are only used to organize pull requests. -- [needs: rebase](https://github.com/coq/coq/pulls?utf8=%E2%9C%93&q=is%3Aopen%20is%3Apr%20label%3A%22needs%3A%20rebase%22%20) indicates the PR should be rebased on top of the latest `master` branch. See the [GitHub documentation](https://help.github.com/articles/about-git-rebase/) for a brief introduction to using `git rebase`. +- [needs: rebase](https://github.com/coq/coq/pulls?utf8=%E2%9C%93&q=is%3Aopen%20is%3Apr%20label%3A%22needs%3A%20rebase%22) indicates the PR should be rebased on top of the latest `master` branch. See the [GitHub documentation](https://help.github.com/articles/about-git-rebase/) for a brief introduction to using `git rebase`. - [needs: fixing](https://github.com/coq/coq/pulls?q=is%3Aopen+is%3Apr+label%3A%22needs%3A+fixing%22) indicates the PR needs a fix, as discussed in the comments. -- [needs: testing](https://github.com/coq/coq/pulls?q=is%3Aopen+is%3Apr+label%3A%22needs%3A+testing%22) indicates the PR needs testing. This is often used when testing beyond what the test suite can handle is required. For example, performance benchmarking is currently performed with a different infrastructure. Unless some followup is specifically requested you aren't expected to do this additional testing. +- [needs: benchmarking](https://github.com/coq/coq/pulls?q=is%3Aopen+is%3Apr+label%3A%22needs%3A+benchmarking%22) and [needs: testing](https://github.com/coq/coq/pulls?q=is%3Aopen+is%3Apr+label%3A%22needs%3A+testing%22) indicate the PR needs testing beyond what the test suite can handle. For example, performance benchmarking is currently performed with a different infrastructure. Unless some followup is specifically requested you aren't expected to do this additional testing. -The release manager uses the following filter to know which PRs seem ready for merge. If you are waiting for a PR to be merged, make sure it appears in this list: - -- [Pull requests ready for merge](https://github.com/coq/coq/pulls?utf8=%E2%9C%93&q=is%3Apr%20is%3Aopen%20-label%3A%22needs%3A%20discussion%22%20-label%3A%22needs%3A%20testing%22%20-label%3A%22needs%3A%20fixing%22%20-label%3A%22needs%3A%20progress%22%20-label%3A%22needs%3A%20rebase%22%20-label%3A%22needs%3A%20review%22%20-label%3A%22needs%3A%20help%22%20-label%3A%22needs%3A%20independent%20fix%22%20-label%3A%22needs%3A%20feedback%22%20-label%3A%22help%20wanted%22%20-review%3Achanges_requested%20-status%3Apending%20base%3Amaster%20sort%3Aupdated-asc%20-label%3A%22needs%3A%20squashing%22%20) +To learn more about the merging process, you can read the [merging documentation for Coq maintainers](/dev/doc/MERGING.md). ## Documentation @@ -52,7 +50,7 @@ Currently the process for contributing to the documentation is the same as for c Our issue tracker includes a flag to mark bugs related to documentation. You can view a list of documentation-related bugs using a [GitHub issue search](https://github.com/coq/coq/issues?q=is%3Aopen+is%3Aissue+label%3A%22kind%3A+documentation%22). Many of these bugs can be fixed by contributing writing, without knowledge of Coq's OCaml source code. -The sources for the [Coq reference manual](https://coq.inria.fr/distrib/current/refman/) are at [`doc/refman`](/doc/refman). These are written in LaTeX and compiled to HTML with [HeVeA](http://hevea.inria.fr/). +The sources for the [Coq reference manual](https://coq.inria.fr/distrib/current/refman/) are at [`doc/sphinx`](/doc/sphinx). These are written in reStructuredText and compiled to HTML and PDF with [Sphinx](http://www.sphinx-doc.org/). You may also contribute to the informal documentation available in [Cocorico](https://github.com/coq/coq/wiki) (the Coq wiki), and the [Coq FAQ](https://github.com/coq/coq/wiki/The-Coq-FAQ). Both of these are editable by anyone with a GitHub account. @@ -1,5 +1,5 @@ - INSTALLATION PROCEDURES FOR THE COQ V8.7 SYSTEM + INSTALLATION PROCEDURES FOR THE COQ V8.8 SYSTEM ----------------------------------------------- @@ -27,7 +27,7 @@ WHAT DO YOU NEED ? port install coq - To compile Coq V8.7 yourself, you need: + To compile Coq V8.8 yourself, you need: - OCaml version 4.02.3 or later (available at https://ocaml.org/) @@ -45,6 +45,10 @@ WHAT DO YOU NEED ? - for Coqide, the Lablgtk development files, and the GTK libraries including gtksourceview, see INSTALL.ide for more details + Note that camlp5 and lablgtk should be properly registered with + findlib/ocamlfind as Coq's makefile will use it to locate the + libraries during the build. + Opam (https://opam.ocaml.org/) is recommended to install ocaml and the corresponding packages. @@ -52,6 +56,16 @@ WHAT DO YOU NEED ? should get you a reasonable OCaml environment to compile Coq. + Advanced users may want to experiment with the OCaml Flambda + compiler as way to improve the performance of Coq. In order to + profit from Flambda, a special build of the OCaml compiler that has + the Flambda optimizer enabled must be installed. For OPAM users, + this amounts to installing a compiler switch ending in `+flambda`, + such as `4.06.1+flambda`. For other users, YMMV. Once `ocamlopt + -config` reports that Flambda is available, some further + optimization options can be used; see the entry about -flambda-opts + below for more details. + QUICK INSTALLATION PROCEDURE. ============================= @@ -66,7 +80,7 @@ INSTALLATION PROCEDURE IN DETAILS (NORMAL USERS). computer and that "ocamlc" (or, better, its native code version "ocamlc.opt") lies in a directory which is present in your $PATH environment variable. At the time of writing this sentence, all - versions of Objective Caml later or equal to 4.02.1 are + versions of Objective Caml later or equal to 4.02.3 are supported. To get Coq in native-code, (it runs 4 to 10 times faster than @@ -129,9 +143,10 @@ INSTALLATION PROCEDURE IN DETAILS (NORMAL USERS). and will be replaced by the URL. -flambda-opts <flags> - This experimental option will pass specific user flags to the + This experimental option will pass specific user flags to the OCaml optimizing compiler. In most cases, this option is used - to tweak the flambda backend; we recommend using + to tweak the flambda backend; for maximum performance we + recommend using -flambda-opts `-O3 -unbox-closures` @@ -144,7 +159,7 @@ INSTALLATION PROCEDURE IN DETAILS (NORMAL USERS). a large amount of RAM (>= 10GiB) in some particular files. We recommend disabling native compilation (`-native-compiler no`) - with flambda unless you use a modern (>= 4.06.0) OCaml. + with flambda unless you use OCaml >= 4.07.0. c.f. https://caml.inria.fr/mantis/view.php?id=7630 @@ -20,7 +20,7 @@ package "clib" ( version = "8.8" directory = "clib" - requires = "str, unix, threads" + requires = "num, str, unix, threads" archive(byte) = "clib.cma" archive(native) = "clib.cmxa" diff --git a/Makefile.doc b/Makefile.doc index 4a247f1d9..e52da403a 100644 --- a/Makefile.doc +++ b/Makefile.doc @@ -58,17 +58,11 @@ DOCCOMMON:=doc/common/version.tex doc/common/title.tex doc/common/macros.tex REFMANCOQTEXFILES:=$(addprefix doc/refman/, \ RefMan-gal.v.tex \ - RefMan-oth.v.tex RefMan-ltac.v.tex \ - RefMan-pro.v.tex \ - Coercion.v.tex Extraction.v.tex \ - Program.v.tex Polynom.v.tex Nsatz.v.tex \ - Setoid.v.tex Classes.v.tex Universes.v.tex \ - Misc.v.tex) + RefMan-ltac.v.tex \ + Universes.v.tex) REFMANTEXFILES:=$(addprefix doc/refman/, \ - headers.sty Reference-Manual.tex \ - RefMan-uti.tex \ - AsyncProofs.tex) \ + headers.sty Reference-Manual.tex) \ $(REFMANCOQTEXFILES) \ REFMANEPSFILES:=doc/refman/coqide.eps doc/refman/coqide-queries.eps diff --git a/clib/cArray.ml b/clib/cArray.ml index b6c033f6d..5eb20bc16 100644 --- a/clib/cArray.ml +++ b/clib/cArray.ml @@ -41,6 +41,8 @@ sig ('a -> 'b -> 'c -> 'a) -> 'a -> 'b array -> 'c array -> 'a val fold_left3 : ('a -> 'b -> 'c -> 'd -> 'a) -> 'a -> 'b array -> 'c array -> 'd array -> 'a + val fold_left4 : + ('a -> 'b -> 'c -> 'd -> 'e -> 'a) -> 'a -> 'b array -> 'c array -> 'd array -> 'e array -> 'a val fold_left2_i : (int -> 'a -> 'b -> 'c -> 'a) -> 'a -> 'b array -> 'c array -> 'a val fold_left_from : int -> ('a -> 'b -> 'a) -> 'a -> 'b array -> 'a @@ -267,6 +269,16 @@ let fold_left3 f a v1 v2 v3 = invalid_arg "Array.fold_left2"; fold a 0 +let fold_left4 f a v1 v2 v3 v4 = + let lv1 = Array.length v1 in + let rec fold a n = + if n >= lv1 then a + else fold (f a (uget v1 n) (uget v2 n) (uget v3 n) (uget v4 n)) (succ n) + in + if Array.length v2 <> lv1 || Array.length v3 <> lv1 || Array.length v4 <> lv1 then + invalid_arg "Array.fold_left4"; + fold a 0 + let fold_left_from n f a v = let len = Array.length v in let () = if n < 0 then invalid_arg "Array.fold_left_from" in diff --git a/clib/cArray.mli b/clib/cArray.mli index 97038b0ac..f4f60f8aa 100644 --- a/clib/cArray.mli +++ b/clib/cArray.mli @@ -66,6 +66,8 @@ sig ('a -> 'b -> 'c -> 'a) -> 'a -> 'b array -> 'c array -> 'a val fold_left3 : ('a -> 'b -> 'c -> 'd -> 'a) -> 'a -> 'b array -> 'c array -> 'd array -> 'a + val fold_left4 : + ('a -> 'b -> 'c -> 'd -> 'e -> 'a) -> 'a -> 'b array -> 'c array -> 'd array -> 'e array -> 'a val fold_left2_i : (int -> 'a -> 'b -> 'c -> 'a) -> 'a -> 'b array -> 'c array -> 'a val fold_left_from : int -> ('a -> 'b -> 'a) -> 'a -> 'b array -> 'a diff --git a/dev/build/osx/make-macos-dmg.sh b/dev/build/osx/make-macos-dmg.sh index dc33838f1..c450e8157 100755 --- a/dev/build/osx/make-macos-dmg.sh +++ b/dev/build/osx/make-macos-dmg.sh @@ -10,19 +10,19 @@ VERSION=$(sed -n -e '/^let coq_version/ s/^[^"]*"\([^"]*\)"$/\1/p' configure.ml) APP=bin/CoqIDE_${VERSION}.app # Create a .app file with CoqIDE, without signing it -make PRIVATEBINARIES=$APP -j $NJOBS -l2 $APP +make PRIVATEBINARIES="$APP" -j "$NJOBS" -l2 "$APP" # Add Coq to the .app file -make OLDROOT=$OUTDIR COQINSTALLPREFIX=$APP/Contents/Resources/ install-coq install-ide-toploop +make OLDROOT="$OUTDIR" COQINSTALLPREFIX="$APP/Contents/Resources/" install-coq install-ide-toploop # Create the dmg bundle -mkdir -p $DMGDIR -ln -sf /Applications $DMGDIR/Applications -cp -r $APP $DMGDIR +mkdir -p "$DMGDIR" +ln -sf /Applications "$DMGDIR/Applications" +cp -r "$APP" "$DMGDIR" mkdir -p _build # Temporary countermeasure to hdiutil error 5341 # head -c9703424 /dev/urandom > $DMGDIR/.padding -hdiutil create -imagekey zlib-level=9 -volname coq-$VERSION-installer-macos -srcfolder $DMGDIR -ov -format UDZO _build/coq-$VERSION-installer-macos.dmg +hdiutil create -imagekey zlib-level=9 -volname "coq-$VERSION-installer-macos" -srcfolder "$DMGDIR" -ov -format UDZO "_build/coq-$VERSION-installer-macos.dmg" diff --git a/dev/build/windows/MakeCoq_88git_installer.bat b/dev/build/windows/MakeCoq_88git_installer.bat new file mode 100755 index 000000000..b016fb389 --- /dev/null +++ b/dev/build/windows/MakeCoq_88git_installer.bat @@ -0,0 +1,27 @@ +@ECHO OFF
+
+REM ========== COPYRIGHT/COPYLEFT ==========
+
+REM (C) 2016 Intel Deutschland GmbH
+REM Author: Michael Soegtrop
+
+REM Released to the public by Intel under the
+REM GNU Lesser General Public License Version 2.1 or later
+REM See https://www.gnu.org/licenses/old-licenses/lgpl-2.1.html
+
+REM ========== BUILD COQ ==========
+
+call MakeCoq_SetRootPath
+
+call MakeCoq_MinGW.bat ^
+ -arch=64 ^
+ -installer=Y ^
+ -coqver=git-v8.8 ^
+ -destcyg=%ROOTPATH%\cygwin_coq64_88_inst ^
+ -destcoq=%ROOTPATH%\coq64_88_inst ^
+ -addon=bignums
+
+IF %ERRORLEVEL% NEQ 0 (
+ ECHO MakeCoq_88git_installer.bat failed with error code %ERRORLEVEL%
+ EXIT /b %ERRORLEVEL%
+)
diff --git a/dev/build/windows/MakeCoq_MinGW.bat b/dev/build/windows/MakeCoq_MinGW.bat index ccf22cc86..f960ff008 100644 --- a/dev/build/windows/MakeCoq_MinGW.bat +++ b/dev/build/windows/MakeCoq_MinGW.bat @@ -34,7 +34,7 @@ REM see -ocaml in ReadMe.txt SET INSTALLOCAML=N REM see -make in ReadMe.txt -SET INSTALLMAKE=Y +SET INSTALLMAKE=N REM see -destcyg in ReadMe.txt SET DESTCYG=C:\bin\cygwin_coq @@ -267,7 +267,6 @@ IF "%INSTALLMODE%" == "mingwincygwin" ( IF "%MAKEINSTALLER%" == "Y" ( SET INSTALLMODE=relocatable SET INSTALLOCAML=Y - SET INSTALLMAKE=Y ) REM ========== CONFIRM PARAMETERS ========== diff --git a/dev/build/windows/configure_profile.sh b/dev/build/windows/configure_profile.sh index 16c972e80..7e606b554 100644 --- a/dev/build/windows/configure_profile.sh +++ b/dev/build/windows/configure_profile.sh @@ -14,30 +14,30 @@ rcfile=~/.bash_profile donefile=~/.bash_profile.upated +# to learn about `exec >> $file`, see https://www.tldp.org/LDP/abs/html/x17974.html +exec >> $rcfile + if [ ! -f $donefile ] ; then - echo >> $rcfile - - if [ "$1" != "" -a "$1" != " " ]; then - echo export http_proxy="http://$1" >> $rcfile - echo export https_proxy="http://$1" >> $rcfile - echo export ftp_proxy="http://$1" >> $rcfile + if [ "$1" != "" ] && [ "$1" != " " ]; then + echo export http_proxy="http://$1" + echo export https_proxy="http://$1" + echo export ftp_proxy="http://$1" fi - - mkdir -p $RESULT_INSTALLDIR_CFMT/bin + + mkdir -p "$RESULT_INSTALLDIR_CFMT/bin" # A tightly controlled path helps to avoid issues # Note: the order is important: first have the cygwin binaries, then the mingw binaries in the path! # Note: /bin is mounted at /usr/bin and /lib at /usr/lib and it is common to use /usr/bin in PATH # See cat /proc/mounts - echo "export PATH=/usr/local/bin:/usr/bin:$RESULT_INSTALLDIR_CFMT/bin:/usr/$TARGET_ARCH/sys-root/mingw/bin:/cygdrive/c/Windows/system32:/cygdrive/c/Windows" >> $rcfile + echo "export PATH=/usr/local/bin:/usr/bin:$RESULT_INSTALLDIR_CFMT/bin:/usr/$TARGET_ARCH/sys-root/mingw/bin:/cygdrive/c/Windows/system32:/cygdrive/c/Windows" # find and xargs complain if the environment is larger than (I think) 8k. # ORIGINAL_PATH (set by cygwin) can be a few k and exceed the limit - echo unset ORIGINAL_PATH >> $rcfile - + echo unset ORIGINAL_PATH # Other installations of OCaml will mess up things - echo unset OCAMLLIB >> $rcfile + echo unset OCAMLLIB touch $donefile fi diff --git a/dev/build/windows/difftar-folder.sh b/dev/build/windows/difftar-folder.sh index cbcf14ec2..3bba451ec 100644 --- a/dev/build/windows/difftar-folder.sh +++ b/dev/build/windows/difftar-folder.sh @@ -42,7 +42,7 @@ fi if [ "$strip" -gt 0 ] ; then # Get the path/name of the first file from teh tar and extract the first $strip path components # This assumes that the first file in the tar file has at least $strip many path components - prefix=$(tar -t -f $tarfile | head -1 | cut -d / -f -$strip)/ + prefix=$(tar -t -f "$tarfile" | head -1 | cut -d / -f -$strip)/ else prefix= fi @@ -60,13 +60,13 @@ mkdir -p "$empty" # Print information (this is ignored by patch) -echo diff/patch file created on $(date) with: -echo difftar-folder.sh $@ -echo TARFILE= $tarfile -echo FOLDER= $folder -echo TARSTRIP= $strip -echo TARPREFIX= $prefix -echo ORIGFOLDER= $orig +echo diff/patch file created on "$(date)" with: +echo difftar-folder.sh "$@" +echo TARFILE= "$tarfile" +echo FOLDER= "$folder" +echo TARSTRIP= "$strip" +echo TARPREFIX= "$prefix" +echo ORIGFOLDER= "$orig" # Make sure tar uses english output (for Mod time differs) export LC_ALL=C @@ -76,14 +76,14 @@ tar --diff -a -f "$tarfile" --strip $strip --directory "$folder" | grep "Mod tim # Substitute ': Mod time differs' with nothing file=${file/: Mod time differs/} # Check if file exists - if [ -f "$folder/$file" ] ; then + if [ -f "$folder/$file" ] ; then # Extract original file tar -x -a -f "$tarfile" --strip $strip --directory "$orig" "$prefix$file" # Compute diff - diff -u "$orig/$file" "$folder/$file" + diff -u "$orig/$file" "$folder/$file" fi done if [ -d "$new" ] ; then - diff -u -r --unidirectional-new-file $empty $new + diff -u -r --unidirectional-new-file "$empty" "$new" fi diff --git a/dev/build/windows/makecoq_mingw.sh b/dev/build/windows/makecoq_mingw.sh index 8e0d2341d..18f1a2f16 100644 --- a/dev/build/windows/makecoq_mingw.sh +++ b/dev/build/windows/makecoq_mingw.sh @@ -67,7 +67,7 @@ RMDIR_BEFORE_BUILD=1 ###################### ARCHITECTURES ##################### # The OS on which the build of the tool/lib runs -BUILD=`gcc -dumpmachine` +BUILD=$(gcc -dumpmachine) # The OS on which the tool runs # "`find /bin -name "*mingw32-gcc.exe"`" -dumpmachine @@ -132,34 +132,38 @@ CYGWIN_REPO_FOLDER=${CYGWIN_REPO_FOLDER//\//%2f} # Copy files cp "$CYGWIN_LOCAL_CACHE_WFMT/$CYGWIN_REPO_FOLDER/$CYGWINARCH/setup.ini" $TARBALLS cp /etc/setup/installed.db $TARBALLS - + ###################### LOGGING ##################### # The folder which receives log files mkdir -p buildlogs -LOGS=`pwd`/buildlogs +LOGS=$(pwd)/buildlogs # The current log target (first part of the log file name) LOGTARGET=other +# Log command output - take log target name from command name (like log1 make => log target is "<module>-make") log1() { - "$@" > $LOGS/$LOGTARGET-$1.log 2> $LOGS/$LOGTARGET-$1.err + "$@" > "$LOGS/$LOGTARGET-$1.log" 2> "$LOGS/$LOGTARGET-$1.err" } +# Log command output - take log target name from command name and first argument (like log2 make install => log target is "<module>-make-install") log2() { - "$@" > $LOGS/$LOGTARGET-$1-$2.log 2> $LOGS/$LOGTARGET-$1-$2.err + "$@" > "$LOGS/$LOGTARGET-$1-$2.log" 2> "$LOGS/$LOGTARGET-$1-$2.err" } +# Log command output - take log target name from command name and second argument (like log_1_3 ocaml setup.ml -configure => log target is "<module>-ocaml--configure") log_1_3() { - "$@" > $LOGS/$LOGTARGET-$1-$3.log 2> $LOGS/$LOGTARGET-$1-$3.err + "$@" > "$LOGS/$LOGTARGET-$1-$3.log" 2> "$LOGS/$LOGTARGET-$1-$3.err" } +# Log command output - log target name is first argument (like logn untar tar xvaf ... => log target is "<module>-untar") logn() { LOGTARGETEX=$1 shift - "$@" > $LOGS/$LOGTARGET-$LOGTARGETEX.log 2> $LOGS/$LOGTARGET-$LOGTARGETEX.err + "$@" > "$LOGS/$LOGTARGET-$LOGTARGETEX.log" 2> "$LOGS/$LOGTARGET-$LOGTARGETEX.err" } - + ###################### 'UNFIX' SED ##################### # In Cygwin SED used to do CR-LF to LF conversion, but since sed 4.4-1 this was changed @@ -183,7 +187,7 @@ logn() { # - create build folder # - extract source archive # - patch source file if patch exists -# +# # Parameters # $1 file server name including protocol prefix # $2 file name (without extension) @@ -206,68 +210,68 @@ function get_expand_source_tar { else name=$2 fi - + if [ "$#" -ge 6 ] ; then folder=$6 else folder=$name fi - + # Set logging target logtargetold=$LOGTARGET LOGTARGET=$name - + # Get the source archive either from the source cache or online - if [ ! -f $TARBALLS/$name.$3 ] ; then + if [ ! -f "$TARBALLS/$name.$3" ] ; then if [ -f "$SOURCE_LOCAL_CACHE_CFMT/$name.$3" ] ; then - cp "$SOURCE_LOCAL_CACHE_CFMT/$name.$3" $TARBALLS + cp "$SOURCE_LOCAL_CACHE_CFMT/$name.$3" "$TARBALLS" else - wget $1/$2.$3 - if file -i $2.$3 | grep text/html; then - echo Download failed: $1/$2.$3 + wget "$1/$2.$3" + if file -i "$2.$3" | grep text/html; then + echo Download failed: "$1/$2.$3" echo The file wget downloaded is an html file: - cat $2.$3 + cat "$2.$3" exit 1 fi if [ ! "$2.$3" == "$name.$3" ] ; then - mv $2.$3 $name.$3 + mv "$2.$3" "$name.$3" fi - mv $name.$3 $TARBALLS + mv "$name.$3" "$TARBALLS" # Save the source archive in the source cache if [ -d "$SOURCE_LOCAL_CACHE_CFMT" ] ; then - cp $TARBALLS/$name.$3 "$SOURCE_LOCAL_CACHE_CFMT" + cp "$TARBALLS/$name.$3" "$SOURCE_LOCAL_CACHE_CFMT" fi fi fi - + # Remove build directory (clean build) if [ $RMDIR_BEFORE_BUILD -eq 1 ] ; then - rm -f -r $folder + rm -f -r "$folder" fi - + # Create build directory and cd - mkdir -p $folder - cd $folder - + mkdir -p "$folder" + cd "$folder" + # Extract source archive if [ "$3" == "zip" ] ; then - log1 unzip $TARBALLS/$name.$3 + log1 unzip "$TARBALLS/$name.$3" if [ "$strip" == "1" ] ; then # Ok, this is dirty, but it works and it fails if there are name clashes - mv */* . + mv -- */* . else echo "Unzip strip count not supported" return 1 fi else - logn untar tar xvaf $TARBALLS/$name.$3 --strip $strip + logn untar tar xvaf "$TARBALLS/$name.$3" --strip $strip fi - + # Patch if patch file exists - if [ -f $PATCHES/$name.patch ] ; then - log1 patch -p1 -i $PATCHES/$name.patch + if [ -f "$PATCHES/$name.patch" ] ; then + log1 patch -p1 -i "$PATCHES/$name.patch" fi - + # Go back to base folder cd .. @@ -283,7 +287,7 @@ function get_expand_source_tar { # - cd to build folder and extract source archive # - create bin_special subfolder and add it to $PATH # - remember things for build_post -# +# # Parameters # $1 file server name including protocol prefix # $2 file name (without extension) @@ -305,27 +309,27 @@ function build_prep { else name=$2 fi - + # Check if build is already done - if [ ! -f flagfiles/$name.finished ] ; then + if [ ! -f "flagfiles/$name.finished" ] ; then BUILD_PACKAGE_NAME=$name BUILD_OLDPATH=$PATH - BUILD_OLDPWD=`pwd` + BUILD_OLDPWD=$(pwd) LOGTARGET=$name - touch flagfiles/$name.started - - get_expand_source_tar $1 $2 $3 $strip $name - - cd $name - + touch "flagfiles/$name.started" + + get_expand_source_tar "$1" "$2" "$3" "$strip" "$name" + + cd "$name" + # Create a folder and add it to path, where we can put special binaries # The path is restored in build_post mkdir bin_special - PATH=`pwd`/bin_special:$PATH - + PATH=$(pwd)/bin_special:$PATH + return 0 - else + else return 1 fi } @@ -337,9 +341,9 @@ function build_prep { # ------------------------------------------------------------------------------ function build_post { - if [ ! -f flagfiles/$BUILD_PACKAGE_NAME.finished ]; then - cd $BUILD_OLDPWD - touch flagfiles/$BUILD_PACKAGE_NAME.finished + if [ ! -f "flagfiles/$BUILD_PACKAGE_NAME.finished" ]; then + cd "$BUILD_OLDPWD" + touch "flagfiles/$BUILD_PACKAGE_NAME.finished" PATH=$BUILD_OLDPATH LOGTARGET=other fi @@ -362,9 +366,10 @@ function build_post { # ------------------------------------------------------------------------------ function build_conf_make_inst { - if build_prep $1 $2 $3 ; then + if build_prep "$1" "$2" "$3" ; then $4 - logn configure ./configure --build=$BUILD --host=$HOST --target=$TARGET --prefix="$PREFIX" "${@:5}" + logn configure ./configure --build="$BUILD" --host="$HOST" --target="$TARGET" --prefix="$PREFIX" "${@:5}" + # shellcheck disable=SC2086 log1 make $MAKE_OPT log2 make install log2 make clean @@ -383,6 +388,7 @@ function build_conf_make_inst { function install_glob { # Check if any files matching the pattern exist if [ "$(echo $1)" != "$1" ] ; then + # shellcheck disable=SC2086 install -D -t $2 $1 fi } @@ -398,7 +404,7 @@ function install_glob { # ------------------------------------------------------------------------------ function install_rec { - ( cd $1 && find -type f -name "$2" -exec install -D -T $1/{} $3/{} \; ) + ( cd "$1" && find . -type f -name "$2" -exec install -D -T "$1"/{} "$3"/{} \; ) } # ------------------------------------------------------------------------------ @@ -411,7 +417,7 @@ function install_rec { function list_files { if [ ! -e "/build/filelists/$1" ] ; then - ( cd "$PREFIXCOQ" && find -type f | sort > /build/filelists/$1 ) + ( cd "$PREFIXCOQ" && find . -type f | sort > /build/filelists/"$1" ) fi } @@ -439,7 +445,7 @@ function diff_files { # ------------------------------------------------------------------------------ function filter_files { - egrep "$3" "/build/filelists/$2" > "/build/filelists/$1" + grep -E "$3" "/build/filelists/$2" > "/build/filelists/$1" } # ------------------------------------------------------------------------------ @@ -453,7 +459,7 @@ function files_to_nsis { # Split the path in the file list into path and filename and create SetOutPath and File instructions # Note: File /oname cannot be used, because it does not create the paths as SetOutPath does # Note: I didn't check if the redundant SetOutPath instructions have a bad impact on installer size or install time - cat "/build/filelists/$1" | tr '/' '\\' | sed -r 's/^\.(.*)\\([^\\]+)$/SetOutPath $INSTDIR\\\1\nFile ${COQ_SRC_PATH}\\\1\\\2/' > "/build/filelists/$1.nsh" + tr '/' '\\' < "/build/filelists/$1" | sed -r 's/^\.(.*)\\([^\\]+)$/SetOutPath $INSTDIR\\\1\nFile ${COQ_SRC_PATH}\\\1\\\2/' > "/build/filelists/$1.nsh" } @@ -501,7 +507,7 @@ function make_fontconfig { make_freetype make_expat # CONFIGURE PARAMETERS - # build/install fails without --disable-docs + # build/install fails without --disable-docs build_conf_make_inst http://www.freedesktop.org/software/fontconfig/release fontconfig-2.11.94 tar.gz true --disable-docs } @@ -532,7 +538,7 @@ function make_ncurses { # # CONFIGURE PARAMETERS # --enable-term-driver --enable-sp-funcs is rewuired for mingw (see README.MinGW) - # additional changes + # additional changes # ADD --with-pkg-config # ADD --enable-pc-files # ADD --without-manpages @@ -604,7 +610,7 @@ function make_gdk-pixbuf { # CONFIGURE PARAMETERS # --with-included-loaders=yes statically links the image file format handlers # This avoids "Cannot open pixbuf loader module file '/usr/x86_64-w64-mingw32/sys-root/mingw/lib/gdk-pixbuf-2.0/2.10.0/loaders.cache': No such file or directory" - build_conf_make_inst http://ftp.gnome.org/pub/GNOME/sources/gdk-pixbuf/2.32 gdk-pixbuf-2.32.1 tar.xz true --with-included-loaders=yes + build_conf_make_inst http://ftp.gnome.org/pub/GNOME/sources/gdk-pixbuf/2.32 gdk-pixbuf-2.32.1 tar.xz true --with-included-loaders=yes } ##### CAIRO ##### @@ -657,8 +663,8 @@ function make_gtk3 { build_conf_make_inst http://ftp.gnome.org/pub/gnome/sources/gtk+/3.16 gtk+-3.16.7 tar.xz true # make all incl. tests and examples runs through fine - # make install fails with issue with - # + # make install fails with issue with + # # make[5]: Entering directory '/home/soegtrop/GTK/gtk+-3.16.7/demos/gtk-demo' # test -n "" || ../../gtk/gtk-update-icon-cache --ignore-theme-index --force "/usr/x86_64-w64-mingw32/sys-root/mingw/share/icons/hicolor" # gtk-update-icon-cache.exe: Failed to open file /usr/x86_64-w64-mingw32/sys-root/mingw/share/icons/hicolor/.icon-theme.cache : No such file or directory @@ -676,7 +682,8 @@ function make_libxml2 { if build_prep https://git.gnome.org/browse/libxml2/snapshot libxml2-2.9.1 tar.xz ; then # ./autogen.sh --build=$BUILD --host=$HOST --target=$TARGET --prefix="$PREFIX" --disable-shared --without-python # shared library required by gtksourceview - ./autogen.sh --build=$BUILD --host=$HOST --target=$TARGET --prefix="$PREFIX" --without-python + ./autogen.sh --build="$BUILD" --host="$HOST" --target="$TARGET" --prefix="$PREFIX" --without-python + # shellcheck disable=SC2086 log1 make $MAKE_OPT all log2 make install log2 make clean @@ -708,12 +715,12 @@ function make_gtk_sourceview2 { # Install flexdll objects function install_flexdll { - cp flexdll.h /usr/$TARGET_ARCH/sys-root/mingw/include + cp flexdll.h "/usr/$TARGET_ARCH/sys-root/mingw/include" if [ "$TARGET_ARCH" == "i686-w64-mingw32" ]; then - cp flexdll*_mingw.o /usr/$TARGET_ARCH/bin + cp flexdll*_mingw.o "/usr/$TARGET_ARCH/bin" cp flexdll*_mingw.o "$PREFIXOCAML/bin" elif [ "$TARGET_ARCH" == "x86_64-w64-mingw32" ]; then - cp flexdll*_mingw64.o /usr/$TARGET_ARCH/bin + cp flexdll*_mingw64.o "/usr/$TARGET_ARCH/bin" cp flexdll*_mingw64.o "$PREFIXOCAML/bin" else echo "Unknown target architecture" @@ -724,8 +731,8 @@ function install_flexdll { # Install flexlink function install_flexlink { - cp flexlink.exe /usr/$TARGET_ARCH/bin - + cp flexlink.exe "/usr/$TARGET_ARCH/bin" + cp flexlink.exe "$PREFIXOCAML/bin" } @@ -745,8 +752,10 @@ function get_flex_dll_link_bin { function make_flex_dll_link { if build_prep http://alain.frisch.fr/flexdll flexdll-0.34 tar.gz ; then if [ "$TARGET_ARCH" == "i686-w64-mingw32" ]; then + # shellcheck disable=SC2086 log1 make $MAKE_OPT build_mingw flexlink.exe elif [ "$TARGET_ARCH" == "x86_64-w64-mingw32" ]; then + # shellcheck disable=SC2086 log1 make $MAKE_OPT build_mingw64 flexlink.exe else echo "Unknown target architecture" @@ -769,11 +778,11 @@ function make_ln { if [ ! -f flagfiles/myln.finished ] ; then touch flagfiles/myln.started mkdir -p myln - cd myln + ( cd myln cp $PATCHES/ln.c . - $TARGET_ARCH-gcc -DUNICODE -D_UNICODE -DIGNORE_SYMBOLIC -mconsole -o ln.exe ln.c + "$TARGET_ARCH-gcc" -DUNICODE -D_UNICODE -DIGNORE_SYMBOLIC -mconsole -o ln.exe ln.c install -D ln.exe "$PREFIXCOQ/bin/ln.exe" - cd .. + ) touch flagfiles/myln.finished fi } @@ -799,14 +808,14 @@ function make_ocaml { # Prefix is fixed in make file - replace it with the real one # TODO: this might not work if PREFIX contains spaces sed -i "s|^PREFIX=.*|PREFIX=$PREFIXOCAML|" config/Makefile - + # We don't want to mess up Coq's directory structure so put the OCaml library in a separate folder # If we refer to the make variable ${PREFIX} below, camlp5 ends up having the wrong path: # D:\bin\coq64_buildtest_abs_ocaml4\bin>ocamlc -where => D:/bin/coq64_buildtest_abs_ocaml4/libocaml # D:\bin\coq64_buildtest_abs_ocaml4\bin>camlp4 -where => ${PREFIX}/libocaml\camlp4 # So we put an explicit path in there sed -i "s|^LIBDIR=.*|LIBDIR=$PREFIXOCAML/libocaml|" config/Makefile - + # Note: ocaml doesn't support -j 8, so don't pass MAKE_OPT # I verified that 4.02.3 still doesn't support parallel build log2 make world -f Makefile.nt @@ -815,12 +824,12 @@ function make_ocaml { log2 make opt.opt -f Makefile.nt log2 make install -f Makefile.nt # TODO log2 make clean -f Makefile.nt Temporarily disabled for ocamlbuild development - + # Move license files and other into into special folder if [ "$INSTALLMODE" == "absolute" ] || [ "$INSTALLMODE" == "relocatable" ]; then mkdir -p "$PREFIXOCAML/license_readme/ocaml" # 4.01 installs these files, 4.02 doesn't. So delete them and copy them from the sources. - rm -f *.txt + rm -f ./*.txt cp LICENSE "$PREFIXOCAML/license_readme/ocaml/License.txt" cp INSTALL "$PREFIXOCAML/license_readme/ocaml/Install.txt" cp README "$PREFIXOCAML/license_readme/ocaml/ReadMe.txt" @@ -909,9 +918,10 @@ function make_camlp5 { make_ocaml make_findlib if build_prep http://camlp5.gforge.inria.fr/distrib/src camlp5-6.14 tgz 1 ; then - logn configure ./configure + logn configure ./configure # Somehow my virus scanner has the boot.new/SAVED directory locked after the move for a second => repeat until success sed -i 's/mv boot.new boot/until mv boot.new boot; do sleep 1; done/' Makefile + # shellcheck disable=SC2086 log1 make world.opt $MAKE_OPT log2 make install # For some reason gramlib.a is not copied, but it is required by Coq @@ -939,15 +949,15 @@ function make_lablgtk { make_gtk_sourceview2 if build_prep https://forge.ocamlcore.org/frs/download.php/1479 lablgtk-2.18.3 tar.gz 1 ; then # configure should be fixed to search for $TARGET_ARCH-pkg-config.exe - cp /bin/$TARGET_ARCH-pkg-config.exe bin_special/pkg-config.exe - logn configure ./configure --build=$BUILD --host=$HOST --target=$TARGET --prefix="$PREFIXOCAML" - + cp "/bin/$TARGET_ARCH-pkg-config.exe" bin_special/pkg-config.exe + logn configure ./configure --build="$BUILD" --host="$HOST" --target="$TARGET" --prefix="$PREFIXOCAML" + # lablgtk shows occasional errors with -j, so don't pass $MAKE_OPT - + # See https://sympa.inria.fr/sympa/arc/caml-list/2015-10/msg00204.html for the make || true + strip logn make-world-pre make world || true - $TARGET_ARCH-strip.exe --strip-unneeded src/dlllablgtk2.dll - + "$TARGET_ARCH-strip.exe" --strip-unneeded src/dlllablgtk2.dll + log2 make world log2 make install log2 make clean @@ -978,7 +988,7 @@ function make_stdint { function copy_coq_dll { if [ "$INSTALLMODE" == "absolute" ] || [ "$INSTALLMODE" == "relocatable" ]; then - cp /usr/${ARCH}-w64-mingw32/sys-root/mingw/bin/$1 "$PREFIXCOQ/bin/$1" + cp "/usr/${ARCH}-w64-mingw32/sys-root/mingw/bin/$1" "$PREFIXCOQ/bin/$1" fi } @@ -994,7 +1004,7 @@ function copy_coq_dlls { # Do this recursively until there are no further missing DLLs (File close + reopen) # For running this quickly, just do "cd coq-<ver> ; call copy_coq_dlls ; cd .." at the end of this script. # Do the same for coqc and ocamlc (usually doesn't result in additional files) - + copy_coq_dll LIBATK-1.0-0.DLL copy_coq_dll LIBCAIRO-2.DLL copy_coq_dll LIBEXPAT-1.DLL @@ -1018,7 +1028,7 @@ function copy_coq_dlls { copy_coq_dll LIBXML2-2.DLL copy_coq_dll ZLIB1.DLL - # Depends on if GTK is built from sources + # Depends on if GTK is built from sources if [ "$GTK_FROM_SOURCES" == "Y" ]; then copy_coq_dll libiconv-2.dll else @@ -1036,21 +1046,21 @@ function copy_coq_dlls { i686) copy_coq_dll LIBGCC_S_SJLJ-1.DLL ;; *) false ;; esac - + # Win pthread version change copy_coq_dll LIBWINPTHREAD-1.DLL } function copy_coq_objects { # copy objects only from folders which exist in the target lib directory - find . -type d | while read FOLDER ; do + find . -type d | while read -r FOLDER ; do if [ -e "$PREFIXCOQ/lib/$FOLDER" ] ; then - install_glob $FOLDER/'*.cmxa' "$PREFIXCOQ/lib/$FOLDER" - install_glob $FOLDER/'*.cmi' "$PREFIXCOQ/lib/$FOLDER" - install_glob $FOLDER/'*.cma' "$PREFIXCOQ/lib/$FOLDER" - install_glob $FOLDER/'*.cmo' "$PREFIXCOQ/lib/$FOLDER" - install_glob $FOLDER/'*.a' "$PREFIXCOQ/lib/$FOLDER" - install_glob $FOLDER/'*.o' "$PREFIXCOQ/lib/$FOLDER" + install_glob "$FOLDER"/'*.cmxa' "$PREFIXCOQ/lib/$FOLDER" + install_glob "$FOLDER"/'*.cmi' "$PREFIXCOQ/lib/$FOLDER" + install_glob "$FOLDER"/'*.cma' "$PREFIXCOQ/lib/$FOLDER" + install_glob "$FOLDER"/'*.cmo' "$PREFIXCOQ/lib/$FOLDER" + install_glob "$FOLDER"/'*.a' "$PREFIXCOQ/lib/$FOLDER" + install_glob "$FOLDER"/'*.o' "$PREFIXCOQ/lib/$FOLDER" fi done } @@ -1066,7 +1076,7 @@ function copq_coq_gtk { install_glob "$PREFIX/share/gtksourceview-2.0/language-specs/"'*' "$PREFIXCOQ/share/gtksourceview-2.0/language-specs" install_glob "$PREFIX/share/gtksourceview-2.0/styles/"'*' "$PREFIXCOQ/share/gtksourceview-2.0/styles" install_rec "$PREFIX/share/themes/" '*' "$PREFIXCOQ/share/themes" - + # This below item look like a bug in make install if [ -d "$PREFIXCOQ/share/coq/" ] ; then COQSHARE="$PREFIXCOQ/share/coq/" @@ -1111,11 +1121,11 @@ function make_coq { case $COQ_VERSION in # e.g. git-v8.6 => download from https://github.com/coq/coq/archive/v8.6.zip # e.g. git-trunk => download from https://github.com/coq/coq/archive/trunk.zip - git-*) + git-*) COQ_BUILD_PATH=/build/coq-${COQ_VERSION} - build_prep https://github.com/coq/coq/archive ${COQ_VERSION##git-} zip 1 coq-${COQ_VERSION} + build_prep https://github.com/coq/coq/archive "${COQ_VERSION##git-}" zip 1 "coq-${COQ_VERSION}" ;; - + # e.g. /cygdrive/d/coqgit /*) # Todo: --exclude-vcs-ignores doesn't work because tools/coqdoc/coqdoc.sty is excluded => fix .gitignore @@ -1124,11 +1134,11 @@ function make_coq { tar -zcf $TARBALLS/coq-local.tar.gz --exclude-vcs -C "${COQ_VERSION%/*}" "${COQ_VERSION##*/}" build_prep NEVER-DOWNLOADED coq-local tar.gz ;; - + # e.g. 8.6 => https://coq.inria.fr/distrib/8.6/files/coq-8.6.tar.gz *) COQ_BUILD_PATH=/build/coq-$COQ_VERSION - build_prep https://coq.inria.fr/distrib/V$COQ_VERSION/files coq-$COQ_VERSION tar.gz + build_prep "https://coq.inria.fr/distrib/V$COQ_VERSION/files" "coq-$COQ_VERSION" tar.gz ;; esac then @@ -1142,16 +1152,17 @@ function make_coq { fi # The windows resource compiler binary name is hard coded - sed -i "s/i686-w64-mingw32-windres/$TARGET_ARCH-windres/" Makefile.build + sed -i "s/i686-w64-mingw32-windres/$TARGET_ARCH-windres/" Makefile.build sed -i "s/i686-w64-mingw32-windres/$TARGET_ARCH-windres/" Makefile.ide || true # 8.4x doesn't support parallel make if [[ $COQ_VERSION == 8.4* ]] ; then log1 make else + # shellcheck disable=SC2086 make $MAKE_OPT fi - + if [ "$INSTALLMODE" == "relocatable" ]; then ./configure -with-doc no -prefix "$PREFIXCOQ" -libdir "$PREFIXCOQ/lib" -mandir "$PREFIXCOQ/man" fi @@ -1161,7 +1172,7 @@ function make_coq { if [ "$INSTALLOCAML" == "Y" ]; then copy_coq_objects fi - + copq_coq_gtk copy_coq_license @@ -1169,7 +1180,7 @@ function make_coq { # 1.) find | xargs fails on cygwin, can be fixed by sed -i 's|\| xargs rm -f|-exec rm -fv \{\} \+|' Makefile # 2.) clean of test suites fails with "cannot run complexity tests (no bogomips found)" # make clean - + build_post fi } @@ -1180,7 +1191,7 @@ function make_mingw_make { if build_prep http://ftp.gnu.org/gnu/make make-4.2 tar.bz2 ; then # The config.h.win32 file is fine - don't edit it # We need to copy the mingw gcc here as "gcc" - then the batch file will use it - cp /usr/bin/${ARCH}-w64-mingw32-gcc-6.4.0.exe ./gcc.exe + cp "/usr/bin/${ARCH}-w64-mingw32-gcc-6.4.0.exe" ./gcc.exe # By some magic cygwin bash can run batch files logn build ./build_w32.bat gcc # Copy make to Coq folder @@ -1193,7 +1204,8 @@ function make_mingw_make { function make_binutils { if build_prep http://ftp.gnu.org/gnu/binutils binutils-2.27 tar.gz ; then - logn configure ./configure --build=$BUILD --host=$HOST --target=$TARGET --prefix="$PREFIXCOQ" --program-prefix=$TARGET- + logn configure ./configure --build="$BUILD" --host="$HOST" --target="$TARGET" --prefix="$PREFIXCOQ" --program-prefix="$TARGET-" + # shellcheck disable=SC2086 log1 make $MAKE_OPT log2 make install # log2 make clean @@ -1219,12 +1231,13 @@ function make_gcc { mkdir -p "$PREFIXCOQ/mingw/include" # See https://gcc.gnu.org/install/configure.html - logn configure ./configure --build=$BUILD --host=$HOST --target=$TARGET \ - --prefix="$PREFIXCOQ" --program-prefix=$TARGET- --disable-win32-registry --with-sysroot="$PREFIXCOQ" \ + logn configure ./configure --build="$BUILD" --host="$HOST" --target="$TARGET" \ + --prefix="$PREFIXCOQ" --program-prefix="$TARGET-" --disable-win32-registry --with-sysroot="$PREFIXCOQ" \ --enable-languages=c --disable-nls \ --disable-libsanitizer --disable-libssp --disable-libquadmath --disable-libgomp --disable-libvtv --disable-lto # --disable-decimal-float seems to be required # --with-sysroot="$PREFIX" results in configure error that this is not an absolute path + # shellcheck disable=SC2086 log1 make $MAKE_OPT log2 make install # log2 make clean @@ -1252,21 +1265,22 @@ function get_cygwin_mingw_sources { # Take the 2nd field of the last line => ${SOURCE} = x86_64/release/mingw64-x86_64-gcc/mingw64-x86_64-gcc-5.4.0-2-src.tar.xz # Remove that path part => ${SOURCEFILE} = mingw64-x86_64-gcc-5.4.0-2-src.tar.xz - grep "mingw" /etc/setup/installed.db | sed 's/\.tar\.bz2 [0-1]$//' | sed 's/ /\//' | while read ARCHIVE ; do + grep "mingw" /etc/setup/installed.db | sed 's/\.tar\.bz2 [0-1]$//' | sed 's/ /\//' | while read -r ARCHIVE ; do local ARCHIVEESC=${ARCHIVE//+/\\+} - local SOURCE=`egrep -A 1 "install: ($CYGWINARCH|noarch)/release/[-+_/a-z0-9]*$ARCHIVEESC" $TARBALLS/setup.ini | tail -1 | cut -d " " -f 2` + local SOURCE + SOURCE=$(grep -E -A 1 "install: ($CYGWINARCH|noarch)/release/[-+_/a-z0-9]*$ARCHIVEESC" $TARBALLS/setup.ini | tail -1 | cut -d " " -f 2) local SOURCEFILE=${SOURCE##*/} # Get the source file (either from the source cache or online) - if [ ! -f $TARBALLS/$SOURCEFILE ] ; then + if [ ! -f "$TARBALLS/$SOURCEFILE" ] ; then if [ -f "$SOURCE_LOCAL_CACHE_CFMT/$SOURCEFILE" ] ; then cp "$SOURCE_LOCAL_CACHE_CFMT/$SOURCEFILE" $TARBALLS else wget "$CYGWIN_REPOSITORY/$SOURCE" - mv $SOURCEFILE $TARBALLS + mv "$SOURCEFILE" "$TARBALLS" # Save the source archive in the source cache if [ -d "$SOURCE_LOCAL_CACHE_CFMT" ] ; then - cp $TARBALLS/$SOURCEFILE "$SOURCE_LOCAL_CACHE_CFMT" + cp "$TARBALLS/$SOURCEFILE" "$SOURCE_LOCAL_CACHE_CFMT" fi fi fi @@ -1281,26 +1295,25 @@ function get_cygwin_mingw_sources { function make_coq_installer { make_coq - make_mingw_make get_cygwin_mingw_sources # Prepare the file lists for the installer. We created to file list dumps of the target folder during the build: # ocaml: ocaml + menhir + camlp5 + findlib # ocaml_coq: as above + coq # ocaml_coq_addons: as above + lib/user-contrib/* - + # Create coq file list as ocaml_coq / ocaml diff_files coq ocaml_coq ocaml - + # Filter out object files - filter_files coq_objects coq '\.(cmxa|cmi|cma|cmo|a|o)$' - + filter_files coq_objects coq '\.(cmxa|cmi|cma|cmo|a|o)$' + # Filter out plugin object files filter_files coq_objects_plugins coq_objects '/lib/plugins/.*\.(cmxa|cmi|cma|cmo|a|o)$' - + # Coq objects objects required for plugin development = coq objects except those for pre installed plugins diff_files coq_plugindev coq_objects coq_objects_plugins - + # Addons (TODO: including objects that could go to the plugindev thing, but # then one would have to make that package depend on this one, so not # implemented yet) @@ -1308,45 +1321,46 @@ function make_coq_installer { # Coq files, except objects needed only for plugin development diff_files coq_base coq coq_plugindev - + # Convert section files to NSIS format files_to_nsis coq_base files_to_nsis coq_addons files_to_nsis coq_plugindev files_to_nsis ocaml - + # Get and extract NSIS Binaries if build_prep http://downloads.sourceforge.net/project/nsis/NSIS%202/2.51 nsis-2.51 zip ; then - NSIS=`pwd`/makensis.exe + NSIS=$(pwd)/makensis.exe chmod u+x "$NSIS" # Change to Coq folder - cd $COQ_BUILD_PATH + cd "$COQ_BUILD_PATH" # Copy patched nsi file cp ../patches/coq_new.nsi dev/nsis cp ../patches/StrRep.nsh dev/nsis cp ../patches/ReplaceInFile.nsh dev/nsis - VERSION=`grep '^VERSION=' config/Makefile | cut -d = -f 2 | tr -d '\r'` + VERSION=$(grep '^VERSION=' config/Makefile | cut -d = -f 2 | tr -d '\r') cd dev/nsis - logn nsis-installer "$NSIS" -DVERSION=$VERSION -DARCH=$ARCH -DCOQ_SRC_PATH="$PREFIXCOQ" -DCOQ_ICON=..\\..\\ide\\coq.ico -DCOQ_ADDONS="$COQ_ADDONS" coq_new.nsi - + logn nsis-installer "$NSIS" -DVERSION="$VERSION" -DARCH="$ARCH" -DCOQ_SRC_PATH="$PREFIXCOQ" -DCOQ_ICON=..\\..\\ide\\coq.ico -DCOQ_ADDONS="$COQ_ADDONS" coq_new.nsi + build_post fi } ###################### ADDONS ##################### + function make_addon_bignums { - if build_prep https://github.com/coq/bignums/archive/ V8.8+beta1 zip 1; then + if build_prep https://github.com/coq/bignums/archive/ V8.8+beta1 zip 1 bignums-8.8+beta1; then # To make command lines shorter :-( echo 'COQ_SRC_SUBDIRS:=$(filter-out plugins/%,$(COQ_SRC_SUBDIRS)) plugins/syntax' >> Makefile.coq.local - logn make make all - logn make-install make install + log1 make all + log2 make install build_post fi } function make_addons { for addon in $COQ_ADDONS; do - make_addon_$addon + "make_addon_$addon" done } @@ -1374,4 +1388,3 @@ list_files ocaml_coq_addons if [ "$MAKEINSTALLER" == "Y" ] ; then make_coq_installer fi - diff --git a/dev/ci/appveyor.sh b/dev/ci/appveyor.sh index 524a55a42..93e7bd99a 100644 --- a/dev/ci/appveyor.sh +++ b/dev/ci/appveyor.sh @@ -4,6 +4,6 @@ wget https://github.com/fdopen/opam-repository-mingw/releases/download/0.0.0.1/o tar -xf opam64.tar.xz bash opam64/install.sh opam init -a mingw https://github.com/fdopen/opam-repository-mingw.git --comp 4.02.3+mingw64c --switch 4.02.3+mingw64c -eval $(opam config env) +eval "$(opam config env)" opam install -y ocamlfind camlp5 -cd $APPVEYOR_BUILD_FOLDER && ./configure -local && make && make byte && make -C test-suite all INTERACTIVE= && make validate +cd "$APPVEYOR_BUILD_FOLDER" && ./configure -local && make && make byte && make -C test-suite all INTERACTIVE= && make validate diff --git a/dev/ci/ci-bignums.sh b/dev/ci/ci-bignums.sh index c90e516ae..008291967 100755 --- a/dev/ci/ci-bignums.sh +++ b/dev/ci/ci-bignums.sh @@ -6,11 +6,11 @@ ci_dir="$(dirname "$0")" # Let's avoid to source ci-common twice in this case if [ -z "${CI_BUILD_DIR}" ]; then - source ${ci_dir}/ci-common.sh + . "${ci_dir}/ci-common.sh" fi -bignums_CI_DIR=${CI_BUILD_DIR}/Bignums +bignums_CI_DIR="${CI_BUILD_DIR}/Bignums" -git_checkout ${bignums_CI_BRANCH} ${bignums_CI_GITURL} ${bignums_CI_DIR} +git_checkout "${bignums_CI_BRANCH}" "${bignums_CI_GITURL}" "${bignums_CI_DIR}" -( cd ${bignums_CI_DIR} && make && make install) +( cd "${bignums_CI_DIR}" && make && make install) diff --git a/dev/ci/ci-color.sh b/dev/ci/ci-color.sh index 558e8cbb8..8ce5f2418 100755 --- a/dev/ci/ci-color.sh +++ b/dev/ci/ci-color.sh @@ -1,10 +1,10 @@ #!/usr/bin/env bash ci_dir="$(dirname "$0")" -source ${ci_dir}/ci-common.sh +. "${ci_dir}/ci-common.sh" CoLoR_CI_DIR=${CI_BUILD_DIR}/color # Compile CoLoR -git_checkout ${CoLoR_CI_BRANCH} ${CoLoR_CI_GITURL} ${CoLoR_CI_DIR} -( cd ${CoLoR_CI_DIR} && make ) +git_checkout "${CoLoR_CI_BRANCH}" "${CoLoR_CI_GITURL}" "${CoLoR_CI_DIR}" +( cd "${CoLoR_CI_DIR}" && make ) diff --git a/dev/ci/ci-common.sh b/dev/ci/ci-common.sh index d7a356930..189734a0b 100644 --- a/dev/ci/ci-common.sh +++ b/dev/ci/ci-common.sh @@ -20,7 +20,8 @@ else export CI_PULL_REQUEST="$CIRCLE_PR_NUMBER" export CI_BRANCH="$CIRCLE_BRANCH" else # assume local - export CI_BRANCH="$(git rev-parse --abbrev-ref HEAD)" + CI_BRANCH="$(git rev-parse --abbrev-ref HEAD)" + export CI_BRANCH fi export COQBIN="$PWD/bin" fi @@ -35,10 +36,10 @@ ls "$COQBIN" CI_BUILD_DIR="$PWD/_build_ci" # shellcheck source=ci-basic-overlay.sh -source "${ci_dir}/ci-basic-overlay.sh" +. "${ci_dir}/ci-basic-overlay.sh" for overlay in "${ci_dir}"/user-overlays/*.sh; do # shellcheck source=/dev/null - source "${overlay}" + . "${overlay}" done mathcomp_CI_DIR="${CI_BUILD_DIR}/math-comp" @@ -68,7 +69,7 @@ git_checkout() checkout_mathcomp() { - git_checkout ${mathcomp_CI_BRANCH} ${mathcomp_CI_GITURL} ${1} + git_checkout "${mathcomp_CI_BRANCH}" "${mathcomp_CI_GITURL}" "${1}" } make() diff --git a/dev/ci/ci-compcert.sh b/dev/ci/ci-compcert.sh index 6a0ce2aef..fbdeff20c 100755 --- a/dev/ci/ci-compcert.sh +++ b/dev/ci/ci-compcert.sh @@ -1,11 +1,11 @@ #!/usr/bin/env bash ci_dir="$(dirname "$0")" -source ${ci_dir}/ci-common.sh +. "${ci_dir}/ci-common.sh" -CompCert_CI_DIR=${CI_BUILD_DIR}/CompCert +CompCert_CI_DIR="${CI_BUILD_DIR}/CompCert" opam install -j "$NJOBS" -y menhir -git_checkout ${CompCert_CI_BRANCH} ${CompCert_CI_GITURL} ${CompCert_CI_DIR} +git_checkout "${CompCert_CI_BRANCH}" "${CompCert_CI_GITURL}" "${CompCert_CI_DIR}" -( cd ${CompCert_CI_DIR} && ./configure -ignore-coq-version x86_32-linux && make && make check-proof ) +( cd "${CompCert_CI_DIR}" && ./configure -ignore-coq-version x86_32-linux && make && make check-proof ) diff --git a/dev/ci/ci-coq-dpdgraph.sh b/dev/ci/ci-coq-dpdgraph.sh index 5d6bd6a36..5d57fce1c 100755 --- a/dev/ci/ci-coq-dpdgraph.sh +++ b/dev/ci/ci-coq-dpdgraph.sh @@ -1,10 +1,10 @@ #!/usr/bin/env bash ci_dir="$(dirname "$0")" -source ${ci_dir}/ci-common.sh +. "${ci_dir}/ci-common.sh" -coq_dpdgraph_CI_DIR=${CI_BUILD_DIR}/coq-dpdgraph +coq_dpdgraph_CI_DIR="${CI_BUILD_DIR}/coq-dpdgraph" -git_checkout ${coq_dpdgraph_CI_BRANCH} ${coq_dpdgraph_CI_GITURL} ${coq_dpdgraph_CI_DIR} +git_checkout "${coq_dpdgraph_CI_BRANCH}" "${coq_dpdgraph_CI_GITURL}" "${coq_dpdgraph_CI_DIR}" -( cd ${coq_dpdgraph_CI_DIR} && autoconf && ./configure && make && make test-suite ) +( cd "${coq_dpdgraph_CI_DIR}" && autoconf && ./configure && make && make test-suite ) diff --git a/dev/ci/ci-coquelicot.sh b/dev/ci/ci-coquelicot.sh index 40eff03b7..d86d61ef6 100755 --- a/dev/ci/ci-coquelicot.sh +++ b/dev/ci/ci-coquelicot.sh @@ -1,12 +1,12 @@ #!/usr/bin/env bash ci_dir="$(dirname "$0")" -source ${ci_dir}/ci-common.sh +. "${ci_dir}/ci-common.sh" -Coquelicot_CI_DIR=${CI_BUILD_DIR}/coquelicot +Coquelicot_CI_DIR="${CI_BUILD_DIR}/coquelicot" install_ssreflect -git_checkout ${Coquelicot_CI_BRANCH} ${Coquelicot_CI_GITURL} ${Coquelicot_CI_DIR} +git_checkout "${Coquelicot_CI_BRANCH}" "${Coquelicot_CI_GITURL}" "${Coquelicot_CI_DIR}" -( cd ${Coquelicot_CI_DIR} && ./autogen.sh && ./configure && ./remake -j${NJOBS} ) +( cd "${Coquelicot_CI_DIR}" && ./autogen.sh && ./configure && ./remake "-j${NJOBS}" ) diff --git a/dev/ci/ci-corn.sh b/dev/ci/ci-corn.sh index 54cad5df4..9298fc70a 100755 --- a/dev/ci/ci-corn.sh +++ b/dev/ci/ci-corn.sh @@ -1,10 +1,10 @@ #!/usr/bin/env bash ci_dir="$(dirname "$0")" -source ${ci_dir}/ci-common.sh +. "${ci_dir}/ci-common.sh" -Corn_CI_DIR=${CI_BUILD_DIR}/corn +Corn_CI_DIR="${CI_BUILD_DIR}/corn" -git_checkout ${Corn_CI_BRANCH} ${Corn_CI_GITURL} ${Corn_CI_DIR} +git_checkout "${Corn_CI_BRANCH}" "${Corn_CI_GITURL}" "${Corn_CI_DIR}" -( cd ${Corn_CI_DIR} && make && make install ) +( cd "${Corn_CI_DIR}" && make && make install ) diff --git a/dev/ci/ci-cpdt.sh b/dev/ci/ci-cpdt.sh index 8b725f6fe..ca759c7b3 100755 --- a/dev/ci/ci-cpdt.sh +++ b/dev/ci/ci-cpdt.sh @@ -1,10 +1,9 @@ #!/usr/bin/env bash ci_dir="$(dirname "$0")" -source ${ci_dir}/ci-common.sh +. "${ci_dir}/ci-common.sh" wget http://adam.chlipala.net/cpdt/cpdt.tgz tar xvfz cpdt.tgz ( cd cpdt && make clean && make ) - diff --git a/dev/ci/ci-elpi.sh b/dev/ci/ci-elpi.sh index c44e0a655..9c58034be 100755 --- a/dev/ci/ci-elpi.sh +++ b/dev/ci/ci-elpi.sh @@ -1,10 +1,10 @@ #!/usr/bin/env bash ci_dir="$(dirname "$0")" -source ${ci_dir}/ci-common.sh +. "${ci_dir}/ci-common.sh" -Elpi_CI_DIR=${CI_BUILD_DIR}/elpi +Elpi_CI_DIR="${CI_BUILD_DIR}/elpi" -git_checkout ${Elpi_CI_BRANCH} ${Elpi_CI_GITURL} ${Elpi_CI_DIR} +git_checkout "${Elpi_CI_BRANCH}" "${Elpi_CI_GITURL}" "${Elpi_CI_DIR}" -( cd ${Elpi_CI_DIR} && make && make install ) +( cd "${Elpi_CI_DIR}" && make && make install ) diff --git a/dev/ci/ci-equations.sh b/dev/ci/ci-equations.sh index 62854afac..98735b4ec 100755 --- a/dev/ci/ci-equations.sh +++ b/dev/ci/ci-equations.sh @@ -1,10 +1,10 @@ #!/usr/bin/env bash ci_dir="$(dirname "$0")" -source ${ci_dir}/ci-common.sh +. "${ci_dir}/ci-common.sh" -Equations_CI_DIR=${CI_BUILD_DIR}/Equations +Equations_CI_DIR="${CI_BUILD_DIR}/Equations" -git_checkout ${Equations_CI_BRANCH} ${Equations_CI_GITURL} ${Equations_CI_DIR} +git_checkout "${Equations_CI_BRANCH}" "${Equations_CI_GITURL}" "${Equations_CI_DIR}" -( cd ${Equations_CI_DIR} && coq_makefile -f _CoqProject -o Makefile && make && make test-suite && make examples && make install) +( cd "${Equations_CI_DIR}" && coq_makefile -f _CoqProject -o Makefile && make && make test-suite && make examples && make install) diff --git a/dev/ci/ci-fiat-crypto.sh b/dev/ci/ci-fiat-crypto.sh index 5ca3ac47f..6c8dce5bd 100755 --- a/dev/ci/ci-fiat-crypto.sh +++ b/dev/ci/ci-fiat-crypto.sh @@ -1,11 +1,11 @@ #!/usr/bin/env bash ci_dir="$(dirname "$0")" -source ${ci_dir}/ci-common.sh +. "${ci_dir}/ci-common.sh" -fiat_crypto_CI_DIR=${CI_BUILD_DIR}/fiat-crypto +fiat_crypto_CI_DIR="${CI_BUILD_DIR}/fiat-crypto" -git_checkout ${fiat_crypto_CI_BRANCH} ${fiat_crypto_CI_GITURL} ${fiat_crypto_CI_DIR} -( cd ${fiat_crypto_CI_DIR} && git submodule update --init --recursive ) +git_checkout "${fiat_crypto_CI_BRANCH}" "${fiat_crypto_CI_GITURL}" "${fiat_crypto_CI_DIR}" +( cd "${fiat_crypto_CI_DIR}" && git submodule update --init --recursive ) -( cd ${fiat_crypto_CI_DIR} && make lite ) +( cd "${fiat_crypto_CI_DIR}" && make lite ) diff --git a/dev/ci/ci-fiat-parsers.sh b/dev/ci/ci-fiat-parsers.sh index 292331b81..35c228405 100755 --- a/dev/ci/ci-fiat-parsers.sh +++ b/dev/ci/ci-fiat-parsers.sh @@ -1,10 +1,10 @@ #!/usr/bin/env bash ci_dir="$(dirname "$0")" -source ${ci_dir}/ci-common.sh +. "${ci_dir}/ci-common.sh" -fiat_parsers_CI_DIR=${CI_BUILD_DIR}/fiat +fiat_parsers_CI_DIR="${CI_BUILD_DIR}/fiat" -git_checkout ${fiat_parsers_CI_BRANCH} ${fiat_parsers_CI_GITURL} ${fiat_parsers_CI_DIR} +git_checkout "${fiat_parsers_CI_BRANCH}" "${fiat_parsers_CI_GITURL}" "${fiat_parsers_CI_DIR}" -( cd ${fiat_parsers_CI_DIR} && make parsers parsers-examples && make fiat-core ) +( cd "${fiat_parsers_CI_DIR}" && make parsers parsers-examples && make fiat-core ) diff --git a/dev/ci/ci-flocq.sh b/dev/ci/ci-flocq.sh index ec19bd993..8599e4d50 100755 --- a/dev/ci/ci-flocq.sh +++ b/dev/ci/ci-flocq.sh @@ -1,10 +1,10 @@ #!/usr/bin/env bash ci_dir="$(dirname "$0")" -source ${ci_dir}/ci-common.sh +. "${ci_dir}/ci-common.sh" -Flocq_CI_DIR=${CI_BUILD_DIR}/flocq +Flocq_CI_DIR="${CI_BUILD_DIR}/flocq" -git_checkout ${Flocq_CI_BRANCH} ${Flocq_CI_GITURL} ${Flocq_CI_DIR} +git_checkout "${Flocq_CI_BRANCH}" "${Flocq_CI_GITURL}" "${Flocq_CI_DIR}" -( cd ${Flocq_CI_DIR} && ./autogen.sh && ./configure && ./remake -j${NJOBS} ) +( cd "${Flocq_CI_DIR}" && ./autogen.sh && ./configure && ./remake "-j${NJOBS}" ) diff --git a/dev/ci/ci-formal-topology.sh b/dev/ci/ci-formal-topology.sh index 53eb55fc4..118d15150 100755 --- a/dev/ci/ci-formal-topology.sh +++ b/dev/ci/ci-formal-topology.sh @@ -1,10 +1,10 @@ #!/usr/bin/env bash ci_dir="$(dirname "$0")" -source ${ci_dir}/ci-common.sh +. "${ci_dir}/ci-common.sh" -formal_topology_CI_DIR=${CI_BUILD_DIR}/formal-topology +formal_topology_CI_DIR="${CI_BUILD_DIR}/formal-topology" -git_checkout ${formal_topology_CI_BRANCH} ${formal_topology_CI_GITURL} ${formal_topology_CI_DIR} +git_checkout "${formal_topology_CI_BRANCH}" "${formal_topology_CI_GITURL}" "${formal_topology_CI_DIR}" -( cd ${formal_topology_CI_DIR} && make ) +( cd "${formal_topology_CI_DIR}" && make ) diff --git a/dev/ci/ci-geocoq.sh b/dev/ci/ci-geocoq.sh index 8e6448e76..bd1d88993 100755 --- a/dev/ci/ci-geocoq.sh +++ b/dev/ci/ci-geocoq.sh @@ -1,12 +1,12 @@ #!/usr/bin/env bash ci_dir="$(dirname "$0")" -source ${ci_dir}/ci-common.sh +. "${ci_dir}/ci-common.sh" -GeoCoq_CI_DIR=${CI_BUILD_DIR}/GeoCoq +GeoCoq_CI_DIR="${CI_BUILD_DIR}/GeoCoq" -git_checkout ${GeoCoq_CI_BRANCH} ${GeoCoq_CI_GITURL} ${GeoCoq_CI_DIR} +git_checkout "${GeoCoq_CI_BRANCH}" "${GeoCoq_CI_GITURL}" "${GeoCoq_CI_DIR}" -( cd ${GeoCoq_CI_DIR} && \ +( cd "${GeoCoq_CI_DIR}" && \ ./configure-ci.sh && \ make ) diff --git a/dev/ci/ci-hott.sh b/dev/ci/ci-hott.sh index 693135a4c..6ded97984 100755 --- a/dev/ci/ci-hott.sh +++ b/dev/ci/ci-hott.sh @@ -1,10 +1,10 @@ #!/usr/bin/env bash ci_dir="$(dirname "$0")" -source ${ci_dir}/ci-common.sh +. "${ci_dir}/ci-common.sh" -HoTT_CI_DIR=${CI_BUILD_DIR}/HoTT +HoTT_CI_DIR="${CI_BUILD_DIR}"/HoTT -git_checkout ${HoTT_CI_BRANCH} ${HoTT_CI_GITURL} ${HoTT_CI_DIR} +git_checkout "${HoTT_CI_BRANCH}" "${HoTT_CI_GITURL}" "${HoTT_CI_DIR}" -( cd ${HoTT_CI_DIR} && ./autogen.sh && ./configure && make ) +( cd "${HoTT_CI_DIR}" && ./autogen.sh && ./configure && make ) diff --git a/dev/ci/ci-iris-lambda-rust.sh b/dev/ci/ci-iris-lambda-rust.sh index 267e13359..b019fa059 100755 --- a/dev/ci/ci-iris-lambda-rust.sh +++ b/dev/ci/ci-iris-lambda-rust.sh @@ -1,11 +1,11 @@ #!/usr/bin/env bash ci_dir="$(dirname "$0")" -source ${ci_dir}/ci-common.sh +. "${ci_dir}/ci-common.sh" -stdpp_CI_DIR=${CI_BUILD_DIR}/coq-stdpp -Iris_CI_DIR=${CI_BUILD_DIR}/iris-coq -lambdaRust_CI_DIR=${CI_BUILD_DIR}/lambdaRust +stdpp_CI_DIR="${CI_BUILD_DIR}/coq-stdpp" +Iris_CI_DIR="${CI_BUILD_DIR}/iris-coq" +lambdaRust_CI_DIR="${CI_BUILD_DIR}/lambdaRust" install_ssreflect @@ -13,29 +13,29 @@ install_ssreflect opam repo add iris-dev https://gitlab.mpi-sws.org/FP/opam-dev.git -p 0 || opam update iris-dev # Setup lambdaRust first -git_checkout ${lambdaRust_CI_BRANCH} ${lambdaRust_CI_GITURL} ${lambdaRust_CI_DIR} +git_checkout "${lambdaRust_CI_BRANCH}" "${lambdaRust_CI_GITURL}" "${lambdaRust_CI_DIR}" # Extract required version of Iris -Iris_VERSION=$(cat ${lambdaRust_CI_DIR}/opam | fgrep coq-iris | egrep 'dev\.([0-9.-]+)' -o) -Iris_URL=$(opam show coq-iris.$Iris_VERSION -f upstream-url) -read -a Iris_URL_PARTS <<< $(echo $Iris_URL | tr '#' ' ') +Iris_VERSION=$(grep -F coq-iris < "${lambdaRust_CI_DIR}/opam" | grep -E 'dev\.([0-9.-]+)' -o) +Iris_URL=$(opam show "coq-iris.$Iris_VERSION" -f upstream-url) +read -r -a Iris_URL_PARTS <<< "$(echo "$Iris_URL" | tr '#' ' ')" # Setup Iris -git_checkout ${Iris_CI_BRANCH} ${Iris_URL_PARTS[0]} ${Iris_CI_DIR} ${Iris_URL_PARTS[1]} +git_checkout "${Iris_CI_BRANCH}" "${Iris_URL_PARTS[0]}" "${Iris_CI_DIR}" "${Iris_URL_PARTS[1]}" # Extract required version of std++ -stdpp_VERSION=$(cat ${Iris_CI_DIR}/opam | fgrep coq-stdpp | egrep 'dev\.([0-9.-]+)' -o) -stdpp_URL=$(opam show coq-stdpp.$stdpp_VERSION -f upstream-url) -read -a stdpp_URL_PARTS <<< $(echo $stdpp_URL | tr '#' ' ') +stdpp_VERSION=$(grep -F coq-stdpp < "${Iris_CI_DIR}/opam" | grep -E 'dev\.([0-9.-]+)' -o) +stdpp_URL=$(opam show "coq-stdpp.$stdpp_VERSION" -f upstream-url) +read -r -a stdpp_URL_PARTS <<< "$(echo "$stdpp_URL" | tr '#' ' ')" # Setup std++ -git_checkout ${stdpp_CI_BRANCH} ${stdpp_URL_PARTS[0]} ${stdpp_CI_DIR} ${stdpp_URL_PARTS[1]} +git_checkout "${stdpp_CI_BRANCH}" "${stdpp_URL_PARTS[0]}" "${stdpp_CI_DIR}" "${stdpp_URL_PARTS[1]}" # Build std++ -( cd ${stdpp_CI_DIR} && make && make install ) +( cd "${stdpp_CI_DIR}" && make && make install ) # Build and validate (except on Travis, i.e., skip if TRAVIS is non-empty) Iris -( cd ${Iris_CI_DIR} && make && (test -n "${TRAVIS}" || make validate) && make install ) +( cd "${Iris_CI_DIR}" && make && (test -n "${TRAVIS}" || make validate) && make install ) # Build lambdaRust -( cd ${lambdaRust_CI_DIR} && make && make install ) +( cd "${lambdaRust_CI_DIR}" && make && make install ) diff --git a/dev/ci/ci-ltac2.sh b/dev/ci/ci-ltac2.sh index 820ff89ee..5981aaaae 100755 --- a/dev/ci/ci-ltac2.sh +++ b/dev/ci/ci-ltac2.sh @@ -1,10 +1,10 @@ #!/usr/bin/env bash ci_dir="$(dirname "$0")" -source ${ci_dir}/ci-common.sh +. "${ci_dir}/ci-common.sh" -ltac2_CI_DIR=${CI_BUILD_DIR}/ltac2 +ltac2_CI_DIR="${CI_BUILD_DIR}/ltac2" -git_checkout ${ltac2_CI_BRANCH} ${ltac2_CI_GITURL} ${ltac2_CI_DIR} +git_checkout "${ltac2_CI_BRANCH}" "${ltac2_CI_GITURL}" "${ltac2_CI_DIR}" -( cd ${ltac2_CI_DIR} && make && make tests && make install ) +( cd "${ltac2_CI_DIR}" && make && make tests && make install ) diff --git a/dev/ci/ci-math-classes.sh b/dev/ci/ci-math-classes.sh index db4a31e54..4fc06e895 100755 --- a/dev/ci/ci-math-classes.sh +++ b/dev/ci/ci-math-classes.sh @@ -1,10 +1,10 @@ #!/usr/bin/env bash ci_dir="$(dirname "$0")" -source ${ci_dir}/ci-common.sh +. "${ci_dir}/ci-common.sh" -math_classes_CI_DIR=${CI_BUILD_DIR}/math-classes +math_classes_CI_DIR="${CI_BUILD_DIR}/math-classes" -git_checkout ${math_classes_CI_BRANCH} ${math_classes_CI_GITURL} ${math_classes_CI_DIR} +git_checkout "${math_classes_CI_BRANCH}" "${math_classes_CI_GITURL}" "${math_classes_CI_DIR}" -( cd ${math_classes_CI_DIR} && make && make install ) +( cd "${math_classes_CI_DIR}" && make && make install ) diff --git a/dev/ci/ci-math-comp.sh b/dev/ci/ci-math-comp.sh index 701403f2c..8c6b910bb 100755 --- a/dev/ci/ci-math-comp.sh +++ b/dev/ci/ci-math-comp.sh @@ -2,14 +2,14 @@ # $0 is not the safest way, but... ci_dir="$(dirname "$0")" -source ${ci_dir}/ci-common.sh +. "${ci_dir}/ci-common.sh" -mathcomp_CI_DIR=${CI_BUILD_DIR}/math-comp +mathcomp_CI_DIR="${CI_BUILD_DIR}/math-comp" -checkout_mathcomp ${mathcomp_CI_DIR} +checkout_mathcomp "${mathcomp_CI_DIR}" # odd_order takes too much time for travis. -( cd ${mathcomp_CI_DIR}/mathcomp && \ +( cd "${mathcomp_CI_DIR}/mathcomp" && \ sed -i.bak '/PFsection/d' Make && \ sed -i.bak '/stripped_odd_order_theorem/d' Make && \ make Makefile.coq && make -f Makefile.coq all ) diff --git a/dev/ci/ci-metacoq.sh b/dev/ci/ci-metacoq.sh index c813b1fe9..a66dc1e76 100755 --- a/dev/ci/ci-metacoq.sh +++ b/dev/ci/ci-metacoq.sh @@ -1,19 +1,19 @@ #!/usr/bin/env bash ci_dir="$(dirname "$0")" -source ${ci_dir}/ci-common.sh +. "${ci_dir}/ci-common.sh" unicoq_CI_DIR=${CI_BUILD_DIR}/unicoq metacoq_CI_DIR=${CI_BUILD_DIR}/MetaCoq # Setup UniCoq -git_checkout ${unicoq_CI_BRANCH} ${unicoq_CI_GITURL} ${unicoq_CI_DIR} +git_checkout "${unicoq_CI_BRANCH}" "${unicoq_CI_GITURL}" "${unicoq_CI_DIR}" -( cd ${unicoq_CI_DIR} && coq_makefile -f Make -o Makefile && make && make install ) +( cd "${unicoq_CI_DIR}" && coq_makefile -f Make -o Makefile && make && make install ) # Setup MetaCoq -git_checkout ${metacoq_CI_BRANCH} ${metacoq_CI_GITURL} ${metacoq_CI_DIR} +git_checkout "${metacoq_CI_BRANCH}" "${metacoq_CI_GITURL}" "${metacoq_CI_DIR}" -( cd ${metacoq_CI_DIR} && coq_makefile -f _CoqProject -o Makefile && make ) +( cd "${metacoq_CI_DIR}" && coq_makefile -f _CoqProject -o Makefile && make ) diff --git a/dev/ci/ci-sf.sh b/dev/ci/ci-sf.sh index 4e8c7e145..58bbb7229 100755 --- a/dev/ci/ci-sf.sh +++ b/dev/ci/ci-sf.sh @@ -1,35 +1,16 @@ #!/usr/bin/env bash ci_dir="$(dirname "$0")" -source ${ci_dir}/ci-common.sh +. "${ci_dir}/ci-common.sh" -mkdir -p ${CI_BUILD_DIR} && cd ${CI_BUILD_DIR} -wget -qO- ${sf_lf_CI_TARURL} | tar xvz -wget -qO- ${sf_plf_CI_TARURL} | tar xvz -wget -qO- ${sf_vfa_CI_TARURL} | tar xvz +mkdir -p "${CI_BUILD_DIR}" && cd "${CI_BUILD_DIR}" || exit 1 +wget -qO- "${sf_lf_CI_TARURL}" | tar xvz +wget -qO- "${sf_plf_CI_TARURL}" | tar xvz +wget -qO- "${sf_vfa_CI_TARURL}" | tar xvz sed -i.bak '1i From Coq Require Extraction.' lf/Extraction.v sed -i.bak '1i From Coq Require Extraction.' vfa/Extract.v -# Delete useless calls to try omega; unfold -patch vfa/SearchTree.v <<EOF -*** SearchTree.v.bak 2017-09-06 19:12:59.000000000 +0200 ---- SearchTree.v 2017-11-21 16:34:41.000000000 +0100 -*************** -*** 674,683 **** - forall i j : key, ~ (i > j) -> ~ (i < j) -> i=j. - Proof. - intros. -- try omega. (* Oops! [omega] cannot solve this one. -- The problem is that [i] and [j] have type [key] instead of type [nat]. -- The solution is easy enough: *) -- unfold key in *. - omega. - - (** So, if you get stuck on an [omega] that ought to work, ---- 674,679 ---- -EOF - ( cd lf && make clean && make ) ( cd plf && sed -i.bak 's/(K,N)/((K,N))/' LibTactics.v && make clean && make ) diff --git a/dev/ci/ci-template.sh b/dev/ci/ci-template.sh index 25da01a82..e77a55304 100755 --- a/dev/ci/ci-template.sh +++ b/dev/ci/ci-template.sh @@ -1,12 +1,12 @@ #!/usr/bin/env bash ci_dir="$(dirname "$0")" -source ${ci_dir}/ci-common.sh +. "${ci_dir}/ci-common.sh" Template_CI_BRANCH=master Template_CI_GITURL=https://github.com/Template/Template -Template_CI_DIR=${CI_BUILD_DIR}/Template +Template_CI_DIR="${CI_BUILD_DIR}/Template" -git_checkout ${Template_CI_BRANCH} ${Template_CI_GITURL} ${Template_CI_DIR} +git_checkout "${Template_CI_BRANCH}" "${Template_CI_GITURL}" "${Template_CI_DIR}" -( cd ${Template_CI_DIR} && make ) +( cd "${Template_CI_DIR}" && make ) diff --git a/dev/ci/ci-tlc.sh b/dev/ci/ci-tlc.sh index 8ecd8c441..31387c8dd 100755 --- a/dev/ci/ci-tlc.sh +++ b/dev/ci/ci-tlc.sh @@ -1,10 +1,10 @@ #!/usr/bin/env bash ci_dir="$(dirname "$0")" -source ${ci_dir}/ci-common.sh +. "${ci_dir}/ci-common.sh" -tlc_CI_DIR=${CI_BUILD_DIR}/tlc +tlc_CI_DIR="${CI_BUILD_DIR}/tlc" -git_checkout ${tlc_CI_BRANCH} ${tlc_CI_GITURL} ${tlc_CI_DIR} +git_checkout "${tlc_CI_BRANCH}" "${tlc_CI_GITURL}" "${tlc_CI_DIR}" -( cd ${tlc_CI_DIR} && make ) +( cd "${tlc_CI_DIR}" && make ) diff --git a/dev/ci/ci-unimath.sh b/dev/ci/ci-unimath.sh index 66b56add7..62a949f59 100755 --- a/dev/ci/ci-unimath.sh +++ b/dev/ci/ci-unimath.sh @@ -1,14 +1,13 @@ #!/usr/bin/env bash ci_dir="$(dirname "$0")" -source ${ci_dir}/ci-common.sh +. "${ci_dir}/ci-common.sh" -UniMath_CI_DIR=${CI_BUILD_DIR}/UniMath +UniMath_CI_DIR="${CI_BUILD_DIR}/UniMath" -git_checkout ${UniMath_CI_BRANCH} ${UniMath_CI_GITURL} ${UniMath_CI_DIR} +git_checkout "${UniMath_CI_BRANCH}" "${UniMath_CI_GITURL}" "${UniMath_CI_DIR}" -( cd ${UniMath_CI_DIR} && \ +( cd "${UniMath_CI_DIR}" && \ sed -i.bak '/Folds/d' Makefile && \ sed -i.bak '/HomologicalAlgebra/d' Makefile && \ make BUILD_COQ=no ) - diff --git a/dev/ci/ci-vst.sh b/dev/ci/ci-vst.sh index 5760fbafb..3c0044bfe 100755 --- a/dev/ci/ci-vst.sh +++ b/dev/ci/ci-vst.sh @@ -1,13 +1,13 @@ #!/usr/bin/env bash ci_dir="$(dirname "$0")" -source ${ci_dir}/ci-common.sh +. "${ci_dir}/ci-common.sh" -VST_CI_DIR=${CI_BUILD_DIR}/VST +VST_CI_DIR="${CI_BUILD_DIR}/VST" # opam install -j ${NJOBS} -y menhir -git_checkout ${VST_CI_BRANCH} ${VST_CI_GITURL} ${VST_CI_DIR} +git_checkout "${VST_CI_BRANCH}" "${VST_CI_GITURL}" "${VST_CI_DIR}" # Targets are: msl veric floyd progs , we remove progs to save time # Patch to avoid the upper version limit -( cd ${VST_CI_DIR} && make IGNORECOQVERSION=true .loadpath version.vo msl veric floyd ) +( cd "${VST_CI_DIR}" && make IGNORECOQVERSION=true .loadpath version.vo msl veric floyd ) diff --git a/dev/ci/user-overlays/00669-maximedenes-ssr-merge.sh b/dev/ci/user-overlays/00669-maximedenes-ssr-merge.sh index 7716bcb59..e9ba11414 100644 --- a/dev/ci/user-overlays/00669-maximedenes-ssr-merge.sh +++ b/dev/ci/user-overlays/00669-maximedenes-ssr-merge.sh @@ -1,3 +1,5 @@ +#!/bin/sh + if [ "$CI_PULL_REQUEST" = "669" ] || [ "$CI_BRANCH" = "ssr-merge" ]; then mathcomp_CI_BRANCH=ssr-merge mathcomp_CI_GITURL=https://github.com/maximedenes/math-comp.git diff --git a/dev/ci/user-overlays/06405-maximedenes-rm-local-polymorphic-flag.sh b/dev/ci/user-overlays/06405-maximedenes-rm-local-polymorphic-flag.sh deleted file mode 100644 index c2e367038..000000000 --- a/dev/ci/user-overlays/06405-maximedenes-rm-local-polymorphic-flag.sh +++ /dev/null @@ -1,4 +0,0 @@ -if [ "$CI_PULL_REQUEST" = "6405" ] || [ "$CI_BRANCH" = "rm-local-polymorphic-flag" ]; then - Equations_CI_BRANCH=rm-local-polymorphic-flag - Equations_CI_GITURL=https://github.com/maximedenes/Coq-Equations -fi diff --git a/dev/ci/user-overlays/06482-ppedrot-check-poly-effects.sh b/dev/ci/user-overlays/06482-ppedrot-check-poly-effects.sh deleted file mode 100644 index 78789a6fc..000000000 --- a/dev/ci/user-overlays/06482-ppedrot-check-poly-effects.sh +++ /dev/null @@ -1,4 +0,0 @@ -if [ "$TRAVIS_PULL_REQUEST" = "6483" ] || [ "$TRAVIS_BRANCH" = "check-poly-effects" ]; then - HoTT_CI_BRANCH=check-poly-effects - HoTT_CI_GITURL=https://github.com/ppedrot/HoTT.git -fi diff --git a/dev/ci/user-overlays/06493-gares-API-remove-big-file.sh b/dev/ci/user-overlays/06493-gares-API-remove-big-file.sh deleted file mode 100644 index 9677b3525..000000000 --- a/dev/ci/user-overlays/06493-gares-API-remove-big-file.sh +++ /dev/null @@ -1,8 +0,0 @@ -if [ "$CI_PULL_REQUEST" = "6493" ] || [ "$CI_BRANCH" = "API/remove-big-file" ]; then - Equations_CI_BRANCH=API-removal - Equations_CI_GITURL=https://github.com/gares/Coq-Equations.git - coq_dpdgraph_CI_BRANCH=API-removal - coq_dpdgraph_CI_GITURL=https://github.com/gares/coq-dpdgraph.git - ltac2_CI_BRANCH=API-removal - ltac2_CI_GITURL=https://github.com/gares/ltac2.git -fi diff --git a/dev/ci/user-overlays/06511-ejgallego-econstr+more_fix.sh b/dev/ci/user-overlays/06511-ejgallego-econstr+more_fix.sh deleted file mode 100644 index 4b681909d..000000000 --- a/dev/ci/user-overlays/06511-ejgallego-econstr+more_fix.sh +++ /dev/null @@ -1,7 +0,0 @@ - if [ "$CI_PULL_REQUEST" = "6511" ] || [ "$CI_BRANCH" = "econstr+more_fix" ]; then - ltac2_CI_BRANCH=econstr+more_fix - ltac2_CI_GITURL=https://github.com/ejgallego/ltac2 - - Equations_CI_BRANCH=econstr+more_fix - Equations_CI_GITURL=https://github.com/ejgallego/Coq-Equations -fi diff --git a/dev/ci/user-overlays/06535-fix-push-rel-to-named.sh b/dev/ci/user-overlays/06535-fix-push-rel-to-named.sh deleted file mode 100644 index 8a50fb111..000000000 --- a/dev/ci/user-overlays/06535-fix-push-rel-to-named.sh +++ /dev/null @@ -1,4 +0,0 @@ -if [ "$CI_PULL_REQUEST" = "6535" ] || [ "$CI_BRANCH" = "fix-push-rel-to-named" ]; then - Equations_CI_BRANCH=fix-6535 - Equations_CI_GITURL=https://github.com/ppedrot/Coq-Equations -fi diff --git a/dev/ci/user-overlays/06676-gares-proofview-goals-come-with-a-state.sh b/dev/ci/user-overlays/06676-gares-proofview-goals-come-with-a-state.sh deleted file mode 100644 index 2451657d4..000000000 --- a/dev/ci/user-overlays/06676-gares-proofview-goals-come-with-a-state.sh +++ /dev/null @@ -1,6 +0,0 @@ -if [ "$CI_PULL_REQUEST" = "6676" ] || [ "$CI_BRANCH" = "proofview/goal-w-state" ]; then - ltac2_CI_BRANCH=fix-for/6676 - ltac2_CI_GITURL=https://github.com/gares/ltac2.git - Equations_CI_BRANCH=fix-for/6676 - Equations_CI_GITURL=https://github.com/gares/Coq-Equations.git -fi diff --git a/dev/ci/user-overlays/06686-ccnv-no-proj.sh b/dev/ci/user-overlays/06686-ccnv-no-proj.sh deleted file mode 100644 index 3a3ab44e0..000000000 --- a/dev/ci/user-overlays/06686-ccnv-no-proj.sh +++ /dev/null @@ -1,4 +0,0 @@ -if [ "$CI_PULL_REQUEST" = "6686" ] || [ "$CI_BRANCH" = "ccnv-no-proj" ]; then - Equations_CI_BRANCH=ccnv-fixes - Equations_CI_GITURL=https://github.com/SkySkimmer/Coq-Equations -fi diff --git a/dev/ci/user-overlays/06745-ejgallego-located+vernac.sh b/dev/ci/user-overlays/06745-ejgallego-located+vernac.sh deleted file mode 100644 index d1d61fec2..000000000 --- a/dev/ci/user-overlays/06745-ejgallego-located+vernac.sh +++ /dev/null @@ -1,13 +0,0 @@ -if [ "$CI_PULL_REQUEST" = "6745" ] || [ "$CI_BRANCH" = "located+vernac" ]; then - ltac2_CI_BRANCH=located+vernac - ltac2_CI_GITURL=https://github.com/ejgallego/ltac2 - - Equations_CI_BRANCH=located+vernac - Equations_CI_GITURL=https://github.com/ejgallego/Coq-Equations - - fiat_parsers_CI_BRANCH=located+vernac - fiat_parsers_CI_GITURL=https://github.com/ejgallego/fiat - - Elpi_CI_BRANCH=located+vernac - Elpi_CI_GITURL=https://github.com/ejgallego/coq-elpi.git -fi diff --git a/dev/ci/user-overlays/06775-univ-cumul-weak.sh b/dev/ci/user-overlays/06775-univ-cumul-weak.sh deleted file mode 100644 index 8afcbf78a..000000000 --- a/dev/ci/user-overlays/06775-univ-cumul-weak.sh +++ /dev/null @@ -1,4 +0,0 @@ -if [ "$CI_PULL_REQUEST" = "6775" ] || [ "$CI_BRANCH" = "univ-cumul" ]; then - Elpi_CI_BRANCH=coq-master - Elpi_CI_GITURL=https://github.com/SkySkimmer/coq-elpi.git -fi diff --git a/dev/ci/user-overlays/06831-ejgallego-located+vernac_2.sh b/dev/ci/user-overlays/06831-ejgallego-located+vernac_2.sh deleted file mode 100644 index df3e9cef2..000000000 --- a/dev/ci/user-overlays/06831-ejgallego-located+vernac_2.sh +++ /dev/null @@ -1,14 +0,0 @@ -if [ "$CI_PULL_REQUEST" = "6831" ] || [ "$CI_BRANCH" = "located+vernac_2" ]; then - - ltac2_CI_BRANCH=located+vernac_2 - ltac2_CI_GITURL=https://github.com/ejgallego/ltac2 - - Equations_CI_BRANCH=located+vernac_2 - Equations_CI_GITURL=https://github.com/ejgallego/Coq-Equations - - # fiat_parsers_CI_BRANCH=located+vernac - # fiat_parsers_CI_GITURL=https://github.com/ejgallego/fiat - - Elpi_CI_BRANCH=located+vernac_2 - Elpi_CI_GITURL=https://github.com/ejgallego/coq-elpi.git -fi diff --git a/dev/ci/user-overlays/06837-ejgallego-located+libnames.sh b/dev/ci/user-overlays/06837-ejgallego-located+libnames.sh deleted file mode 100644 index a785290e7..000000000 --- a/dev/ci/user-overlays/06837-ejgallego-located+libnames.sh +++ /dev/null @@ -1,15 +0,0 @@ -if [ "$CI_PULL_REQUEST" = "6837" ] || [ "$CI_BRANCH" = "located+libnames" ]; then - - ltac2_CI_BRANCH=located+libnames - ltac2_CI_GITURL=https://github.com/ejgallego/ltac2 - - Equations_CI_BRANCH=located+libnames - Equations_CI_GITURL=https://github.com/ejgallego/Coq-Equations - - Elpi_CI_BRANCH=located+libnames - Elpi_CI_GITURL=https://github.com/ejgallego/coq-elpi.git - - coq_dpdgraph_CI_BRANCH=located+libnames - coq_dpdgraph_CI_GITURL=https://github.com/ejgallego/coq-dpdgraph.git - -fi diff --git a/dev/ci/user-overlays/06869-ejgallego-ssr+correct_packing.sh b/dev/ci/user-overlays/06869-ejgallego-ssr+correct_packing.sh deleted file mode 100644 index 5dedca0ca..000000000 --- a/dev/ci/user-overlays/06869-ejgallego-ssr+correct_packing.sh +++ /dev/null @@ -1,12 +0,0 @@ -if [ "$CI_PULL_REQUEST" = "6869" ] || [ "$CI_BRANCH" = "ssr+correct_packing" ]; then - - Equations_CI_BRANCH=ssr+correct_packing - Equations_CI_GITURL=https://github.com/ejgallego/Coq-Equations - - ltac2_CI_BRANCH=ssr+correct_packing - ltac2_CI_GITURL=https://github.com/ejgallego/ltac2 - - Elpi_CI_BRANCH=ssr+correct_packing - Elpi_CI_GITURL=https://github.com/ejgallego/coq-elpi.git - -fi diff --git a/dev/ci/user-overlays/06923-ppedrot-export-options.sh b/dev/ci/user-overlays/06923-ppedrot-export-options.sh deleted file mode 100644 index 333a9e84b..000000000 --- a/dev/ci/user-overlays/06923-ppedrot-export-options.sh +++ /dev/null @@ -1,7 +0,0 @@ -if [ "$CI_PULL_REQUEST" = "6923" ] || [ "$CI_BRANCH" = "export-options" ]; then - ltac2_CI_BRANCH=export-options - ltac2_CI_GITURL=https://github.com/ppedrot/ltac2 - - Equations_CI_BRANCH=export-options - Equations_CI_GITURL=https://github.com/ppedrot/Coq-Equations -fi diff --git a/dev/ci/user-overlays/06960-ejgallego-ltac+tacdepr.sh b/dev/ci/user-overlays/06960-ejgallego-ltac+tacdepr.sh new file mode 100644 index 000000000..cf2af9ae9 --- /dev/null +++ b/dev/ci/user-overlays/06960-ejgallego-ltac+tacdepr.sh @@ -0,0 +1,12 @@ +if [ "$CI_PULL_REQUEST" = "6960" ] || [ "$CI_BRANCH" = "ltac+tacdepr" ]; then + + # Equations_CI_BRANCH=ssr+correct_packing + # Equations_CI_GITURL=https://github.com/ejgallego/Coq-Equations + + ltac2_CI_BRANCH=ltac+tacdepr + ltac2_CI_GITURL=https://github.com/ejgallego/ltac2 + + # Elpi_CI_BRANCH=ssr+correct_packing + # Elpi_CI_GITURL=https://github.com/ejgallego/coq-elpi.git + +fi diff --git a/dev/ci/user-overlays/README.md b/dev/ci/user-overlays/README.md index 9f0377cee..a7474e324 100644 --- a/dev/ci/user-overlays/README.md +++ b/dev/ci/user-overlays/README.md @@ -7,6 +7,8 @@ The name of your overlay file should be of the form `five_digit_PR_number-GitHub Example: `00669-maximedenes-ssr-merge.sh` containing ``` +#!/bin/sh + if [ "$CI_PULL_REQUEST" = "669" ] || [ "$CI_BRANCH" = "ssr-merge" ]; then mathcomp_CI_BRANCH=ssr-merge mathcomp_CI_GITURL=https://github.com/maximedenes/math-comp.git diff --git a/dev/doc/MERGING.md b/dev/doc/MERGING.md index 71fc39608..3a2df6a81 100644 --- a/dev/doc/MERGING.md +++ b/dev/doc/MERGING.md @@ -1,6 +1,7 @@ # Merging changes in Coq -This document describes how patches (submitted as Pull Requests) should be +This document describes how patches (submitted as pull requests +on the `master` branch) should be merged into the main repository (https://github.com/coq/coq). ## Code owners @@ -65,14 +66,57 @@ In some rare cases (e.g. the conflicts are in the CHANGES file), it is ok to fix the conflicts in the merge commit (following the same steps as below), and push to `master` directly. Don't use the GitHub interface to fix these conflicts. -The command to be used is: +To merge the PR proceed in the following way ``` +$ git checkout master +$ git pull $ dev/tools/merge-pr XXXX +$ git push upstream ``` -where `XXXX` is the number of the PR to be merged. This operation should be followed by a push. +where `XXXX` is the number of the PR to be merged and `upstream` is the name +of your remote pointing to `git@github.com:coq/coq.git`. +Note that you are only supposed to merge PRs into `master`. PRs should rarely +target the stable branch, but when it is the case they are the responsibility +of the release manager. + +This script conducts various checks before proceeding to merge. Don't bypass them +without a good reason to, and in that case, write a comment in the PR thread to +explain the reason. Maintainers MUST NOT merge their own patches. DON'T USE the GitHub interface for merging, since it will prevent the automated backport script from operating properly, generates bad commit messages, and a messy history when there are conflicts. + +### What to do if the PR has overlays + +If the PR breaks compatibility of some developments in CI, then the author must +have prepared overlays for these developments (see [`dev/ci/README.md`](/dev/ci/README.md)) +and the PR must absolutely update the `CHANGES` file. + +There are two cases to consider: + +- If the patch is backward compatible (best scenario), then you should get + upstream maintainers to integrate it before merging the PR. +- If the patch is not backward compatible (which is often the case when + patching plugins after an update to the Coq API), then you can proceed to + merge the PR and then notify upstream they can merge the patch. This is a + less preferable scenario because it is probably going to create + spurious CI failures for unrelated PRs. + +### Merge script dependencies + +The merge script passes option `-S` to `git merge` to ensure merge commits +are signed. Consequently, it depends on the GnuPG command utility being +installed and a GPG key being available. Here is a short tutorial to +creating your own GPG key: +<https://ekaia.org/blog/2009/05/10/creating-new-gpgkey/> + +The script depends on a few other utilities. If you are a Nix user, the +simplest way of getting them is to run `nix-shell` first. + +**Note for homebrew (MacOS) users:** it has been reported that installing GnuPG +is not out of the box. Installing explicitly "pinentry-mac" seems important for +typing of passphrase to work correctly (see also this +[Stack Overflow Q-and-A](https://stackoverflow.com/questions/39494631/gpg-failed-to-sign-the-data-fatal-failed-to-write-commit-object-git-2-10-0)). diff --git a/dev/lint-repository.sh b/dev/lint-repository.sh index ee9c8777a..cd09b6d30 100755 --- a/dev/lint-repository.sh +++ b/dev/lint-repository.sh @@ -31,4 +31,6 @@ fi find . "(" -path ./.git -prune ")" -o -type f -print0 | xargs -0 dev/tools/check-eof-newline.sh || CODE=1 +dev/tools/check-overlays.sh || CODE=1 + exit $CODE diff --git a/dev/tools/backport-pr.sh b/dev/tools/backport-pr.sh index e4359f703..5205350a6 100755 --- a/dev/tools/backport-pr.sh +++ b/dev/tools/backport-pr.sh @@ -27,9 +27,9 @@ BRANCH=backport-pr-${PRNUM} RANGE=$(git log master --grep "Merge PR #${PRNUM}" --format="%P" | sed 's/ /../') MESSAGE=$(git log master --grep "Merge PR #${PRNUM}" --format="%s" | sed 's/Merge/Backport/') -if git checkout -b ${BRANCH}; then +if git checkout -b "${BRANCH}"; then - if ! git cherry-pick -x ${RANGE}; then + if ! git cherry-pick -x "${RANGE}"; then echo "Please fix the conflicts, then exit." bash while ! git cherry-pick --continue; do @@ -50,7 +50,7 @@ else fi -if ! git diff --exit-code HEAD ${BRANCH} -- "*.mli"; then +if ! git diff --exit-code HEAD "${BRANCH}" -- "*.mli"; then echo read -p "Some mli files are modified. Bypass? [y/N] " -n 1 -r echo @@ -63,8 +63,8 @@ if [[ "${OPTION}" == "--stop-before-merging" ]]; then exit 0 fi -git merge -S --no-ff ${BRANCH} -m "${MESSAGE}" -git branch -d ${BRANCH} +git merge -S --no-ff "${BRANCH}" -m "${MESSAGE}" +git branch -d "${BRANCH}" # To-Do: # - Support for backporting a PR before it is merged diff --git a/dev/tools/check-overlays.sh b/dev/tools/check-overlays.sh new file mode 100755 index 000000000..f7e05b51c --- /dev/null +++ b/dev/tools/check-overlays.sh @@ -0,0 +1,11 @@ +#!/usr/bin/env bash + +for f in dev/ci/user-overlays/* +do + if ! ([[ $f = dev/ci/user-overlays/README.md ]] || [[ $f == *.sh ]]) + then + >&2 echo "Bad overlay '$f'." + >&2 echo "User overlays need to have extension .sh to be picked up!" + exit 1 + fi +done diff --git a/dev/tools/merge-pr.sh b/dev/tools/merge-pr.sh index 2f6f1af54..1c94f630f 100755 --- a/dev/tools/merge-pr.sh +++ b/dev/tools/merge-pr.sh @@ -4,11 +4,20 @@ set -e set -o pipefail API=https://api.github.com/repos/coq/coq -OFFICIAL_REMOTE_URL="git@github.com:coq/coq" +OFFICIAL_REMOTE_GIT_URL="git@github.com:coq/coq" +OFFICIAL_REMOTE_HTTPS_URL="https://github.com/coq/coq" -# This script depends (at least) on git and jq. +# This script depends (at least) on git (>= 2.7) and jq. # It should be used like this: dev/tools/merge-pr.sh /PR number/ +# Set SLOW_CONF to have the confirmation output wait for a newline +# E.g. call $ SLOW_CONF= dev/tools/merge-pr.sh /PR number/ +if [ -z ${SLOW_CONF+x} ]; then + QUICK_CONF="-n 1" +else + QUICK_CONF="" +fi + RED="\033[31m" RESET="\033[0m" GREEN="\033[32m" @@ -32,7 +41,7 @@ fi } ask_confirmation() { - read -p "Continue anyway? [y/N] " -n 1 -r + read -p "Continue anyway? [y/N] " $QUICK_CONF -r echo if [[ ! $REPLY =~ ^[Yy]$ ]] then @@ -61,10 +70,12 @@ fi # Fetching PR metadata -TITLE=$(curl -s "$API/pulls/$PR" | jq -r '.title') +PRDATA=$(curl -s "$API/pulls/$PR") + +TITLE=$(echo "$PRDATA" | jq -r '.title') info "title for PR $PR is ${BLUE}$TITLE" -BASE_BRANCH=$(curl -s "$API/pulls/$PR" | jq -r '.base.label') +BASE_BRANCH=$(echo "$PRDATA" | jq -r '.base.label') info "PR $PR targets branch ${BLUE}$BASE_BRANCH" CURRENT_LOCAL_BRANCH=$(git rev-parse --abbrev-ref HEAD) @@ -77,11 +88,13 @@ if [ -z "$REMOTE" ]; then error "please run: git branch --set-upstream-to=THE_REMOTE/$CURRENT_LOCAL_BRANCH" exit 1 fi -REMOTE_URL=$(git remote get-url "$REMOTE" --push) -if [ "$REMOTE_URL" != "$OFFICIAL_REMOTE_URL" -a \ - "$REMOTE_URL" != "$OFFICIAL_REMOTE_URL.git" ]; then +REMOTE_URL=$(git remote get-url "$REMOTE" --all) +if [ "$REMOTE_URL" != "${OFFICIAL_REMOTE_GIT_URL}" ] && \ + [ "$REMOTE_URL" != "${OFFICIAL_REMOTE_GIT_URL}.git" ] && \ + [ "$REMOTE_URL" != "${OFFICIAL_REMOTE_HTTPS_URL}" ] && \ + [ "$REMOTE_URL" != "${OFFICIAL_REMOTE_HTTPS_URL}.git" ]; then error "remote ${BLUE}$REMOTE${RESET} does not point to the official Coq repo" - error "that is ${BLUE}$OFFICIAL_REMOTE_URL" + error "that is ${BLUE}$OFFICIAL_REMOTE_GIT_URL" error "it points to ${BLUE}$REMOTE_URL${RESET} instead" ask_confirmation fi @@ -105,19 +118,39 @@ if [ "$BASE_BRANCH" != "coq:$CURRENT_LOCAL_BRANCH" ]; then ask_confirmation fi; +# Sanity check: the local branch is up-to-date with upstream + +LOCAL_BRANCH_COMMIT=$(git rev-parse HEAD) +UPSTREAM_COMMIT=$(git rev-parse @{u}) +if [ "$LOCAL_BRANCH_COMMIT" != "$UPSTREAM_COMMIT" ]; then + + # Is it just that the upstream branch is behind? + # It could just be that we merged other PRs and we didn't push yet + + if git merge-base --is-ancestor -- "$UPSTREAM_COMMIT" "$LOCAL_BRANCH_COMMIT"; then + warning "Your branch is ahead of ${REMOTE}." + warning "You should see this warning only if you've just merged another PR and did not push yet." + ask_confirmation + else + error "Local branch is not up-to-date with ${REMOTE}." + error "Pull before merging." + ask_confirmation + fi +fi + # Sanity check: CI failed -STATUS=$(curl -s "$API/commits/$COMMIT/status" | jq -r '.state') +STATUS=$(curl -s "$API/commits/$COMMIT/status") -if [ "$STATUS" != "success" ]; then - error "CI unsuccessful on ${BLUE}$(curl -s "$API/commits/$COMMIT/status" | +if [ "$(echo "$STATUS" | jq -r '.state')" != "success" ]; then + error "CI unsuccessful on ${BLUE}$(echo "$STATUS" | jq -r -c '.statuses|map(select(.state != "success"))|map(.context)')" ask_confirmation fi; # Sanity check: has labels named "needs:" -NEEDS_LABELS=$(curl -s "$API/pulls/$PR" | jq -rc '.labels | map(select(.name | match("needs:"))) | map(.name)') +NEEDS_LABELS=$(echo "$PRDATA" | jq -rc '.labels | map(select(.name | match("needs:"))) | map(.name)') if [ "$NEEDS_LABELS" != "[]" ]; then error "needs:something labels still present: ${BLUE}$NEEDS_LABELS" ask_confirmation @@ -125,7 +158,7 @@ fi # Sanity check: has milestone -MILESTONE=$(curl -s "$API/pulls/$PR" | jq -rc '.milestone.title') +MILESTONE=$(echo "$PRDATA" | jq -rc '.milestone.title') if [ "$MILESTONE" = "null" ]; then error "no milestone set, please set one" ask_confirmation @@ -133,7 +166,7 @@ fi # Sanity check: has kind -KIND=$(curl -s "$API/pulls/$PR" | jq -rc '.labels | map(select(.name | match("kind:"))) | map(.name)') +KIND=$(echo "$PRDATA" | jq -rc '.labels | map(select(.name | match("kind:"))) | map(.name)') if [ "$KIND" = "[]" ]; then error "no kind:something label set, please set one" ask_confirmation diff --git a/dev/tools/pre-commit b/dev/tools/pre-commit index c9cdee84a..a514b8866 100755 --- a/dev/tools/pre-commit +++ b/dev/tools/pre-commit @@ -5,6 +5,8 @@ set -e +dev/tools/check-overlays.sh + if ! git diff --cached --name-only -z | xargs -0 dev/tools/check-eof-newline.sh || ! git diff-index --check --cached HEAD >/dev/null 2>&1 ; then diff --git a/doc/refman/AsyncProofs.tex b/doc/refman/AsyncProofs.tex deleted file mode 100644 index 8f9d876cb..000000000 --- a/doc/refman/AsyncProofs.tex +++ /dev/null @@ -1,221 +0,0 @@ -\achapter{Asynchronous and Parallel Proof Processing\label{Asyncprocessing}} -%HEVEA\cutname{async-proofs.html} -\aauthor{Enrico Tassi} - -\label{pralitp} -\index{Asynchronous and Parallel Proof Processing!presentation} - -This chapter explains how proofs can be asynchronously processed by Coq. -This feature improves the reactivity of the system when used in interactive -mode via CoqIDE. In addition, it allows Coq to take advantage of -parallel hardware when used as a batch compiler by decoupling the checking -of statements and definitions from the construction and checking of proofs -objects. - -This feature is designed to help dealing with huge libraries of theorems -characterized by long proofs. In the current state, it may not be beneficial -on small sets of short files. - -This feature has some technical limitations that may make it unsuitable for -some use cases. - -For example, in interactive mode, some errors coming from the kernel of Coq -are signaled late. The type of errors belonging to this category -are universe inconsistencies. - -At the time of writing, only opaque proofs (ending with \texttt{Qed} or \texttt{Admitted}) can be processed asynchronously. - -Finally, asynchronous processing is disabled when running CoqIDE in Windows. The -current implementation of the feature is not stable on Windows. It can be -enabled, as described below at \ref{interactivecaveats}, though doing so is not -recommended. - -\section{Proof annotations} - -To process a proof asynchronously Coq needs to know the precise statement -of the theorem without looking at the proof. This requires some annotations -if the theorem is proved inside a \texttt{Section} (see Section~\ref{Section}). - -When a section ends, Coq looks at the proof object to decide which -section variables are actually used and hence have to be quantified in the -statement of the theorem. To avoid making the construction of proofs -mandatory when ending a section, one can start each proof with the -\texttt{Proof using} command (Section~\ref{ProofUsing}) that declares which -section variables the theorem uses. - -The presence of \texttt{Proof using} is needed to process proofs -asynchronously in interactive mode. - -It is not strictly mandatory in batch mode if it is not the first time -the file is compiled and if the file itself did not change. When the -proof does not begin with \texttt{Proof using}, the system records in an -auxiliary file, produced along with the \texttt{.vo} file, the list of -section variables used. - -\subsubsection{Automatic suggestion of proof annotations} - -The command \texttt{Set Suggest Proof Using} makes Coq suggest, when a -\texttt{Qed} command is processed, a correct proof annotation. It is up -to the user to modify the proof script accordingly. - -\section{Proof blocks and error resilience} - -Coq 8.6 introduces a mechanism for error resiliency: in interactive mode Coq -is able to completely check a document containing errors instead of bailing -out at the first failure. - -Two kind of errors are supported: errors occurring in vernacular commands and -errors occurring in proofs. - -To properly recover from a failing tactic, Coq needs to recognize the structure of -the proof in order to confine the error to a sub proof. Proof block detection -is performed by looking at the syntax of the proof script (i.e. also looking at indentation). -Coq comes with four kind of proof blocks, and an ML API to add new ones. - -\begin{description} -\item[curly] blocks are delimited by \texttt{\{} and \texttt{\}}, see \ref{Proof-handling} -\item[par] blocks are atomic, i.e. just one tactic introduced by the \texttt{par:} goal selector -\item[indent] blocks end with a tactic indented less than the previous one -\item[bullet] blocks are delimited by two equal bullet signs at the same indentation level -\end{description} - -\subsection{Caveats} - -When a vernacular command fails the subsequent error messages may be bogus, i.e. caused by -the first error. Error resiliency for vernacular commands can be switched off passing -\texttt{-async-proofs-command-error-resilience off} to CoqIDE. - -An incorrect proof block detection can result into an incorrect error recovery and -hence in bogus errors. Proof block detection cannot be precise for bullets or -any other non well parenthesized proof structure. Error resiliency can be -turned off or selectively activated for any set of block kind passing to -CoqIDE one of the following options: -\texttt{-async-proofs-tactic-error-resilience off}, -\texttt{-async-proofs-tactic-error-resilience all}, -\texttt{-async-proofs-tactic-error-resilience $blocktype_1$,..., $blocktype_n$}. -Valid proof block types are: ``curly'', ``par'', ``indent'', ``bullet''. - -\section{Interactive mode} - -At the time of writing the only user interface supporting asynchronous proof -processing is CoqIDE. - -When CoqIDE is started, two Coq processes are created. The master one follows -the user, giving feedback as soon as possible by skipping proofs, which are -delegated to the worker process. The worker process, whose state can be seen -by clicking on the button in the lower right corner of the main CoqIDE window, -asynchronously processes the proofs. If a proof contains an error, it is -reported in red in the label of the very same button, that can also be used to -see the list of errors and jump to the corresponding line. - -If a proof is processed asynchronously the corresponding \texttt{Qed} command -is colored using a lighter color that usual. This signals that -the proof has been delegated to a worker process (or will be processed -lazily if the \texttt{-async-proofs lazy} option is used). Once finished, the -worker process will provide the proof object, but this will not be -automatically checked by the kernel of the main process. To force -the kernel to check all the proof objects, one has to click the button -with the gears. Only then are all the universe constraints checked. - -\subsubsection{Caveats} -\label{interactivecaveats} - -The number of worker processes can be increased by passing CoqIDE the -\texttt{-async-proofs-j $n$} flag. Note that the memory consumption -increases too, since each worker requires the same amount of memory as -the master process. Also note that increasing the number of workers may -reduce the reactivity of the master process to user commands. - -To disable this feature, one can pass the \texttt{-async-proofs off} flag to -CoqIDE. Conversely, on Windows, where the feature is disabled by default, -pass the \texttt{-async-proofs on} flag to enable it. - -Proofs that are known to take little time to process are not delegated to a -worker process. The threshold can be configure with \texttt{-async-proofs-delegation-threshold}. Default is 0.03 seconds. - -\section{Batch mode} - -When Coq is used as a batch compiler by running \texttt{coqc} or -\texttt{coqtop -compile}, it produces a \texttt{.vo} file for each -\texttt{.v} file. A \texttt{.vo} file contains, among other things, -theorems statements and proofs. Hence to produce a \texttt{.vo} Coq need -to process all the proofs of the \texttt{.v} file. - -The asynchronous processing of proofs can decouple the generation of a -compiled file (like the \texttt{.vo} one) that can be loaded by -\texttt{Require} from the generation and checking of the proof objects. -The \texttt{-quick} flag can be passed to \texttt{coqc} or -\texttt{coqtop} to produce, quickly, \texttt{.vio} files. Alternatively, -when using a \texttt{Makefile} produced by \texttt{coq\_makefile}, the -\texttt{quick} target can be used to compile all files using the -\texttt{-quick} flag. - -A \texttt{.vio} file can be loaded using \texttt{Require} exactly as a -\texttt{.vo} file but proofs will not be available (the \texttt{Print} -command produces an error). Moreover, some universe constraints might be -missing, so universes inconsistencies might go unnoticed. A -\texttt{.vio} file does not contain proof objects, but proof tasks, -i.e. what a worker process can transform into a proof object. - -Compiling a set of files with the \texttt{-quick} flag allows one to work, -interactively, on any file without waiting for all the proofs to be checked. - -When working interactively, one can fully check all the \texttt{.v} files by -running \texttt{coqc} as usual. - -Alternatively one can turn each \texttt{.vio} into the corresponding -\texttt{.vo}. All \texttt{.vio} files can be processed in parallel, -hence this alternative might be faster. The command \texttt{coqtop - -schedule-vio2vo 2 a b c} can be used to obtain a good scheduling for 2 -workers to produce \texttt{a.vo}, \texttt{b.vo}, and \texttt{c.vo}. When -using a \texttt{Makefile} produced by \texttt{coq\_makefile}, the -\texttt{vio2vo} target can be used for that purpose. Variable \texttt{J} -should be set to the number of workers, e.g. \texttt{make vio2vo J=2}. -The only caveat is that, while the \texttt{.vo} files obtained from -\texttt{.vio} files are complete (they contain all proof terms and -universe constraints), the satisfiability of all universe constraints has -not been checked globally (they are checked to be consistent for every -single proof). Constraints will be checked when these \texttt{.vo} files -are (recursively) loaded with \texttt{Require}. - -There is an extra, possibly even faster, alternative: just check the -proof tasks stored in \texttt{.vio} files without producing the -\texttt{.vo} files. This is possibly faster because all the proof tasks -are independent, hence one can further partition the job to be done -between workers. The \texttt{coqtop -schedule-vio-checking 6 a b c} -command can be used to obtain a good scheduling for 6 workers to check -all the proof tasks of \texttt{a.vio}, \texttt{b.vio}, and -\texttt{c.vio}. Auxiliary files are used to predict how long a proof task -will take, assuming it will take the same amount of time it took last -time. When using a \texttt{Makefile} produced by \texttt{coq\_makefile}, -the \texttt{checkproofs} target can be used to check all \texttt{.vio} -files. Variable \texttt{J} should be set to the number of workers, -e.g. \texttt{make checkproofs J=6}. As when converting \texttt{.vio} -files to \texttt{.vo} files, universe constraints are not checked to be -globally consistent. Hence this compilation mode is only useful for quick -regression testing and on developments not making heavy use of the $Type$ -hierarchy. - -\section{Limiting the number of parallel workers} -\label{coqworkmgr} - -Many Coq processes may run on the same computer, and each of them may start -many additional worker processes. -The \texttt{coqworkmgr} utility lets one limit the number of workers, globally. - -The utility accepts the \texttt{-j} argument to specify the maximum number of -workers (defaults to 2). \texttt{coqworkmgr} automatically starts in the -background and prints an environment variable assignment like -\texttt{COQWORKMGR\_SOCKET=localhost:45634}. The user must set this variable in -all the shells from which Coq processes will be started. If one uses just -one terminal running the bash shell, then \texttt{export `coqworkmgr -j 4`} will -do the job. - -After that, all Coq processes, e.g. \texttt{coqide} and \texttt{coqc}, -will honor the limit, globally. - - -%%% Local Variables: -%%% mode: latex -%%% TeX-master: "Reference-Manual" -%%% End: diff --git a/doc/refman/Classes.tex b/doc/refman/Classes.tex deleted file mode 100644 index da798a238..000000000 --- a/doc/refman/Classes.tex +++ /dev/null @@ -1,578 +0,0 @@ -\def\Haskell{\textsc{Haskell}\xspace} -\def\eol{\setlength\parskip{0pt}\par} -\def\indent#1{\noindent\kern#1} -\def\cst#1{\textsf{#1}} - -\newcommand\tele[1]{\overrightarrow{#1}} - -\achapter{\protect{Type Classes}} -%HEVEA\cutname{type-classes.html} -\aauthor{Matthieu Sozeau} -\label{typeclasses} - -This chapter presents a quick reference of the commands related to type -classes. For an actual introduction to type classes, there is a -description of the system \cite{sozeau08} and the literature on type -classes in \Haskell which also applies. - -\asection{Class and Instance declarations} -\label{ClassesInstances} - -The syntax for class and instance declarations is the same as -record syntax of \Coq: -\def\kw{\texttt} -\def\classid{\texttt} - -\begin{center} -\[\begin{array}{l} -\kw{Class}~\classid{Id}~(\alpha_1 : \tau_1) \cdots (\alpha_n : \tau_n) -[: \sort] := \{\\ -\begin{array}{p{0em}lcl} - & \cst{f}_1 & : & \type_1 ; \\ - & \vdots & & \\ - & \cst{f}_m & : & \type_m \}. -\end{array}\end{array}\] -\end{center} -\begin{center} -\[\begin{array}{l} -\kw{Instance}~\ident~:~\classid{Id}~\term_1 \cdots \term_n := \{\\ -\begin{array}{p{0em}lcl} - & \cst{f}_1 & := & \term_{f_1} ; \\ - & \vdots & & \\ - & \cst{f}_m & := & \term_{f_m} \}. -\end{array}\end{array}\] -\end{center} -\begin{coq_eval} - Reset Initial. - Generalizable All Variables. -\end{coq_eval} - -The $\tele{\alpha_i : \tau_i}$ variables are called the \emph{parameters} -of the class and the $\tele{f_k : \type_k}$ are called the -\emph{methods}. Each class definition gives rise to a corresponding -record declaration and each instance is a regular definition whose name -is given by $\ident$ and type is an instantiation of the record type. - -We'll use the following example class in the rest of the chapter: - -\begin{coq_example*} -Class EqDec (A : Type) := { - eqb : A -> A -> bool ; - eqb_leibniz : forall x y, eqb x y = true -> x = y }. -\end{coq_example*} - -This class implements a boolean equality test which is compatible with -Leibniz equality on some type. An example implementation is: - -\begin{coq_example*} -Instance unit_EqDec : EqDec unit := -{ eqb x y := true ; - eqb_leibniz x y H := - match x, y return x = y with tt, tt => eq_refl tt end }. -\end{coq_example*} - -If one does not give all the members in the \texttt{Instance} -declaration, Coq enters the proof-mode and the user is asked to build -inhabitants of the remaining fields, e.g.: - -\begin{coq_example*} -Instance eq_bool : EqDec bool := -{ eqb x y := if x then y else negb y }. -\end{coq_example*} -\begin{coq_example} -Proof. intros x y H. - destruct x ; destruct y ; (discriminate || reflexivity). -Defined. -\end{coq_example} - -One has to take care that the transparency of every field is determined -by the transparency of the \texttt{Instance} proof. One can use -alternatively the \texttt{Program} \texttt{Instance} \comindex{Program Instance} variant which has -richer facilities for dealing with obligations. - -\asection{Binding classes} - -Once a type class is declared, one can use it in class binders: -\begin{coq_example} -Definition neqb {A} {eqa : EqDec A} (x y : A) := negb (eqb x y). -\end{coq_example} - -When one calls a class method, a constraint is generated that is -satisfied only in contexts where the appropriate instances can be -found. In the example above, a constraint \texttt{EqDec A} is generated and -satisfied by \texttt{{eqa : EqDec A}}. In case no satisfying constraint can be -found, an error is raised: - -\begin{coq_example} -Fail Definition neqb' (A : Type) (x y : A) := negb (eqb x y). -\end{coq_example} - -The algorithm used to solve constraints is a variant of the eauto tactic -that does proof search with a set of lemmas (the instances). It will use -local hypotheses as well as declared lemmas in the -\texttt{typeclass\_instances} database. Hence the example can also be -written: - -\begin{coq_example} -Definition neqb' A (eqa : EqDec A) (x y : A) := negb (eqb x y). -\end{coq_example} - -However, the generalizing binders should be used instead as they have -particular support for type classes: -\begin{itemize} -\item They automatically set the maximally implicit status for type - class arguments, making derived functions as easy to use as class - methods. In the example above, \texttt{A} and \texttt{eqa} should be - set maximally implicit. -\item They support implicit quantification on partially applied type - classes (\S \ref{implicit-generalization}). - Any argument not given as part of a type class binder will be - automatically generalized. -\item They also support implicit quantification on superclasses - (\S \ref{classes:superclasses}) -\end{itemize} - -Following the previous example, one can write: -\begin{coq_example} -Definition neqb_impl `{eqa : EqDec A} (x y : A) := negb (eqb x y). -\end{coq_example} - -Here \texttt{A} is implicitly generalized, and the resulting function -is equivalent to the one above. - -\asection{Parameterized Instances} - -One can declare parameterized instances as in \Haskell simply by giving -the constraints as a binding context before the instance, e.g.: - -\begin{coq_example} -Instance prod_eqb `(EA : EqDec A, EB : EqDec B) : EqDec (A * B) := -{ eqb x y := match x, y with - | (la, ra), (lb, rb) => andb (eqb la lb) (eqb ra rb) - end }. -\end{coq_example} -\begin{coq_eval} -Admitted. -\end{coq_eval} - -These instances are used just as well as lemmas in the instance hint database. - -\asection{Sections and contexts} -\label{SectionContext} -To ease the parametrization of developments by type classes, we provide -a new way to introduce variables into section contexts, compatible with -the implicit argument mechanism. -The new command works similarly to the \texttt{Variables} vernacular -(see \ref{Variable}), except it accepts any binding context as argument. -For example: - -\begin{coq_example} -Section EqDec_defs. - Context `{EA : EqDec A}. -\end{coq_example} - -\begin{coq_example*} - Global Instance option_eqb : EqDec (option A) := - { eqb x y := match x, y with - | Some x, Some y => eqb x y - | None, None => true - | _, _ => false - end }. -\end{coq_example*} -\begin{coq_eval} -Proof. -intros x y ; destruct x ; destruct y ; intros H ; -try discriminate ; try apply eqb_leibniz in H ; -subst ; auto. -Defined. -\end{coq_eval} - -\begin{coq_example} -End EqDec_defs. -About option_eqb. -\end{coq_example} - -Here the \texttt{Global} modifier redeclares the instance at the end of -the section, once it has been generalized by the context variables it uses. - -\asection{Building hierarchies} - -\subsection{Superclasses} -\label{classes:superclasses} -One can also parameterize classes by other classes, generating a -hierarchy of classes and superclasses. In the same way, we give the -superclasses as a binding context: - -\begin{coq_example*} -Class Ord `(E : EqDec A) := - { le : A -> A -> bool }. -\end{coq_example*} - -Contrary to \Haskell, we have no special syntax for superclasses, but -this declaration is morally equivalent to: -\begin{verbatim} -Class `(E : EqDec A) => Ord A := - { le : A -> A -> bool }. -\end{verbatim} - -This declaration means that any instance of the \texttt{Ord} class must -have an instance of \texttt{EqDec}. The parameters of the subclass contain -at least all the parameters of its superclasses in their order of -appearance (here \texttt{A} is the only one). -As we have seen, \texttt{Ord} is encoded as a record type with two parameters: -a type \texttt{A} and an \texttt{E} of type \texttt{EqDec A}. However, one can -still use it as if it had a single parameter inside generalizing binders: the -generalization of superclasses will be done automatically. -\begin{coq_example*} -Definition le_eqb `{Ord A} (x y : A) := andb (le x y) (le y x). -\end{coq_example*} - -In some cases, to be able to specify sharing of structures, one may want to give -explicitly the superclasses. It is is possible to do it directly in regular -binders, and using the \texttt{!} modifier in class binders. For -example: -\begin{coq_example*} -Definition lt `{eqa : EqDec A, ! Ord eqa} (x y : A) := - andb (le x y) (neqb x y). -\end{coq_example*} - -The \texttt{!} modifier switches the way a binder is parsed back to the -regular interpretation of Coq. In particular, it uses the implicit -arguments mechanism if available, as shown in the example. - -\subsection{Substructures} - -Substructures are components of a class which are instances of a class -themselves. They often arise when using classes for logical properties, -e.g.: - -\begin{coq_eval} -Require Import Relations. -\end{coq_eval} -\begin{coq_example*} -Class Reflexive (A : Type) (R : relation A) := - reflexivity : forall x, R x x. -Class Transitive (A : Type) (R : relation A) := - transitivity : forall x y z, R x y -> R y z -> R x z. -\end{coq_example*} - -This declares singleton classes for reflexive and transitive relations, -(see \ref{SingletonClass} for an explanation). -These may be used as part of other classes: - -\begin{coq_example*} -Class PreOrder (A : Type) (R : relation A) := -{ PreOrder_Reflexive :> Reflexive A R ; - PreOrder_Transitive :> Transitive A R }. -\end{coq_example*} - -The syntax \texttt{:>} indicates that each \texttt{PreOrder} can be seen -as a \texttt{Reflexive} relation. So each time a reflexive relation is -needed, a preorder can be used instead. This is very similar to the -coercion mechanism of \texttt{Structure} declarations. -The implementation simply declares each projection as an instance. - -One can also declare existing objects or structure -projections using the \texttt{Existing Instance} command to achieve the -same effect. - -\section{Summary of the commands -\label{TypeClassCommands}} - -\subsection{\tt Class {\ident} {\binder$_1$ \ldots~\binder$_n$} - : \sort := \{ field$_1$ ; \ldots ; field$_k$ \}.} -\comindex{Class} -\label{Class} - -The \texttt{Class} command is used to declare a type class with -parameters {\binder$_1$} to {\binder$_n$} and fields {\tt field$_1$} to -{\tt field$_k$}. - -\begin{Variants} -\item \label{SingletonClass} {\tt Class {\ident} {\binder$_1$ \ldots \binder$_n$} - : \sort := \ident$_1$ : \type$_1$.} - This variant declares a \emph{singleton} class whose only method is - {\tt \ident$_1$}. This singleton class is a so-called definitional - class, represented simply as a definition - {\tt {\ident} \binder$_1$ \ldots \binder$_n$ := \type$_1$} and whose - instances are themselves objects of this type. Definitional classes - are not wrapped inside records, and the trivial projection of an - instance of such a class is convertible to the instance itself. This can - be useful to make instances of existing objects easily and to reduce - proof size by not inserting useless projections. The class - constant itself is declared rigid during resolution so that the class - abstraction is maintained. - -\item \label{ExistingClass} {\tt Existing Class {\ident}.\comindex{Existing Class}} - This variant declares a class a posteriori from a constant or - inductive definition. No methods or instances are defined. -\end{Variants} - -\subsection{\tt Instance {\ident} {\binder$_1$ \ldots \binder$_n$} : - {Class} {t$_1$ \ldots t$_n$} [| \textit{priority}] - := \{ field$_1$ := b$_1$ ; \ldots ; field$_i$ := b$_i$ \}} -\comindex{Instance} -\label{Instance} - -The \texttt{Instance} command is used to declare a type class instance -named {\ident} of the class \emph{Class} with parameters {t$_1$} to {t$_n$} and -fields {\tt b$_1$} to {\tt b$_i$}, where each field must be a declared -field of the class. Missing fields must be filled in interactive proof mode. - -An arbitrary context of the form {\tt \binder$_1$ \ldots \binder$_n$} -can be put after the name of the instance and before the colon to -declare a parameterized instance. -An optional \textit{priority} can be declared, 0 being the highest -priority as for auto hints. If the priority is not specified, it defaults to -$n$, the number of binders of the instance. - -\begin{Variants} -\item {\tt Instance {\ident} {\binder$_1$ \ldots \binder$_n$} : - forall {\binder$_{n+1}$ \ldots \binder$_m$}, - {Class} {t$_1$ \ldots t$_n$} [| \textit{priority}] := \term} - This syntax is used for declaration of singleton class instances or - for directly giving an explicit term of type - {\tt forall {\binder$_{n+1}$ \ldots \binder$_m$}, {Class} {t$_1$ \ldots t$_n$}}. - One need not even mention the unique field name for singleton classes. - -\item {\tt Global Instance} One can use the \texttt{Global} modifier on - instances declared in a section so that their generalization is automatically - redeclared after the section is closed. - -\item {\tt Program Instance} \comindex{Program Instance} - Switches the type-checking to \Program~(chapter \ref{Program}) - and uses the obligation mechanism to manage missing fields. - -\item {\tt Declare Instance} \comindex{Declare Instance} - In a {\tt Module Type}, this command states that a corresponding - concrete instance should exist in any implementation of this - {\tt Module Type}. This is similar to the distinction between - {\tt Parameter} vs. {\tt Definition}, or between {\tt Declare Module} - and {\tt Module}. - -\end{Variants} - -Besides the {\tt Class} and {\tt Instance} vernacular commands, there -are a few other commands related to type classes. - -\subsection{\tt Existing Instance {\ident} [| \textit{priority}]} -\comindex{Existing Instance} -\label{ExistingInstance} - -This commands adds an arbitrary constant whose type ends with an applied -type class to the instance database with an optional priority. It can be used -for redeclaring instances at the end of sections, or declaring structure -projections as instances. This is almost equivalent to {\tt Hint Resolve -{\ident} : typeclass\_instances}. - -\begin{Variants} -\item {\tt Existing Instances {\ident}$_1$ \ldots {\ident}$_n$ - [| \textit{priority}]} - \comindex{Existing Instances} - With this command, several existing instances can be declared at once. -\end{Variants} - -\subsection{\tt Context {\binder$_1$ \ldots \binder$_n$}} -\comindex{Context} -\label{Context} - -Declares variables according to the given binding context, which might -use implicit generalization (see \ref{SectionContext}). - -\asubsection{\tt typeclasses eauto} -\tacindex{typeclasses eauto} -\label{typeclasseseauto} - -The {\tt typeclasses eauto} tactic uses a different resolution engine -than {\tt eauto} and {\tt auto}. The main differences are the following: -\begin{itemize} -\item Contrary to {\tt eauto} and {\tt auto}, the resolution is done - entirely in the new proof engine (as of Coq v8.6), meaning that - backtracking is available among dependent subgoals, and shelving goals - is supported. {\tt typeclasses eauto} is a multi-goal tactic. - It analyses the dependencies between subgoals to avoid - backtracking on subgoals that are entirely independent. -\item When called with no arguments, {\tt typeclasses eauto} uses the - {\tt typeclass\_instances} database by default (instead of {\tt - core}). - Dependent subgoals are automatically shelved, and shelved - goals can remain after resolution ends (following the behavior of - \Coq{} 8.5). - - \emph{Note: } As of Coq 8.6, {\tt all:once (typeclasses eauto)} - faithfully mimicks what happens during typeclass resolution when it is - called during refinement/type-inference, except that \emph{only} - declared class subgoals are considered at the start of resolution - during type inference, while ``all'' can select non-class subgoals as - well. It might move to {\tt all:typeclasses eauto} in future versions - when the refinement engine will be able to backtrack. -\item When called with specific databases (e.g. {\tt with}), {\tt - typeclasses eauto} allows shelved goals to remain at any point - during search and treat typeclasses goals like any other. -\item The transparency information of databases is used consistently for - all hints declared in them. It is always used when calling the unifier. - When considering the local hypotheses, we use the transparent - state of the first hint database given. Using an empty database - (created with {\tt Create HintDb} for example) with - unfoldable variables and constants as the first argument of - typeclasses eauto hence makes resolution with the local hypotheses use - full conversion during unification. -\end{itemize} - -\begin{Variants} -\item \label{depth} {\tt typeclasses eauto \zeroone{\num}} - \emph{Warning:} The semantics for the limit {\num} is different than - for {\tt auto}. By default, if no limit is given the search is - unbounded. Contrary to {\tt auto}, introduction steps ({\tt intro}) - are counted, which might result in larger limits being necessary - when searching with {\tt typeclasses eauto} than {\tt auto}. - -\item \label{with} {\tt typeclasses eauto with {\ident}$_1$ \ldots {\ident}$_n$}. - This variant runs resolution with the given hint databases. It treats - typeclass subgoals the same as other subgoals (no shelving of - non-typeclass goals in particular). -\end{Variants} - -\asubsection{\tt autoapply {\term} with {\ident}} -\tacindex{autoapply} - -The tactic {\tt autoapply} applies a term using the transparency -information of the hint database {\ident}, and does \emph{no} typeclass -resolution. This can be used in {\tt Hint Extern}'s for typeclass -instances (in hint db {\tt typeclass\_instances}) to -allow backtracking on the typeclass subgoals created by the lemma -application, rather than doing type class resolution locally at the hint -application time. - -\subsection{\tt Typeclasses Transparent, Opaque {\ident$_1$ \ldots \ident$_n$}} -\comindex{Typeclasses Transparent} -\comindex{Typeclasses Opaque} -\label{TypeclassesTransparency} - -This commands defines the transparency of {\ident$_1$ \ldots \ident$_n$} -during type class resolution. It is useful when some constants prevent some -unifications and make resolution fail. It is also useful to declare -constants which should never be unfolded during proof-search, like -fixpoints or anything which does not look like an abbreviation. This can -additionally speed up proof search as the typeclass map can be indexed -by such rigid constants (see \ref{HintTransparency}). -By default, all constants and local variables are considered transparent. -One should take care not to make opaque any constant that is used to -abbreviate a type, like {\tt relation A := A -> A -> Prop}. - -This is equivalent to {\tt Hint Transparent,Opaque} {\ident} {\tt: typeclass\_instances}. - -\subsection{\tt Set Typeclasses Axioms Are Instances} -\optindex{Typeclasses Axioms Are Instances} - -This option (off by default since 8.8) automatically declares axioms -whose type is a typeclass at declaration time as instances of that -class. - -\subsection{\tt Set Typeclasses Dependency Order} -\optindex{Typeclasses Dependency Order} - -This option (on by default since 8.6) respects the dependency order between -subgoals, meaning that subgoals which are depended on by other subgoals -come first, while the non-dependent subgoals were put before the -dependent ones previously (Coq v8.5 and below). This can result in quite -different performance behaviors of proof search. - -\subsection{\tt Set Typeclasses Filtered Unification} -\optindex{Typeclasses Filtered Unification} - -This option, available since Coq 8.6 and off by default, switches the -hint application procedure to a filter-then-unify strategy. To apply a -hint, we first check that the goal \emph{matches} syntactically the -inferred or specified pattern of the hint, and only then try to -\emph{unify} the goal with the conclusion of the hint. This can -drastically improve performance by calling unification less often, -matching syntactic patterns being very quick. This also provides more -control on the triggering of instances. For example, forcing a constant -to explicitely appear in the pattern will make it never apply on a goal -where there is a hole in that place. - -\subsection{\tt Set Typeclasses Limit Intros} -\optindex{Typeclasses Limit Intros} - -This option (on by default) controls the ability to -apply hints while avoiding (functional) eta-expansions in the generated -proof term. It does so by allowing hints that conclude in a product to -apply to a goal with a matching product directly, avoiding an -introduction. \emph{Warning:} this can be expensive as it requires -rebuilding hint clauses dynamically, and does not benefit from the -invertibility status of the product introduction rule, resulting in -potentially more expensive proof-search (i.e. more useless -backtracking). - -\subsection{\tt Set Typeclass Resolution For Conversion} -\optindex{Typeclass Resolution For Conversion} - -This option (on by default) controls the use of typeclass resolution -when a unification problem cannot be solved during -elaboration/type-inference. With this option on, when a unification -fails, typeclass resolution is tried before launching unification once again. - -\subsection{\tt Set Typeclasses Strict Resolution} -\optindex{Typeclasses Strict Resolution} - -Typeclass declarations introduced when this option is set have a -stricter resolution behavior (the option is off by default). When -looking for unifications of a goal with an instance of this class, we -``freeze'' all the existentials appearing in the goals, meaning that -they are considered rigid during unification and cannot be instantiated. - -\subsection{\tt Set Typeclasses Unique Solutions} -\optindex{Typeclasses Unique Solutions} - -When a typeclass resolution is launched we ensure that it has a single -solution or fail. This ensures that the resolution is canonical, but can -make proof search much more expensive. - -\subsection{\tt Set Typeclasses Unique Instances} -\optindex{Typeclasses Unique Instances} - -Typeclass declarations introduced when this option is set have a -more efficient resolution behavior (the option is off by default). When -a solution to the typeclass goal of this class is found, we never -backtrack on it, assuming that it is canonical. - -\subsection{\tt Typeclasses eauto := [debug] [(dfs) | (bfs)] [\emph{depth}]} -\comindex{Typeclasses eauto} -\label{TypeclassesEauto} - -This command allows more global customization of the type class -resolution tactic. -The semantics of the options are: -\begin{itemize} -\item {\tt debug} In debug mode, the trace of successfully applied - tactics is printed. -\item {\tt dfs, bfs} This sets the search strategy to depth-first search - (the default) or breadth-first search. -\item {\emph{depth}} This sets the depth limit of the search. -\end{itemize} - -\subsection{\tt Set Typeclasses Debug [Verbosity {\num}]} -\optindex{Typeclasses Debug} -\optindex{Typeclasses Debug Verbosity} - -These options allow to see the resolution steps of typeclasses that are -performed during search. The {\tt Debug} option is synonymous to -{\tt Debug Verbosity 1}, and {\tt Debug Verbosity 2} provides more -information (tried tactics, shelving of goals, etc\ldots). - -\subsection{\tt Set Refine Instance Mode} -\optindex{Refine Instance Mode} - -The option {\tt Refine Instance Mode} allows to switch the behavior of instance -declarations made through the {\tt Instance} command. -\begin{itemize} -\item When it is on (the default), instances that have unsolved holes in their -proof-term silently open the proof mode with the remaining obligations to prove. -\item When it is off, they fail with an error instead. -\end{itemize} - -%%% Local Variables: -%%% mode: latex -%%% TeX-master: "Reference-Manual" -%%% End: diff --git a/doc/refman/Coercion.tex b/doc/refman/Coercion.tex deleted file mode 100644 index 9862a9b30..000000000 --- a/doc/refman/Coercion.tex +++ /dev/null @@ -1,563 +0,0 @@ -\achapter{Implicit Coercions} -%HEVEA\cutname{coercions.html} -\aauthor{Amokrane Saïbi} - -\label{Coercions-full} -\index{Coercions!presentation} - -\asection{General Presentation} - -This section describes the inheritance mechanism of {\Coq}. In {\Coq} with -inheritance, we are not interested in adding any expressive power to -our theory, but only convenience. Given a term, possibly not typable, -we are interested in the problem of determining if it can be well -typed modulo insertion of appropriate coercions. We allow to write: - -\begin{itemize} -\item $f~a$ where $f:forall~ x:A, B$ and $a:A'$ when $A'$ can - be seen in some sense as a subtype of $A$. -\item $x:A$ when $A$ is not a type, but can be seen in - a certain sense as a type: set, group, category etc. -\item $f~a$ when $f$ is not a function, but can be seen in a certain sense - as a function: bijection, functor, any structure morphism etc. -\end{itemize} - -\asection{Classes} -\index{Coercions!classes} - A class with $n$ parameters is any defined name with a type -$forall~ (x_1:A_1)..(x_n:A_n), s$ where $s$ is a sort. Thus a class with -parameters is considered as a single class and not as a family of -classes. An object of a class $C$ is any term of type $C~t_1 -.. t_n$. In addition to these user-classes, we have two abstract -classes: - -\begin{itemize} -\item {\tt Sortclass}, the class of sorts; - its objects are the terms whose type is a sort (e.g., \texttt{Prop} - or \texttt{Type}). -\item {\tt Funclass}, the class of functions; - its objects are all the terms with a functional - type, i.e. of form $forall~ x:A, B$. -\end{itemize} - -Formally, the syntax of a classes is defined on Figure~\ref{fig:classes}. -\begin{figure} -\begin{centerframe} -\begin{tabular}{lcl} -{\class} & ::= & {\qualid} \\ - & $|$ & {\tt Sortclass} \\ - & $|$ & {\tt Funclass} -\end{tabular} -\end{centerframe} -\caption{Syntax of classes} -\label{fig:classes} -\end{figure} - -\asection{Coercions} -\index{Coercions!Funclass} -\index{Coercions!Sortclass} - A name $f$ can be declared as a coercion between a source user-class -$C$ with $n$ parameters and a target class $D$ if one of these -conditions holds: - -\newcommand{\oftype}{\!:\!} - -\begin{itemize} -\item $D$ is a user-class, then the type of $f$ must have the form - $forall~ (x_1 \oftype A_1)..(x_n \oftype A_n)(y\oftype C~x_1..x_n), D~u_1..u_m$ where $m$ - is the number of parameters of $D$. -\item $D$ is {\tt Funclass}, then the type of $f$ must have the form - $forall~ (x_1\oftype A_1)..(x_n\oftype A_n)(y\oftype C~x_1..x_n)(x:A), B$. -\item $D$ is {\tt Sortclass}, then the type of $f$ must have the form - $forall~ (x_1\oftype A_1)..(x_n\oftype A_n)(y\oftype C~x_1..x_n), s$ with $s$ a sort. -\end{itemize} - -We then write $f:C \mbox{\texttt{>->}} D$. The restriction on the type -of coercions is called {\em the uniform inheritance condition}. -Remark: the abstract class {\tt Sortclass} can be used as source class, -but the abstract class {\tt Funclass} cannot. - -To coerce an object $t:C~t_1..t_n$ of $C$ towards $D$, we have to -apply the coercion $f$ to it; the obtained term $f~t_1..t_n~t$ is -then an object of $D$. - -\asection{Identity Coercions} -\index{Coercions!identity} - - Identity coercions are special cases of coercions used to go around -the uniform inheritance condition. Let $C$ and $D$ be two classes -with respectively $n$ and $m$ parameters and -$f:forall~(x_1:T_1)..(x_k:T_k)(y:C~u_1..u_n), D~v_1..v_m$ a function which -does not verify the uniform inheritance condition. To declare $f$ as -coercion, one has first to declare a subclass $C'$ of $C$: - -$$C' := fun~ (x_1:T_1)..(x_k:T_k) => C~u_1..u_n$$ - -\noindent We then define an {\em identity coercion} between $C'$ and $C$: -\begin{eqnarray*} -Id\_C'\_C & := & fun~ (x_1:T_1)..(x_k:T_k)(y:C'~x_1..x_k) => (y:C~u_1..u_n)\\ -\end{eqnarray*} - -We can now declare $f$ as coercion from $C'$ to $D$, since we can -``cast'' its type as -$forall~ (x_1:T_1)..(x_k:T_k)(y:C'~x_1..x_k),D~v_1..v_m$.\\ The identity -coercions have a special status: to coerce an object $t:C'~t_1..t_k$ -of $C'$ towards $C$, we does not have to insert explicitly $Id\_C'\_C$ -since $Id\_C'\_C~t_1..t_k~t$ is convertible with $t$. However we -``rewrite'' the type of $t$ to become an object of $C$; in this case, -it becomes $C~u_1^*..u_k^*$ where each $u_i^*$ is the result of the -substitution in $u_i$ of the variables $x_j$ by $t_j$. - - -\asection{Inheritance Graph} -\index{Coercions!inheritance graph} -Coercions form an inheritance graph with classes as nodes. We call -{\em coercion path} an ordered list of coercions between two nodes of -the graph. A class $C$ is said to be a subclass of $D$ if there is a -coercion path in the graph from $C$ to $D$; we also say that $C$ -inherits from $D$. Our mechanism supports multiple inheritance since a -class may inherit from several classes, contrary to simple inheritance -where a class inherits from at most one class. However there must be -at most one path between two classes. If this is not the case, only -the {\em oldest} one is valid and the others are ignored. So the order -of declaration of coercions is important. - -We extend notations for coercions to coercion paths. For instance -$[f_1;..;f_k]:C \mbox{\texttt{>->}} D$ is the coercion path composed -by the coercions $f_1..f_k$. The application of a coercion path to a -term consists of the successive application of its coercions. - -\asection{Declaration of Coercions} - -%%%%% "Class" is useless, since classes are implicitely defined via coercions. - -% \asubsection{\tt Class {\qualid}.}\comindex{Class} -% Declares {\qualid} as a new class. - -% \begin{ErrMsgs} -% \item {\qualid} \errindex{not declared} -% \item {\qualid} \errindex{is already a class} -% \item \errindex{Type of {\qualid} does not end with a sort} -% \end{ErrMsgs} - -% \begin{Variant} -% \item {\tt Class Local {\qualid}.} \\ -% Declares the construction denoted by {\qualid} as a new local class to -% the current section. -% \end{Variant} - -% END "Class" is useless - -\asubsection{\tt Coercion {\qualid} : {\class$_1$} >-> {\class$_2$}.} -\comindex{Coercion} - -Declares the construction denoted by {\qualid} as a coercion between -{\class$_1$} and {\class$_2$}. - -% Useless information -% The classes {\class$_1$} and {\class$_2$} are first declared if necessary. - -\begin{ErrMsgs} -\item {\qualid} \errindex{not declared} -\item {\qualid} \errindex{is already a coercion} -\item \errindex{Funclass cannot be a source class} -\item {\qualid} \errindex{is not a function} -\item \errindex{Cannot find the source class of {\qualid}} -\item \errindex{Cannot recognize {\class$_1$} as a source class of {\qualid}} -\item {\qualid} \errindex{does not respect the uniform inheritance condition} -\item \errindex{Found target class {\class} instead of {\class$_2$}} - -\end{ErrMsgs} - -When the coercion {\qualid} is added to the inheritance graph, non -valid coercion paths are ignored; they are signaled by a warning. -\\[0.3cm] -\noindent {\bf Warning :} -\begin{enumerate} -\item \begin{tabbing} -{\tt Ambiguous paths: }\= $[f_1^1;..;f_{n_1}^1] : C_1\mbox{\tt >->}D_1$\\ - \> {\ldots} \\ - \>$[f_1^m;..;f_{n_m}^m] : C_m\mbox{\tt >->}D_m$ - \end{tabbing} -\end{enumerate} - -\begin{Variants} -\item {\tt Local Coercion {\qualid} : {\class$_1$} >-> {\class$_2$}.} -\comindex{Local Coercion}\\ - Declares the construction denoted by {\qualid} as a coercion local to - the current section. - -\item {\tt Coercion {\ident} := {\term}}\comindex{Coercion}\\ - This defines {\ident} just like \texttt{Definition {\ident} := - {\term}}, and then declares {\ident} as a coercion between it - source and its target. - -\item {\tt Coercion {\ident} := {\term} : {\type}}\\ - This defines {\ident} just like - \texttt{Definition {\ident} : {\type} := {\term}}, and then - declares {\ident} as a coercion between it source and its target. - -\item {\tt Local Coercion {\ident} := {\term}}\comindex{Local Coercion}\\ - This defines {\ident} just like \texttt{Let {\ident} := - {\term}}, and then declares {\ident} as a coercion between it - source and its target. - -\item Assumptions can be declared as coercions at declaration -time. This extends the grammar of assumptions from -Figure~\ref{sentences-syntax} as follows: -\comindex{Variable \mbox{\rm (and coercions)}} -\comindex{Axiom \mbox{\rm (and coercions)}} -\comindex{Parameter \mbox{\rm (and coercions)}} -\comindex{Hypothesis \mbox{\rm (and coercions)}} - -\begin{tabular}{lcl} -%% Declarations -{\assumption} & ::= & {\assumptionkeyword} {\assums} {\tt .} \\ -&&\\ -{\assums} & ::= & {\simpleassums} \\ - & $|$ & \nelist{{\tt (} \simpleassums {\tt )}}{} \\ -&&\\ -{\simpleassums} & ::= & \nelist{\ident}{} {\tt :}\zeroone{{\tt >}} {\term}\\ -\end{tabular} - -If the extra {\tt >} is present before the type of some assumptions, these -assumptions are declared as coercions. - -\item Constructors of inductive types can be declared as coercions at -definition time of the inductive type. This extends and modifies the -grammar of inductive types from Figure \ref{sentences-syntax} as follows: -\comindex{Inductive \mbox{\rm (and coercions)}} -\comindex{CoInductive \mbox{\rm (and coercions)}} - -\begin{center} -\begin{tabular}{lcl} -%% Inductives -{\inductive} & ::= & - {\tt Inductive} \nelist{\inductivebody}{with} {\tt .} \\ - & $|$ & {\tt CoInductive} \nelist{\inductivebody}{with} {\tt .} \\ - & & \\ -{\inductivebody} & ::= & - {\ident} \zeroone{\binders} {\tt :} {\term} {\tt :=} \\ - && ~~~\zeroone{\zeroone{\tt |} \nelist{\constructor}{|}} \\ - & & \\ -{\constructor} & ::= & {\ident} \zeroone{\binders} \zeroone{{\tt :}\zeroone{\tt >} {\term}} \\ -\end{tabular} -\end{center} - -Especially, if the extra {\tt >} is present in a constructor -declaration, this constructor is declared as a coercion. -\end{Variants} - -\asubsection{\tt Identity Coercion {\ident}:{\class$_1$} >-> {\class$_2$}.} -\comindex{Identity Coercion} - -We check that {\class$_1$} is a constant with a value of the form -$fun~ (x_1:T_1)..(x_n:T_n) => (\mbox{\class}_2~t_1..t_m)$ where $m$ is the -number of parameters of \class$_2$. Then we define an identity -function with the type -$forall~ (x_1:T_1)..(x_n:T_n)(y:\mbox{\class}_1~x_1..x_n), -{\mbox{\class}_2}~t_1..t_m$, and we declare it as an identity -coercion between {\class$_1$} and {\class$_2$}. - -\begin{ErrMsgs} -\item {\class$_1$} \errindex{must be a transparent constant} -\end{ErrMsgs} - -\begin{Variants} -\item {\tt Local Identity Coercion {\ident}:{\ident$_1$} >-> {\ident$_2$}.} \\ -Idem but locally to the current section. - -\item {\tt SubClass {\ident} := {\type}.} \\ -\comindex{SubClass} - If {\type} is a class -{\ident'} applied to some arguments then {\ident} is defined and an -identity coercion of name {\tt Id\_{\ident}\_{\ident'}} is -declared. Otherwise said, this is an abbreviation for - -{\tt Definition {\ident} := {\type}.} - - followed by - -{\tt Identity Coercion Id\_{\ident}\_{\ident'}:{\ident} >-> {\ident'}}. - -\item {\tt Local SubClass {\ident} := {\type}.} \\ -Same as before but locally to the current section. - -\end{Variants} - -\asection{Displaying Available Coercions} - -\asubsection{\tt Print Classes.} -\comindex{Print Classes} -Print the list of declared classes in the current context. - -\asubsection{\tt Print Coercions.} -\comindex{Print Coercions} -Print the list of declared coercions in the current context. - -\asubsection{\tt Print Graph.} -\comindex{Print Graph} -Print the list of valid coercion paths in the current context. - -\asubsection{\tt Print Coercion Paths {\class$_1$} {\class$_2$}.} -\comindex{Print Coercion Paths} -Print the list of valid coercion paths from {\class$_1$} to {\class$_2$}. - -\asection{Activating the Printing of Coercions} - -\asubsection{\tt Set Printing Coercions.} -\optindex{Printing Coercions} - -This command forces all the coercions to be printed. -Conversely, to skip the printing of coercions, use - {\tt Unset Printing Coercions}. -By default, coercions are not printed. - -\asubsection{\tt Add Printing Coercion {\qualid}.} -\comindex{Add Printing Coercion} -\comindex{Remove Printing Coercion} - -This command forces coercion denoted by {\qualid} to be printed. -To skip the printing of coercion {\qualid}, use - {\tt Remove Printing Coercion {\qualid}}. -By default, a coercion is never printed. - -\asection{Classes as Records} -\label{Coercions-and-records} -\index{Coercions!and records} -We allow the definition of {\em Structures with Inheritance} (or -classes as records) by extending the existing {\tt Record} macro -(see Section~\ref{Record}). Its new syntax is: - -\begin{center} -\begin{tabular}{l} -{\tt Record \zeroone{>}~{\ident} \zeroone{\binders} : {\sort} := \zeroone{\ident$_0$} \verb+{+} \\ -~~~~\begin{tabular}{l} - {\tt \ident$_1$ $[$:$|$:>$]$ \term$_1$ ;} \\ - ... \\ - {\tt \ident$_n$ $[$:$|$:>$]$ \term$_n$ \verb+}+. } - \end{tabular} -\end{tabular} -\end{center} -The identifier {\ident} is the name of the defined record and {\sort} -is its type. The identifier {\ident$_0$} is the name of its -constructor. The identifiers {\ident$_1$}, .., {\ident$_n$} are the -names of its fields and {\term$_1$}, .., {\term$_n$} their respective -types. The alternative {\tt $[$:$|$:>$]$} is ``{\tt :}'' or ``{\tt -:>}''. If {\tt {\ident$_i$}:>{\term$_i$}}, then {\ident$_i$} is -automatically declared as coercion from {\ident} to the class of -{\term$_i$}. Remark that {\ident$_i$} always verifies the uniform -inheritance condition. If the optional ``{\tt >}'' before {\ident} is -present, then {\ident$_0$} (or the default name {\tt Build\_{\ident}} -if {\ident$_0$} is omitted) is automatically declared as a coercion -from the class of {\term$_n$} to {\ident} (this may fail if the -uniform inheritance condition is not satisfied). - -\Rem The keyword {\tt Structure}\comindex{Structure} is a synonym of {\tt -Record}. - -\asection{Coercions and Sections} -\index{Coercions!and sections} - The inheritance mechanism is compatible with the section -mechanism. The global classes and coercions defined inside a section -are redefined after its closing, using their new value and new -type. The classes and coercions which are local to the section are -simply forgotten. -Coercions with a local source class or a local target class, and -coercions which do not verify the uniform inheritance condition any longer -are also forgotten. - -\asection{Coercions and Modules} -\index{Coercions!and modules} - -From Coq version 8.3, the coercions present in a module are activated -only when the module is explicitly imported. Formerly, the coercions -were activated as soon as the module was required, whatever it was -imported or not. - -To recover the behavior of the versions of Coq prior to 8.3, use the -following command: - -\optindex{Automatic Coercions Import} -\begin{verbatim} -Set Automatic Coercions Import. -\end{verbatim} - -To cancel the effect of the option, use instead: - -\begin{verbatim} -Unset Automatic Coercions Import. -\end{verbatim} - -\asection{Examples} - - There are three situations: - -\begin{itemize} -\item $f~a$ is ill-typed where $f:forall~x:A,B$ and $a:A'$. If there is a - coercion path between $A'$ and $A$, $f~a$ is transformed into - $f~a'$ where $a'$ is the result of the application of this - coercion path to $a$. - -We first give an example of coercion between atomic inductive types - -%\begin{\small} -\begin{coq_example} -Definition bool_in_nat (b:bool) := if b then 0 else 1. -Coercion bool_in_nat : bool >-> nat. -Check (0 = true). -Set Printing Coercions. -Check (0 = true). -\end{coq_example} -%\end{small} - -\begin{coq_eval} -Unset Printing Coercions. -\end{coq_eval} - -\Warning ``\verb|Check true=O.|'' fails. This is ``normal'' behaviour of -coercions. To validate \verb|true=O|, the coercion is searched from -\verb=nat= to \verb=bool=. There is none. - -We give an example of coercion between classes with parameters. - -%\begin{\small} -\begin{coq_example} -Parameters - (C : nat -> Set) (D : nat -> bool -> Set) (E : bool -> Set). -Parameter f : forall n:nat, C n -> D (S n) true. -Coercion f : C >-> D. -Parameter g : forall (n:nat) (b:bool), D n b -> E b. -Coercion g : D >-> E. -Parameter c : C 0. -Parameter T : E true -> nat. -Check (T c). -Set Printing Coercions. -Check (T c). -\end{coq_example} -%\end{small} - -\begin{coq_eval} -Unset Printing Coercions. -\end{coq_eval} - -We give now an example using identity coercions. - -%\begin{small} -\begin{coq_example} -Definition D' (b:bool) := D 1 b. -Identity Coercion IdD'D : D' >-> D. -Print IdD'D. -Parameter d' : D' true. -Check (T d'). -Set Printing Coercions. -Check (T d'). -\end{coq_example} -%\end{small} - -\begin{coq_eval} -Unset Printing Coercions. -\end{coq_eval} - - - In the case of functional arguments, we use the monotonic rule of -sub-typing. Approximatively, to coerce $t:forall~x:A, B$ towards -$forall~x:A',B'$, one have to coerce $A'$ towards $A$ and $B$ towards -$B'$. An example is given below: - -%\begin{small} -\begin{coq_example} -Parameters (A B : Set) (h : A -> B). -Coercion h : A >-> B. -Parameter U : (A -> E true) -> nat. -Parameter t : B -> C 0. -Check (U t). -Set Printing Coercions. -Check (U t). -\end{coq_example} -%\end{small} - -\begin{coq_eval} -Unset Printing Coercions. -\end{coq_eval} - - Remark the changes in the result following the modification of the -previous example. - -%\begin{small} -\begin{coq_example} -Parameter U' : (C 0 -> B) -> nat. -Parameter t' : E true -> A. -Check (U' t'). -Set Printing Coercions. -Check (U' t'). -\end{coq_example} -%\end{small} - -\begin{coq_eval} -Unset Printing Coercions. -\end{coq_eval} - -\item An assumption $x:A$ when $A$ is not a type, is ill-typed. It is - replaced by $x:A'$ where $A'$ is the result of the application - to $A$ of the coercion path between the class of $A$ and {\tt - Sortclass} if it exists. This case occurs in the abstraction - $fun~ x:A => t$, universal quantification $forall~x:A, B$, - global variables and parameters of (co-)inductive definitions - and functions. In $forall~x:A, B$, such a coercion path may be - applied to $B$ also if necessary. - -%\begin{small} -\begin{coq_example} -Parameter Graph : Type. -Parameter Node : Graph -> Type. -Coercion Node : Graph >-> Sortclass. -Parameter G : Graph. -Parameter Arrows : G -> G -> Type. -Check Arrows. -Parameter fg : G -> G. -Check fg. -Set Printing Coercions. -Check fg. -\end{coq_example} -%\end{small} - -\begin{coq_eval} -Unset Printing Coercions. -\end{coq_eval} - -\item $f~a$ is ill-typed because $f:A$ is not a function. The term - $f$ is replaced by the term obtained by applying to $f$ the - coercion path between $A$ and {\tt Funclass} if it exists. - -%\begin{small} -\begin{coq_example} -Parameter bij : Set -> Set -> Set. -Parameter ap : forall A B:Set, bij A B -> A -> B. -Coercion ap : bij >-> Funclass. -Parameter b : bij nat nat. -Check (b 0). -Set Printing Coercions. -Check (b 0). -\end{coq_example} -%\end{small} - -\begin{coq_eval} -Unset Printing Coercions. -\end{coq_eval} - -Let us see the resulting graph of this session. - -%\begin{small} -\begin{coq_example} -Print Graph. -\end{coq_example} -%\end{small} - -\end{itemize} - - -%%% Local Variables: -%%% mode: latex -%%% TeX-master: "Reference-Manual" -%%% End: diff --git a/doc/refman/Extraction.tex b/doc/refman/Extraction.tex deleted file mode 100644 index cff7be3e9..000000000 --- a/doc/refman/Extraction.tex +++ /dev/null @@ -1,620 +0,0 @@ -\achapter{Extraction of programs in OCaml and Haskell} -%HEVEA\cutname{extraction.html} -\label{Extraction} -\aauthor{Jean-Christophe Filliâtre and Pierre Letouzey} -\index{Extraction} - -\noindent We present here the \Coq\ extraction commands, used to build certified -and relatively efficient functional programs, extracting them from -either \Coq\ functions or \Coq\ proofs of specifications. The -functional languages available as output are currently \ocaml{}, -\textsc{Haskell} and \textsc{Scheme}. In the following, ``ML'' will -be used (abusively) to refer to any of the three. - -%% \paragraph{Differences with old versions.} -%% The current extraction mechanism is new for version 7.0 of {\Coq}. -%% In particular, the \FW\ toplevel used as an intermediate step between -%% \Coq\ and ML has been withdrawn. It is also not possible -%% any more to import ML objects in this \FW\ toplevel. -%% The current mechanism also differs from -%% the one in previous versions of \Coq: there is no more -%% an explicit toplevel for the language (formerly called \textsc{Fml}). - -Before using any of the commands or options described in this chapter, -the extraction framework should first be loaded explicitly -via {\tt Require Extraction}, or via the more robust -{\tt From Coq Require Extraction}. -Note that in earlier versions of Coq, these commands and options were -directly available without any preliminary {\tt Require}. - -\begin{coq_example} -Require Extraction. -\end{coq_example} - -\asection{Generating ML code} -\comindex{Extraction} -\comindex{Recursive Extraction} -\comindex{Separate Extraction} -\comindex{Extraction Library} -\comindex{Recursive Extraction Library} - -The next two commands are meant to be used for rapid preview of -extraction. They both display extracted term(s) inside \Coq. - -\begin{description} -\item {\tt Extraction \qualid{}.} ~\par - Extraction of a constant or module in the \Coq\ toplevel. - -\item {\tt Recursive Extraction} \qualid$_1$ \dots\ \qualid$_n$. ~\par - Recursive extraction of all the globals (or modules) \qualid$_1$ \dots\ - \qualid$_n$ and all their dependencies in the \Coq\ toplevel. -\end{description} - -%% TODO error messages - -\noindent All the following commands produce real ML files. User can choose to produce -one monolithic file or one file per \Coq\ library. - -\begin{description} -\item {\tt Extraction "{\em file}"} - \qualid$_1$ \dots\ \qualid$_n$. ~\par - Recursive extraction of all the globals (or modules) \qualid$_1$ \dots\ - \qualid$_n$ and all their dependencies in one monolithic file {\em file}. - Global and local identifiers are renamed according to the chosen ML - language to fulfill its syntactic conventions, keeping original - names as much as possible. - -\item {\tt Extraction Library} \ident. ~\par - Extraction of the whole \Coq\ library {\tt\ident.v} to an ML module - {\tt\ident.ml}. In case of name clash, identifiers are here renamed - using prefixes \verb!coq_! or \verb!Coq_! to ensure a - session-independent renaming. - -\item {\tt Recursive Extraction Library} \ident. ~\par - Extraction of the \Coq\ library {\tt\ident.v} and all other modules - {\tt\ident.v} depends on. - -\item {\tt Separate Extraction} - \qualid$_1$ \dots\ \qualid$_n$. ~\par - Recursive extraction of all the globals (or modules) \qualid$_1$ \dots\ - \qualid$_n$ and all their dependencies, just as {\tt - Extraction "{\em file}"}, but instead of producing one monolithic - file, this command splits the produced code in separate ML files, one per - corresponding Coq {\tt .v} file. This command is hence quite similar - to {\tt Recursive Extraction Library}, except that only the needed - parts of Coq libraries are extracted instead of the whole. The - naming convention in case of name clash is the same one as - {\tt Extraction Library}: identifiers are here renamed - using prefixes \verb!coq_! or \verb!Coq_!. -\end{description} - -\noindent The following command is meant to help automatic testing of - the extraction, see for instance the {\tt test-suite} directory - in the \Coq\ sources. - -\begin{description} -\item {\tt Extraction TestCompile} \qualid$_1$ \dots\ \qualid$_n$. ~\par - All the globals (or modules) \qualid$_1$ \dots\ \qualid$_n$ and all - their dependencies are extracted to a temporary {\ocaml} file, just as in - {\tt Extraction "{\em file}"}. Then this temporary file and its - signature are compiled with the same {\ocaml} compiler used to built - \Coq. This command succeeds only if the extraction and the {\ocaml} - compilation succeed (and it fails if the current target language - of the extraction is not {\ocaml}). -\end{description} - -\asection{Extraction options} - -\asubsection{Setting the target language} -\comindex{Extraction Language} - -The ability to fix target language is the first and more important -of the extraction options. Default is {\ocaml}. -\begin{description} -\item {\tt Extraction Language OCaml}. -\item {\tt Extraction Language Haskell}. -\item {\tt Extraction Language Scheme}. -\end{description} - -\asubsection{Inlining and optimizations} - -Since {\ocaml} is a strict language, the extracted code has to -be optimized in order to be efficient (for instance, when using -induction principles we do not want to compute all the recursive calls -but only the needed ones). So the extraction mechanism provides an -automatic optimization routine that will be called each time the user -want to generate {\ocaml} programs. The optimizations can be split in two -groups: the type-preserving ones -- essentially constant inlining and -reductions -- and the non type-preserving ones -- some function -abstractions of dummy types are removed when it is deemed safe in order -to have more elegant types. Therefore some constants may not appear in the -resulting monolithic {\ocaml} program. In the case of modular extraction, -even if some inlining is done, the inlined constant are nevertheless -printed, to ensure session-independent programs. - -Concerning Haskell, type-preserving optimizations are less useful -because of laziness. We still make some optimizations, for example in -order to produce more readable code. - -The type-preserving optimizations are controlled by the following \Coq\ options: - -\begin{description} - -\item \optindex{Extraction Optimize} {\tt Unset Extraction Optimize.} - -Default is Set. This controls all type-preserving optimizations made on -the ML terms (mostly reduction of dummy beta/iota redexes, but also -simplifications on Cases, etc). Put this option to Unset if you want a -ML term as close as possible to the Coq term. - -\item \optindex{Extraction Conservative Types} -{\tt Set Extraction Conservative Types.} - -Default is Unset. This controls the non type-preserving optimizations -made on ML terms (which try to avoid function abstraction of dummy -types). Turn this option to Set to make sure that {\tt e:t} -implies that {\tt e':t'} where {\tt e'} and {\tt t'} are the extracted -code of {\tt e} and {\tt t} respectively. - -\item \optindex{Extraction KeepSingleton} -{\tt Set Extraction KeepSingleton.} - -Default is Unset. Normally, when the extraction of an inductive type -produces a singleton type (i.e. a type with only one constructor, and -only one argument to this constructor), the inductive structure is -removed and this type is seen as an alias to the inner type. -The typical example is {\tt sig}. This option allows disabling this -optimization when one wishes to preserve the inductive structure of types. - -\item \optindex{Extraction AutoInline} {\tt Unset Extraction AutoInline.} - -Default is Set. The extraction mechanism -inlines the bodies of some defined constants, according to some heuristics -like size of bodies, uselessness of some arguments, etc. Those heuristics are -not always perfect; if you want to disable this feature, do it by Unset. - -\item \comindex{Extraction Inline} \comindex{Extraction NoInline} -{\tt Extraction [Inline|NoInline] \qualid$_1$ \dots\ \qualid$_n$}. - -In addition to the automatic inline feature, you can tell to -inline some more constants by the {\tt Extraction Inline} command. Conversely, -you can forbid the automatic inlining of some specific constants by -the {\tt Extraction NoInline} command. -Those two commands enable a precise control of what is inlined and what is not. - -\item \comindex{Print Extraction Inline} -{\tt Print Extraction Inline}. - -Prints the current state of the table recording the custom inlinings -declared by the two previous commands. - -\item \comindex{Reset Extraction Inline} -{\tt Reset Extraction Inline}. - -Puts the table recording the custom inlinings back to empty. - -\end{description} - - -\paragraph{Inlining and printing of a constant declaration.} - -A user can explicitly ask for a constant to be extracted by two means: -\begin{itemize} -\item by mentioning it on the extraction command line -\item by extracting the whole \Coq\ module of this constant. -\end{itemize} -In both cases, the declaration of this constant will be present in the -produced file. -But this same constant may or may not be inlined in the following -terms, depending on the automatic/custom inlining mechanism. - - -For the constants non-explicitly required but needed for dependency -reasons, there are two cases: -\begin{itemize} -\item If an inlining decision is taken, whether automatically or not, -all occurrences of this constant are replaced by its extracted body, and -this constant is not declared in the generated file. -\item If no inlining decision is taken, the constant is normally - declared in the produced file. -\end{itemize} - -\asubsection{Extra elimination of useless arguments} - -The following command provides some extra manual control on the -code elimination performed during extraction, in a way which -is independent but complementary to the main elimination -principles of extraction (logical parts and types). - -\begin{description} -\item \comindex{Extraction Implicit} - {\tt Extraction Implicit} \qualid\ [ \ident$_1$ \dots\ \ident$_n$ ]. - -This experimental command allows declaring some arguments of -\qualid\ as implicit, i.e. useless in extracted code and hence to -be removed by extraction. Here \qualid\ can be any function or -inductive constructor, and \ident$_i$ are the names of the concerned -arguments. In fact, an argument can also be referred by a number -indicating its position, starting from 1. -\end{description} - -\noindent When an actual extraction takes place, an error is normally raised if the -{\tt Extraction Implicit} -declarations cannot be honored, that is if any of the implicited -variables still occurs in the final code. This behavior can be relaxed -via the following option: - -\begin{description} -\item \optindex{Extraction SafeImplicits} {\tt Unset Extraction SafeImplicits.} - -Default is Set. When this option is Unset, a warning is emitted -instead of an error if some implicited variables still occur in the -final code of an extraction. This way, the extracted code may be -obtained nonetheless and reviewed manually to locate the source of the issue -(in the code, some comments mark the location of these remaining -implicited variables). -Note that this extracted code might not compile or run properly, -depending of the use of these remaining implicited variables. - -\end{description} - -\asubsection{Realizing axioms}\label{extraction:axioms} - -Extraction will fail if it encounters an informative -axiom not realized (see Section~\ref{extraction:axioms}). -A warning will be issued if it encounters a logical axiom, to remind the -user that inconsistent logical axioms may lead to incorrect or -non-terminating extracted terms. - -It is possible to assume some axioms while developing a proof. Since -these axioms can be any kind of proposition or object or type, they may -perfectly well have some computational content. But a program must be -a closed term, and of course the system cannot guess the program which -realizes an axiom. Therefore, it is possible to tell the system -what ML term corresponds to a given axiom. - -\comindex{Extract Constant} -\begin{description} -\item{\tt Extract Constant \qualid\ => \str.} ~\par - Give an ML extraction for the given constant. - The \str\ may be an identifier or a quoted string. -\item{\tt Extract Inlined Constant \qualid\ => \str.} ~\par - Same as the previous one, except that the given ML terms will - be inlined everywhere instead of being declared via a let. -\end{description} - -\noindent Note that the {\tt Extract Inlined Constant} command is sugar -for an {\tt Extract Constant} followed by a {\tt Extraction Inline}. -Hence a {\tt Reset Extraction Inline} will have an effect on the -realized and inlined axiom. - -Of course, it is the responsibility of the user to ensure that the ML -terms given to realize the axioms do have the expected types. In -fact, the strings containing realizing code are just copied to the -extracted files. The extraction recognizes whether the realized axiom -should become a ML type constant or a ML object declaration. - -\Example -\begin{coq_example*} -Axiom X:Set. -Axiom x:X. -Extract Constant X => "int". -Extract Constant x => "0". -\end{coq_example*} - -\noindent Notice that in the case of type scheme axiom (i.e. whose type is an -arity, that is a sequence of product finished by a sort), then some type -variables have to be given. The syntax is then: - -\begin{description} -\item{\tt Extract Constant \qualid\ \str$_1$ \dots\ \str$_n$ => \str.} -\end{description} - -\noindent The number of type variables is checked by the system. - -\Example -\begin{coq_example*} -Axiom Y : Set -> Set -> Set. -Extract Constant Y "'a" "'b" => " 'a*'b ". -\end{coq_example*} - -\noindent Realizing an axiom via {\tt Extract Constant} is only useful in the -case of an informative axiom (of sort Type or Set). A logical axiom -have no computational content and hence will not appears in extracted -terms. But a warning is nonetheless issued if extraction encounters a -logical axiom. This warning reminds user that inconsistent logical -axioms may lead to incorrect or non-terminating extracted terms. - -If an informative axiom has not been realized before an extraction, a -warning is also issued and the definition of the axiom is filled with -an exception labeled {\tt AXIOM TO BE REALIZED}. The user must then -search these exceptions inside the extracted file and replace them by -real code. - -\comindex{Extract Inductive} - -The system also provides a mechanism to specify ML terms for inductive -types and constructors. For instance, the user may want to use the ML -native boolean type instead of \Coq\ one. The syntax is the following: - -\begin{description} -\item{\tt Extract Inductive \qualid\ => \str\ [ \str\ \dots\ \str\ ] {\it optstring}.}\par - Give an ML extraction for the given inductive type. You must specify - extractions for the type itself (first \str) and all its - constructors (between square brackets). If given, the final optional - string should contain a function emulating pattern-matching over this - inductive type. If this optional string is not given, the ML - extraction must be an ML inductive datatype, and the native - pattern-matching of the language will be used. -\end{description} - -\noindent For an inductive type with $k$ constructor, the function used to -emulate the match should expect $(k+1)$ arguments, first the $k$ -branches in functional form, and then the inductive element to -destruct. For instance, the match branch \verb$| S n => foo$ gives the -functional form \verb$(fun n -> foo)$. Note that a constructor with no -argument is considered to have one unit argument, in order to block -early evaluation of the branch: \verb$| O => bar$ leads to the functional -form \verb$(fun () -> bar)$. For instance, when extracting {\tt nat} -into {\tt int}, the code to provide has type: -{\tt (unit->'a)->(int->'a)->int->'a}. - -As for {\tt Extract Inductive}, this command should be used with care: -\begin{itemize} -\item The ML code provided by the user is currently \emph{not} checked at all by - extraction, even for syntax errors. - -\item Extracting an inductive type to a pre-existing ML inductive type -is quite sound. But extracting to a general type (by providing an -ad-hoc pattern-matching) will often \emph{not} be fully rigorously -correct. For instance, when extracting {\tt nat} to {\ocaml}'s {\tt -int}, it is theoretically possible to build {\tt nat} values that are -larger than {\ocaml}'s {\tt max\_int}. It is the user's responsibility to -be sure that no overflow or other bad events occur in practice. - -\item Translating an inductive type to an ML type does \emph{not} -magically improve the asymptotic complexity of functions, even if the -ML type is an efficient representation. For instance, when extracting -{\tt nat} to {\ocaml}'s {\tt int}, the function {\tt mult} stays -quadratic. It might be interesting to associate this translation with -some specific {\tt Extract Constant} when primitive counterparts exist. -\end{itemize} - -\Example -Typical examples are the following: -\begin{coq_eval} -Require Extraction. -\end{coq_eval} -\begin{coq_example} -Extract Inductive unit => "unit" [ "()" ]. -Extract Inductive bool => "bool" [ "true" "false" ]. -Extract Inductive sumbool => "bool" [ "true" "false" ]. -\end{coq_example} - -\noindent When extracting to {\ocaml}, if an inductive constructor or type -has arity 2 and the corresponding string is enclosed by parentheses, -and the string meets {\ocaml}'s lexical criteria for an infix symbol, -then the rest of the string is used as infix constructor or type. - -\begin{coq_example} -Extract Inductive list => "list" [ "[]" "(::)" ]. -Extract Inductive prod => "(*)" [ "(,)" ]. -\end{coq_example} - -\noindent As an example of translation to a non-inductive datatype, let's turn -{\tt nat} into {\ocaml}'s {\tt int} (see caveat above): -\begin{coq_example} -Extract Inductive nat => int [ "0" "succ" ] - "(fun fO fS n -> if n=0 then fO () else fS (n-1))". -\end{coq_example} - -\asubsection{Avoiding conflicts with existing filenames} - -\comindex{Extraction Blacklist} - -When using {\tt Extraction Library}, the names of the extracted files -directly depends from the names of the \Coq\ files. It may happen that -these filenames are in conflict with already existing files, -either in the standard library of the target language or in other -code that is meant to be linked with the extracted code. -For instance the module {\tt List} exists both in \Coq\ and in {\ocaml}. -It is possible to instruct the extraction not to use particular filenames. - -\begin{description} -\item{\tt Extraction Blacklist} \ident\ \dots\ \ident. ~\par - Instruct the extraction to avoid using these names as filenames - for extracted code. -\item{\tt Print Extraction Blacklist.} ~\par - Show the current list of filenames the extraction should avoid. -\item{\tt Reset Extraction Blacklist.} ~\par - Allow the extraction to use any filename. -\end{description} - -\noindent For {\ocaml}, a typical use of these commands is -{\tt Extraction Blacklist String List}. - -\asection{Differences between \Coq\ and ML type systems} - - -Due to differences between \Coq\ and ML type systems, -some extracted programs are not directly typable in ML. -We now solve this problem (at least in {\ocaml}) by adding -when needed some unsafe casting {\tt Obj.magic}, which give -a generic type {\tt 'a} to any term. - -For example, here are two kinds of problem that can occur: - -\begin{itemize} - \item If some part of the program is {\em very} polymorphic, there - may be no ML type for it. In that case the extraction to ML works - alright but the generated code may be refused by the ML - type-checker. A very well known example is the {\em distr-pair} - function: -\begin{verbatim} -Definition dp := - fun (A B:Set)(x:A)(y:B)(f:forall C:Set, C->C) => (f A x, f B y). -\end{verbatim} - -In {\ocaml}, for instance, the direct extracted term would be -\begin{verbatim} -let dp x y f = Pair((f () x),(f () y)) -\end{verbatim} - -and would have type -\begin{verbatim} -dp : 'a -> 'a -> (unit -> 'a -> 'b) -> ('b,'b) prod -\end{verbatim} - -which is not its original type, but a restriction. - -We now produce the following correct version: -\begin{verbatim} -let dp x y f = Pair ((Obj.magic f () x), (Obj.magic f () y)) -\end{verbatim} - - \item Some definitions of \Coq\ may have no counterpart in ML. This - happens when there is a quantification over types inside the type - of a constructor; for example: -\begin{verbatim} -Inductive anything : Type := dummy : forall A:Set, A -> anything. -\end{verbatim} - -which corresponds to the definition of an ML dynamic type. -In {\ocaml}, we must cast any argument of the constructor dummy. - -\end{itemize} - -\noindent Even with those unsafe castings, you should never get error like -``segmentation fault''. In fact even if your program may seem -ill-typed to the {\ocaml} type-checker, it can't go wrong: it comes -from a Coq well-typed terms, so for example inductives will always -have the correct number of arguments, etc. - -More details about the correctness of the extracted programs can be -found in \cite{Let02}. - -We have to say, though, that in most ``realistic'' programs, these -problems do not occur. For example all the programs of Coq library are -accepted by Caml type-checker without any {\tt Obj.magic} (see examples below). - - - -\asection{Some examples} - -We present here two examples of extractions, taken from the -\Coq\ Standard Library. We choose \ocaml\ as target language, -but all can be done in the other dialects with slight modifications. -We then indicate where to find other examples and tests of Extraction. - -\asubsection{A detailed example: Euclidean division} - -The file {\tt Euclid} contains the proof of Euclidean division -(theorem {\tt eucl\_dev}). The natural numbers defined in the example -files are unary integers defined by two constructors $O$ and $S$: -\begin{coq_example*} -Inductive nat : Set := - | O : nat - | S : nat -> nat. -\end{coq_example*} - -\noindent This module contains a theorem {\tt eucl\_dev}, whose type is -\begin{verbatim} -forall b:nat, b > 0 -> forall a:nat, diveucl a b -\end{verbatim} -where {\tt diveucl} is a type for the pair of the quotient and the -modulo, plus some logical assertions that disappear during extraction. -We can now extract this program to \ocaml: - -\begin{coq_eval} -Reset Initial. -\end{coq_eval} -\begin{coq_example} -Require Extraction. -Require Import Euclid Wf_nat. -Extraction Inline gt_wf_rec lt_wf_rec induction_ltof2. -Recursive Extraction eucl_dev. -\end{coq_example} - -\noindent The inlining of {\tt gt\_wf\_rec} and others is not -mandatory. It only enhances readability of extracted code. -You can then copy-paste the output to a file {\tt euclid.ml} or let -\Coq\ do it for you with the following command: - -\begin{verbatim} -Extraction "euclid" eucl_dev. -\end{verbatim} - -\noindent Let us play the resulting program: - -\begin{verbatim} -# #use "euclid.ml";; -type nat = O | S of nat -type sumbool = Left | Right -val minus : nat -> nat -> nat = <fun> -val le_lt_dec : nat -> nat -> sumbool = <fun> -val le_gt_dec : nat -> nat -> sumbool = <fun> -type diveucl = Divex of nat * nat -val eucl_dev : nat -> nat -> diveucl = <fun> -# eucl_dev (S (S O)) (S (S (S (S (S O)))));; -- : diveucl = Divex (S (S O), S O) -\end{verbatim} -It is easier to test on \ocaml\ integers: -\begin{verbatim} -# let rec nat_of_int = function 0 -> O | n -> S (nat_of_int (n-1));; -val nat_of_int : int -> nat = <fun> -# let rec int_of_nat = function O -> 0 | S p -> 1+(int_of_nat p);; -val int_of_nat : nat -> int = <fun> -# let div a b = - let Divex (q,r) = eucl_dev (nat_of_int b) (nat_of_int a) - in (int_of_nat q, int_of_nat r);; -val div : int -> int -> int * int = <fun> -# div 173 15;; -- : int * int = (11, 8) -\end{verbatim} - -\noindent Note that these {\tt nat\_of\_int} and {\tt int\_of\_nat} are now -available via a mere {\tt Require Import ExtrOcamlIntConv} and then -adding these functions to the list of functions to extract. This file -{\tt ExtrOcamlIntConv.v} and some others in {\tt plugins/extraction/} -are meant to help building concrete program via extraction. - -\asubsection{Extraction's horror museum} - -Some pathological examples of extraction are grouped in the file\\ -{\tt test-suite/success/extraction.v} of the sources of \Coq. - -\asubsection{Users' Contributions} - -Several of the \Coq\ Users' Contributions use extraction to produce -certified programs. In particular the following ones have an automatic -extraction test: - -\begin{itemize} -\item {\tt additions} -\item {\tt bdds} -\item {\tt canon-bdds} -\item {\tt chinese} -\item {\tt continuations} -\item {\tt coq-in-coq} -\item {\tt exceptions} -\item {\tt firing-squad} -\item {\tt founify} -\item {\tt graphs} -\item {\tt higman-cf} -\item {\tt higman-nw} -\item {\tt hardware} -\item {\tt multiplier} -\item {\tt search-trees} -\item {\tt stalmarck} -\end{itemize} - -\noindent {\tt continuations} and {\tt multiplier} are a bit particular. They are -examples of developments where {\tt Obj.magic} are needed. This is -probably due to an heavy use of impredicativity. After compilation, those -two examples run nonetheless, thanks to the correction of the -extraction~\cite{Let02}. - -%%% Local Variables: -%%% mode: latex -%%% TeX-master: "Reference-Manual" -%%% End: diff --git a/doc/refman/Misc.tex b/doc/refman/Misc.tex deleted file mode 100644 index ab00fbfe3..000000000 --- a/doc/refman/Misc.tex +++ /dev/null @@ -1,63 +0,0 @@ -\achapter{\protect{Miscellaneous extensions}} -%HEVEA\cutname{miscellaneous.html} - -\asection{Program derivation} - -Coq comes with an extension called {\tt Derive}, which supports -program derivation. Typically in the style of Bird and Meertens or -derivations of program refinements. To use the {\tt Derive} extension -it must first be required with {\tt Require Coq.Derive.Derive}. When -the extension is loaded, it provides the following command. - -\subsection[\tt Derive \ident$_1$ SuchThat \term{} As \ident$_2$] - {\tt Derive \ident$_1$ SuchThat \term{} As \ident$_2$\comindex{Derive}} - -The name $\ident_1$ can appear in \term. This command opens a new -proof presenting the user with a goal for \term{} in which the name -$\ident_1$ is bound to a existential variables {\tt ?x} (formally, -there are other goals standing for the existential variables but they -are shelved, as described in Section~\ref{shelve}). - -When the proof ends two constants are defined: -\begin{itemize} -\item The first one is name $\ident_1$ and is defined as the proof of - the shelved goal (which is also the value of {\tt ?x}). It is -always transparent. -\item The second one is name $\ident_2$. It has type {\tt \term}, and - its body is the proof of the initially visible goal. It is opaque if - the proof ends with {\tt Qed}, and transparent if the proof ends - with {\tt Defined}. -\end{itemize} - -\Example -\begin{coq_example*} -Require Coq.derive.Derive. -Require Import Coq.Numbers.Natural.Peano.NPeano. - -Section P. - -Variables (n m k:nat). - -\end{coq_example*} -\begin{coq_example} -Derive p SuchThat ((k*n)+(k*m) = p) As h. -Proof. -rewrite <- Nat.mul_add_distr_l. -subst p. -reflexivity. -\end{coq_example} -\begin{coq_example*} -Qed. - -End P. - -\end{coq_example*} -\begin{coq_example} -Print p. -Check h. -\end{coq_example} - -Any property can be used as \term, not only an equation. In -particular, it could be an order relation specifying some form of -program refinement or a non-executable property from which deriving a -program is convenient. diff --git a/doc/refman/Nsatz.tex b/doc/refman/Nsatz.tex deleted file mode 100644 index 1401af10f..000000000 --- a/doc/refman/Nsatz.tex +++ /dev/null @@ -1,102 +0,0 @@ -\achapter{Nsatz: tactics for proving equalities in integral domains} -%HEVEA\cutname{nsatz.html} -\aauthor{Loïc Pottier} - -The tactic \texttt{nsatz} proves goals of the form - -\[ \begin{array}{l} - \forall X_1,\ldots,X_n \in A,\\ - P_1(X_1,\ldots,X_n) = Q_1(X_1,\ldots,X_n) , \ldots , P_s(X_1,\ldots,X_n) =Q_s(X_1,\ldots,X_n)\\ - \vdash P(X_1,\ldots,X_n) = Q(X_1,\ldots,X_n)\\ - \end{array} -\] -where $P,Q, P_1,Q_1,\ldots,P_s,Q_s$ are polynomials and A is an integral -domain, i.e. a commutative ring with no zero divisor. For example, A can be -$\mathbb{R}$, $\mathbb{Z}$, of $\mathbb{Q}$. Note that the equality $=$ used in these -goals can be any setoid equality -(see \ref{setoidtactics}) -, not only Leibnitz equality. - -It also proves formulas -\[ \begin{array}{l} - \forall X_1,\ldots,X_n \in A,\\ - P_1(X_1,\ldots,X_n) = Q_1(X_1,\ldots,X_n) \wedge \ldots \wedge P_s(X_1,\ldots,X_n) =Q_s(X_1,\ldots,X_n)\\ - \rightarrow P(X_1,\ldots,X_n) = Q(X_1,\ldots,X_n)\\ - \end{array} -\] doing automatic introductions. - -\asection{Using the basic tactic \texttt{nsatz}} -\tacindex{nsatz} - -Load the -\texttt{Nsatz} module: \texttt{Require Import Nsatz}.\\ - and use the tactic \texttt{nsatz}. - -\asection{More about \texttt{nsatz}} - -Hilbert's Nullstellensatz theorem shows how to reduce proofs of equalities on -polynomials on a commutative ring A with no zero divisor to algebraic computations: it is easy to see that if a polynomial -$P$ in $A[X_1,\ldots,X_n]$ verifies $c P^r = \sum_{i=1}^{s} S_i P_i$, with $c -\in A$, $c \not = 0$, $r$ a positive integer, and the $S_i$s in -$A[X_1,\ldots,X_n]$, then $P$ is zero whenever polynomials $P_1,...,P_s$ are -zero (the converse is also true when A is an algebraic closed field: -the method is complete). - -So, proving our initial problem can reduce into finding $S_1,\ldots,S_s$, $c$ -and $r$ such that $c (P-Q)^r = \sum_{i} S_i (P_i-Q_i)$, which will be proved by the -tactic \texttt{ring}. - -This is achieved by the computation of a Groebner basis of the -ideal generated by $P_1-Q_1,...,P_s-Q_s$, with an adapted version of the Buchberger -algorithm. - -This computation is done after a step of {\em reification}, which is -performed using {\em Type Classes} -(see \ref{typeclasses}) -. - -The \texttt{Nsatz} module defines the tactic -\texttt{nsatz}, which can be used without arguments: \\ -\vspace*{3mm} -\texttt{nsatz}\\ -or with the syntax: \\ -\vspace*{3mm} -\texttt{nsatz with radicalmax:={\em number}\%N strategy:={\em number}\%Z parameters:={\em list of variables} variables:={\em list of variables}}\\ -where: - -\begin{itemize} - \item \texttt{radicalmax} is a bound when for searching r s.t.$c (P-Q)^r = -\sum_{i=1..s} S_i (P_i - Q_i)$ - - \item \texttt{strategy} gives the order on variables $X_1,...X_n$ and -the strategy used in Buchberger algorithm (see -\cite{sugar} for details): - - \begin{itemize} - \item strategy = 0: reverse lexicographic order and newest s-polynomial. - \item strategy = 1: reverse lexicographic order and sugar strategy. - \item strategy = 2: pure lexicographic order and newest s-polynomial. - \item strategy = 3: pure lexicographic order and sugar strategy. - \end{itemize} - - \item \texttt{parameters} is the list of variables -$X_{i_1},\ldots,X_{i_k}$ among $X_1,...,X_n$ which are considered as - parameters: computation will be performed with rational fractions in these - variables, i.e. polynomials are considered with coefficients in -$R(X_{i_1},\ldots,X_{i_k})$. In this case, the coefficient $c$ can be a non -constant polynomial in $X_{i_1},\ldots,X_{i_k}$, and the tactic produces a goal -which states that $c$ is not zero. - - \item \texttt{variables} is the list of the variables -in the decreasing order in which they will be used in Buchberger algorithm. If \texttt{variables} = {(@nil -R)}, then \texttt{lvar} is replaced by all the variables which are not in -parameters. - -\end{itemize} - -See file \texttt{Nsatz.v} for many examples, specially in geometry. - -%%% Local Variables: -%%% mode: latex -%%% TeX-master: "Reference-Manual" -%%% End: diff --git a/doc/refman/Polynom.tex b/doc/refman/Polynom.tex deleted file mode 100644 index d9b8b8c52..000000000 --- a/doc/refman/Polynom.tex +++ /dev/null @@ -1,736 +0,0 @@ -\achapter{The \texttt{ring} and \texttt{field} tactic families} -%HEVEA\cutname{ring.html} -\aauthor{Bruno Barras, Benjamin Gr\'egoire, Assia - Mahboubi, Laurent Th\'ery\footnote{based on previous work from - Patrick Loiseleur and Samuel Boutin}} -\label{ring} -\tacindex{ring} - -This chapter presents the tactics dedicated to deal with ring and -field equations. - -\asection{What does this tactic do?} - -\texttt{ring} does associative-commutative rewriting in ring and semi-ring -structures. Assume you have two binary functions $\oplus$ and $\otimes$ -that are associative and commutative, with $\oplus$ distributive on -$\otimes$, and two constants 0 and 1 that are unities for $\oplus$ and -$\otimes$. A \textit{polynomial} is an expression built on variables $V_0, V_1, -\dots$ and constants by application of $\oplus$ and $\otimes$. - -Let an {\it ordered product} be a product of variables $V_{i_1} -\otimes \ldots \otimes V_{i_n}$ verifying $i_1 \le i_2 \le \dots \le -i_n$. Let a \textit{monomial} be the product of a constant and an -ordered product. We can order the monomials by the lexicographic -order on products of variables. Let a \textit{canonical sum} be an -ordered sum of monomials that are all different, i.e. each monomial in -the sum is strictly less than the following monomial according to the -lexicographic order. It is an easy theorem to show that every -polynomial is equivalent (modulo the ring properties) to exactly one -canonical sum. This canonical sum is called the \textit{normal form} -of the polynomial. In fact, the actual representation shares monomials -with same prefixes. So what does \texttt{ring}? It normalizes -polynomials over any ring or semi-ring structure. The basic use of -\texttt{ring} is to simplify ring expressions, so that the user does -not have to deal manually with the theorems of associativity and -commutativity. - -\begin{Examples} -\item In the ring of integers, the normal form of -$x (3 + yx + 25(1 - z)) + zx$ is $28x + (-24)xz + xxy$. -\end{Examples} - -\texttt{ring} is also able to compute a normal form modulo monomial -equalities. For example, under the hypothesis that $2x^2 = yz+1$, - the normal form of $2(x + 1)x - x - zy$ is $x+1$. - -\asection{The variables map} - -It is frequent to have an expression built with + and - $\times$, but rarely on variables only. -Let us associate a number to each subterm of a ring -expression in the \gallina\ language. For example in the ring -\texttt{nat}, consider the expression: - -\begin{quotation} -\begin{verbatim} -(plus (mult (plus (f (5)) x) x) - (mult (if b then (4) else (f (3))) (2))) -\end{verbatim} -\end{quotation} - -\noindent As a ring expression, it has 3 subterms. Give each subterm a -number in an arbitrary order: - -\begin{tabular}{ccl} -0 & $\mapsto$ & \verb|if b then (4) else (f (3))| \\ -1 & $\mapsto$ & \verb|(f (5))| \\ -2 & $\mapsto$ & \verb|x| \\ -\end{tabular} - -\noindent Then normalize the ``abstract'' polynomial - -$$((V_1 \otimes V_2) \oplus V_2) \oplus (V_0 \otimes 2) $$ - -\noindent In our example the normal form is: - -$$(2 \otimes V_0) \oplus (V_1 \otimes V_2) \oplus (V_2 \otimes V_2)$$ - -\noindent Then substitute the variables by their values in the variables map to -get the concrete normal polynomial: - -\begin{quotation} -\begin{verbatim} -(plus (mult (2) (if b then (4) else (f (3)))) - (plus (mult (f (5)) x) (mult x x))) -\end{verbatim} -\end{quotation} - -\asection{Is it automatic?} - -Yes, building the variables map and doing the substitution after -normalizing is automatically done by the tactic. So you can just forget -this paragraph and use the tactic according to your intuition. - -\asection{Concrete usage in \Coq -\tacindex{ring} -\tacindex{ring\_simplify}} - -The {\tt ring} tactic solves equations upon polynomial expressions of -a ring (or semi-ring) structure. It proceeds by normalizing both hand -sides of the equation (w.r.t. associativity, commutativity and -distributivity, constant propagation, rewriting of monomials) -and comparing syntactically the results. - -{\tt ring\_simplify} applies the normalization procedure described -above to the terms given. The tactic then replaces all occurrences of -the terms given in the conclusion of the goal by their normal -forms. If no term is given, then the conclusion should be an equation -and both hand sides are normalized. -The tactic can also be applied in a hypothesis. - -The tactic must be loaded by \texttt{Require Import Ring}. The ring -structures must be declared with the \texttt{Add Ring} command (see -below). The ring of booleans is predefined; if one wants to use the -tactic on \texttt{nat} one must first require the module -\texttt{ArithRing} (exported by \texttt{Arith}); -for \texttt{Z}, do \texttt{Require Import -ZArithRing} or simply \texttt{Require Import ZArith}; -for \texttt{N}, do \texttt{Require Import NArithRing} or -\texttt{Require Import NArith}. - -\Example -\begin{coq_eval} -Reset Initial. -\end{coq_eval} -\begin{coq_example*} -Require Import ZArith. -\end{coq_example*} -\begin{coq_example} -Open Scope Z_scope. -Goal forall a b c:Z, - (a + b + c)^2 = - a * a + b^2 + c * c + 2 * a * b + 2 * a * c + 2 * b * c. -\end{coq_example} -\begin{coq_example} -intros; ring. -\end{coq_example} -\begin{coq_eval} -Abort. -\end{coq_eval} -\begin{coq_example} -Goal forall a b:Z, 2*a*b = 30 -> - (a+b)^2 = a^2 + b^2 + 30. -\end{coq_example} -\begin{coq_example} -intros a b H; ring [H]. -\end{coq_example} -\begin{coq_eval} -Reset Initial. -\end{coq_eval} - -\begin{Variants} - \item {\tt ring [\term$_1$ {\ldots} \term$_n$]} decides the equality of two - terms modulo ring operations and rewriting of the equalities - defined by \term$_1$ {\ldots} \term$_n$. Each of \term$_1$ - {\ldots} \term$_n$ has to be a proof of some equality $m = p$, - where $m$ is a monomial (after ``abstraction''), - $p$ a polynomial and $=$ the corresponding equality of the ring structure. - - \item {\tt ring\_simplify [\term$_1$ {\ldots} \term$_n$] $t_1 \ldots t_m$ in -{\ident}} - performs the simplification in the hypothesis named {\tt ident}. -\end{Variants} - -\Warning \texttt{ring\_simplify \term$_1$; ring\_simplify \term$_2$} is -not equivalent to \texttt{ring\_simplify \term$_1$ \term$_2$}. In the -latter case the variables map is shared between the two terms, and -common subterm $t$ of \term$_1$ and \term$_2$ will have the same -associated variable number. So the first alternative should be -avoided for terms belonging to the same ring theory. - - -\begin{ErrMsgs} -\item \errindex{not a valid ring equation} - The conclusion of the goal is not provable in the corresponding ring - theory. -\item \errindex{arguments of ring\_simplify do not have all the same type} - {\tt ring\_simplify} cannot simplify terms of several rings at the - same time. Invoke the tactic once per ring structure. -\item \errindex{cannot find a declared ring structure over {\tt term}} - No ring has been declared for the type of the terms to be - simplified. Use {\tt Add Ring} first. -\item \errindex{cannot find a declared ring structure for equality - {\tt term}} - Same as above is the case of the {\tt ring} tactic. -\end{ErrMsgs} - -\asection{Adding a ring structure -\comindex{Add Ring}} - -Declaring a new ring consists in proving that a ring signature (a -carrier set, an equality, and ring operations: {\tt -Ring\_theory.ring\_theory} and {\tt Ring\_theory.semi\_ring\_theory}) -satisfies the ring axioms. Semi-rings (rings without $+$ inverse) are -also supported. The equality can be either Leibniz equality, or any -relation declared as a setoid (see~\ref{setoidtactics}). The definition -of ring and semi-rings (see module {\tt Ring\_theory}) is: -\begin{verbatim} -Record ring_theory : Prop := mk_rt { - Radd_0_l : forall x, 0 + x == x; - Radd_sym : forall x y, x + y == y + x; - Radd_assoc : forall x y z, x + (y + z) == (x + y) + z; - Rmul_1_l : forall x, 1 * x == x; - Rmul_sym : forall x y, x * y == y * x; - Rmul_assoc : forall x y z, x * (y * z) == (x * y) * z; - Rdistr_l : forall x y z, (x + y) * z == (x * z) + (y * z); - Rsub_def : forall x y, x - y == x + -y; - Ropp_def : forall x, x + (- x) == 0 -}. - -Record semi_ring_theory : Prop := mk_srt { - SRadd_0_l : forall n, 0 + n == n; - SRadd_sym : forall n m, n + m == m + n ; - SRadd_assoc : forall n m p, n + (m + p) == (n + m) + p; - SRmul_1_l : forall n, 1*n == n; - SRmul_0_l : forall n, 0*n == 0; - SRmul_sym : forall n m, n*m == m*n; - SRmul_assoc : forall n m p, n*(m*p) == (n*m)*p; - SRdistr_l : forall n m p, (n + m)*p == n*p + m*p -}. -\end{verbatim} - -This implementation of {\tt ring} also features a notion of constant -that can be parameterized. This can be used to improve the handling of -closed expressions when operations are effective. It consists in -introducing a type of \emph{coefficients} and an implementation of the -ring operations, and a morphism from the coefficient type to the ring -carrier type. The morphism needs not be injective, nor surjective. - -As -an example, one can consider the real numbers. The set of coefficients -could be the rational numbers, upon which the ring operations can be -implemented. The fact that there exists a morphism is defined by the -following properties: -\begin{verbatim} -Record ring_morph : Prop := mkmorph { - morph0 : [cO] == 0; - morph1 : [cI] == 1; - morph_add : forall x y, [x +! y] == [x]+[y]; - morph_sub : forall x y, [x -! y] == [x]-[y]; - morph_mul : forall x y, [x *! y] == [x]*[y]; - morph_opp : forall x, [-!x] == -[x]; - morph_eq : forall x y, x?=!y = true -> [x] == [y] -}. - -Record semi_morph : Prop := mkRmorph { - Smorph0 : [cO] == 0; - Smorph1 : [cI] == 1; - Smorph_add : forall x y, [x +! y] == [x]+[y]; - Smorph_mul : forall x y, [x *! y] == [x]*[y]; - Smorph_eq : forall x y, x?=!y = true -> [x] == [y] -}. -\end{verbatim} -where {\tt c0} and {\tt cI} denote the 0 and 1 of the coefficient set, -{\tt +!}, {\tt *!}, {\tt -!} are the implementations of the ring -operations, {\tt ==} is the equality of the coefficients, {\tt ?+!} is -an implementation of this equality, and {\tt [x]} is a notation for -the image of {\tt x} by the ring morphism. - - - -Since {\tt Z} is an initial ring (and {\tt N} is an initial -semi-ring), it can always be considered as a set of -coefficients. There are basically three kinds of (semi-)rings: -\begin{description} -\item[abstract rings] to be used when operations are not - effective. The set of coefficients is {\tt Z} (or {\tt N} for - semi-rings). -\item[computational rings] to be used when operations are - effective. The set of coefficients is the ring itself. The user only - has to provide an implementation for the equality. -\item[customized ring] for other cases. The user has to provide the - coefficient set and the morphism. -\end{description} - -This implementation of ring can also recognize simple -power expressions as ring expressions. A power function is specified by -the following property: -\begin{verbatim} -Section POWER. - Variable Cpow : Set. - Variable Cp_phi : N -> Cpow. - Variable rpow : R -> Cpow -> R. - - Record power_theory : Prop := mkpow_th { - rpow_pow_N : forall r n, req (rpow r (Cp_phi n)) (pow_N rI rmul r n) - }. - -End POWER. -\end{verbatim} - - -The syntax for adding a new ring is {\tt Add Ring $name$ : $ring$ -($mod_1$,\dots,$mod_2$)}. The name is not relevant. It is just used -for error messages. The term $ring$ is a proof that the ring signature -satisfies the (semi-)ring axioms. The optional list of modifiers is -used to tailor the behavior of the tactic. The following list -describes their syntax and effects: -\begin{description} -\item[abstract] declares the ring as abstract. This is the default. -\item[decidable \term] declares the ring as computational. The expression - \term{} is - the correctness proof of an equality test {\tt ?=!} (which should be - evaluable). Its type should be of - the form {\tt forall x y, x?=!y = true $\rightarrow$ x == y}. -\item[morphism \term] declares the ring as a customized one. The expression - \term{} is - a proof that there exists a morphism between a set of coefficient - and the ring carrier (see {\tt Ring\_theory.ring\_morph} and {\tt - Ring\_theory.semi\_morph}). -\item[setoid \term$_1$ \term$_2$] forces the use of given setoid. The - expression \term$_1$ is a proof that the equality is indeed a setoid - (see {\tt Setoid.Setoid\_Theory}), and \term$_2$ a proof that the - ring operations are morphisms (see {\tt Ring\_theory.ring\_eq\_ext} and - {\tt Ring\_theory.sring\_eq\_ext}). This modifier needs not be used if the - setoid and morphisms have been declared. -\item[constants [\ltac]] specifies a tactic expression that, given a term, - returns either an object of the coefficient set that is mapped to - the expression via the morphism, or returns {\tt - InitialRing.NotConstant}. The default behavior is to map only 0 and - 1 to their counterpart in the coefficient set. This is generally not - desirable for non trivial computational rings. -\item[preprocess [\ltac]] - specifies a tactic that is applied as a preliminary step for {\tt - ring} and {\tt ring\_simplify}. It can be used to transform a goal - so that it is better recognized. For instance, {\tt S n} can be - changed to {\tt plus 1 n}. -\item[postprocess [\ltac]] specifies a tactic that is applied as a final step - for {\tt ring\_simplify}. For instance, it can be used to undo - modifications of the preprocessor. -\item[power\_tac {\term} [\ltac]] allows {\tt ring} and {\tt ring\_simplify} to - recognize power expressions with a constant positive integer exponent - (example: $x^2$). The term {\term} is a proof that a given power function - satisfies the specification of a power function ({\term} has to be a - proof of {\tt Ring\_theory.power\_theory}) and {\ltac} specifies a - tactic expression that, given a term, ``abstracts'' it into an - object of type {\tt N} whose interpretation via {\tt Cp\_phi} (the - evaluation function of power coefficient) is the original term, or - returns {\tt InitialRing.NotConstant} if not a constant coefficient - (i.e. {\ltac} is the inverse function of {\tt Cp\_phi}). - See files {\tt plugins/setoid\_ring/ZArithRing.v} and - {\tt plugins/setoid\_ring/RealField.v} for examples. - By default the tactic does not recognize power expressions as ring - expressions. -\item[sign {\term}] allows {\tt ring\_simplify} to use a minus operation - when outputting its normal form, i.e writing $x - y$ instead of $x + (-y)$. - The term {\term} is a proof that a given sign function indicates expressions - that are signed ({\term} has to be a - proof of {\tt Ring\_theory.get\_sign}). See {\tt plugins/setoid\_ring/InitialRing.v} for examples of sign function. -\item[div {\term}] allows {\tt ring} and {\tt ring\_simplify} to use monomials -with coefficient other than 1 in the rewriting. The term {\term} is a proof that a given division function satisfies the specification of an euclidean - division function ({\term} has to be a - proof of {\tt Ring\_theory.div\_theory}). For example, this function is - called when trying to rewrite $7x$ by $2x = z$ to tell that $7 = 3 * 2 + 1$. - See {\tt plugins/setoid\_ring/InitialRing.v} for examples of div function. - -\end{description} - - -\begin{ErrMsgs} -\item \errindex{bad ring structure} - The proof of the ring structure provided is not of the expected type. -\item \errindex{bad lemma for decidability of equality} - The equality function provided in the case of a computational ring - has not the expected type. -\item \errindex{ring {\it operation} should be declared as a morphism} - A setoid associated to the carrier of the ring structure as been - found, but the ring operation should be declared as - morphism. See~\ref{setoidtactics}. -\end{ErrMsgs} - -\asection{How does it work?} - -The code of \texttt{ring} is a good example of tactic written using -\textit{reflection}. What is reflection? Basically, it is writing -\Coq{} tactics in \Coq, rather than in \ocaml. From the philosophical -point of view, it is using the ability of the Calculus of -Constructions to speak and reason about itself. For the \texttt{ring} -tactic we used \Coq\ as a programming language and also as a proof -environment to build a tactic and to prove it correctness. - -The interested reader is strongly advised to have a look at the file -\texttt{Ring\_polynom.v}. Here a type for polynomials is defined: - -\begin{small} -\begin{flushleft} -\begin{verbatim} -Inductive PExpr : Type := - | PEc : C -> PExpr - | PEX : positive -> PExpr - | PEadd : PExpr -> PExpr -> PExpr - | PEsub : PExpr -> PExpr -> PExpr - | PEmul : PExpr -> PExpr -> PExpr - | PEopp : PExpr -> PExpr - | PEpow : PExpr -> N -> PExpr. -\end{verbatim} -\end{flushleft} -\end{small} - -Polynomials in normal form are defined as: -\begin{small} -\begin{flushleft} -\begin{verbatim} -Inductive Pol : Type := - | Pc : C -> Pol - | Pinj : positive -> Pol -> Pol - | PX : Pol -> positive -> Pol -> Pol. -\end{verbatim} -\end{flushleft} -\end{small} -where {\tt Pinj n P} denotes $P$ in which $V_i$ is replaced by -$V_{i+n}$, and {\tt PX P n Q} denotes $P \otimes V_1^{n} \oplus Q'$, -$Q'$ being $Q$ where $V_i$ is replaced by $V_{i+1}$. - - -Variables maps are represented by list of ring elements, and two -interpretation functions, one that maps a variables map and a -polynomial to an element of the concrete ring, and the second one that -does the same for normal forms: -\begin{small} -\begin{flushleft} -\begin{verbatim} -Definition PEeval : list R -> PExpr -> R := [...]. -Definition Pphi_dev : list R -> Pol -> R := [...]. -\end{verbatim} -\end{flushleft} -\end{small} - -A function to normalize polynomials is defined, and the big theorem is -its correctness w.r.t interpretation, that is: - -\begin{small} -\begin{flushleft} -\begin{verbatim} -Definition norm : PExpr -> Pol := [...]. -Lemma Pphi_dev_ok : - forall l pe npe, norm pe = npe -> PEeval l pe == Pphi_dev l npe. -\end{verbatim} -\end{flushleft} -\end{small} - -So now, what is the scheme for a normalization proof? Let \texttt{p} -be the polynomial expression that the user wants to normalize. First a -little piece of ML code guesses the type of \texttt{p}, the ring -theory \texttt{T} to use, an abstract polynomial \texttt{ap} and a -variables map \texttt{v} such that \texttt{p} is -$\beta\delta\iota$-equivalent to \verb|(PEeval v ap)|. Then we -replace it by \verb|(Pphi_dev v (norm ap))|, using the -main correctness theorem and we reduce it to a concrete expression -\texttt{p'}, which is the concrete normal form of -\texttt{p}. This is summarized in this diagram: -\begin{center} -\begin{tabular}{rcl} -\texttt{p} & $\rightarrow_{\beta\delta\iota}$ - & \texttt{(PEeval v ap)} \\ - & & $=_{\mathrm{(by\ the\ main\ correctness\ theorem)}}$ \\ -\texttt{p'} - & $\leftarrow_{\beta\delta\iota}$ - & \texttt{(Pphi\_dev v (norm ap))} -\end{tabular} -\end{center} -The user do not see the right part of the diagram. -From outside, the tactic behaves like a -$\beta\delta\iota$ simplification extended with AC rewriting rules. -Basically, the proof is only the application of the main -correctness theorem to well-chosen arguments. - - -\asection{Dealing with fields -\tacindex{field} -\tacindex{field\_simplify} -\tacindex{field\_simplify\_eq}} - - -The {\tt field} tactic is an extension of the {\tt ring} to deal with -rational expression. Given a rational expression $F=0$. It first reduces the -expression $F$ to a common denominator $N/D= 0$ where $N$ and $D$ are two ring -expressions. -For example, if we take $F = (1 - 1/x) x - x + 1$, this gives -$ N= (x -1) x - x^2 + x$ and $D= x$. It then calls {\tt ring} -to solve $N=0$. Note that {\tt field} also generates non-zero conditions -for all the denominators it encounters in the reduction. -In our example, it generates the condition $x \neq 0$. These -conditions appear as one subgoal which is a conjunction if there are -several denominators. -Non-zero conditions are {\it always} polynomial expressions. For example -when reducing the expression $1/(1 + 1/x)$, two side conditions are -generated: $x\neq 0$ and $x + 1 \neq 0$. Factorized expressions are -broken since a field is an integral domain, and when the equality test -on coefficients is complete w.r.t. the equality of the target field, -constants can be proven different from zero automatically. - -The tactic must be loaded by \texttt{Require Import Field}. New field -structures can be declared to the system with the \texttt{Add Field} -command (see below). The field of real numbers is defined in module -\texttt{RealField} (in texttt{plugins/setoid\_ring}). It is exported -by module \texttt{Rbase}, so that requiring \texttt{Rbase} or -\texttt{Reals} is enough to use the field tactics on real -numbers. Rational numbers in canonical form are also declared as a -field in module \texttt{Qcanon}. - - -\Example -\begin{coq_eval} -Reset Initial. -\end{coq_eval} -\begin{coq_example*} -Require Import Reals. -\end{coq_example*} -\begin{coq_example} -Open Scope R_scope. -Goal forall x, x <> 0 -> - (1 - 1/x) * x - x + 1 = 0. -\end{coq_example} -\begin{coq_example} -intros; field; auto. -\end{coq_example} -\begin{coq_eval} -Abort. -\end{coq_eval} -\begin{coq_example} -Goal forall x y, y <> 0 -> y = x -> x/y = 1. -\end{coq_example} -\begin{coq_example} -intros x y H H1; field [H1]; auto. -\end{coq_example} -\begin{coq_eval} -Reset Initial. -\end{coq_eval} - -\begin{Variants} - \item {\tt field [\term$_1$ {\ldots} \term$_n$]} decides the equality of two - terms modulo field operations and rewriting of the equalities - defined by \term$_1$ {\ldots} \term$_n$. Each of \term$_1$ - {\ldots} \term$_n$ has to be a proof of some equality $m = p$, - where $m$ is a monomial (after ``abstraction''), - $p$ a polynomial and $=$ the corresponding equality of the field structure. - Beware that rewriting works with the equality $m=p$ only if $p$ is a - polynomial since rewriting is handled by the underlying {\tt ring} - tactic. - \item {\tt field\_simplify} - performs the simplification in the conclusion of the goal, $F_1 = F_2$ - becomes $N_1/D_1 = N_2/D_2$. A normalization step (the same as the - one for rings) is then applied to $N_1$, $D_1$, $N_2$ and - $D_2$. This way, polynomials remain in factorized form during the - fraction simplifications. This yields smaller expressions when - reducing to the same denominator since common factors can be - canceled. - - \item {\tt field\_simplify [\term$_1$ {\ldots} \term$_n$]} - performs the simplification in the conclusion of the goal using - the equalities - defined by \term$_1$ {\ldots} \term$_n$. - - \item {\tt field\_simplify [\term$_1$ {\ldots} \term$_n$] $t_1$ \ldots -$t_m$} - performs the simplification in the terms $t_1$ \ldots $t_m$ - of the conclusion of the goal using - the equalities - defined by \term$_1$ {\ldots} \term$_n$. - - \item {\tt field\_simplify in $H$} - performs the simplification in the assumption $H$. - - \item {\tt field\_simplify [\term$_1$ {\ldots} \term$_n$] in $H$} - performs the simplification in the assumption $H$ using - the equalities - defined by \term$_1$ {\ldots} \term$_n$. - - \item {\tt field\_simplify [\term$_1$ {\ldots} \term$_n$] $t_1$ \ldots -$t_m$ in $H$} - performs the simplification in the terms $t_1$ \ldots $t_n$ - of the assumption $H$ using - the equalities - defined by \term$_1$ {\ldots} \term$_m$. - - \item {\tt field\_simplify\_eq} - performs the simplification in the conclusion of the goal removing - the denominator. $F_1 = F_2$ - becomes $N_1 D_2 = N_2 D_1$. - - \item {\tt field\_simplify\_eq [\term$_1$ {\ldots} \term$_n$]} - performs the simplification in the conclusion of the goal using - the equalities - defined by \term$_1$ {\ldots} \term$_n$. - - \item {\tt field\_simplify\_eq} in $H$ - performs the simplification in the assumption $H$. - - \item {\tt field\_simplify\_eq [\term$_1$ {\ldots} \term$_n$] in $H$} - performs the simplification in the assumption $H$ using - the equalities - defined by \term$_1$ {\ldots} \term$_n$. -\end{Variants} - -\asection{Adding a new field structure -\comindex{Add Field}} - -Declaring a new field consists in proving that a field signature (a -carrier set, an equality, and field operations: {\tt -Field\_theory.field\_theory} and {\tt Field\_theory.semi\_field\_theory}) -satisfies the field axioms. Semi-fields (fields without $+$ inverse) are -also supported. The equality can be either Leibniz equality, or any -relation declared as a setoid (see~\ref{setoidtactics}). The definition -of fields and semi-fields is: -\begin{verbatim} -Record field_theory : Prop := mk_field { - F_R : ring_theory rO rI radd rmul rsub ropp req; - F_1_neq_0 : ~ 1 == 0; - Fdiv_def : forall p q, p / q == p * / q; - Finv_l : forall p, ~ p == 0 -> / p * p == 1 -}. - -Record semi_field_theory : Prop := mk_sfield { - SF_SR : semi_ring_theory rO rI radd rmul req; - SF_1_neq_0 : ~ 1 == 0; - SFdiv_def : forall p q, p / q == p * / q; - SFinv_l : forall p, ~ p == 0 -> / p * p == 1 -}. -\end{verbatim} - -The result of the normalization process is a fraction represented by -the following type: -\begin{verbatim} -Record linear : Type := mk_linear { - num : PExpr C; - denum : PExpr C; - condition : list (PExpr C) -}. -\end{verbatim} -where {\tt num} and {\tt denum} are the numerator and denominator; -{\tt condition} is a list of expressions that have appeared as a -denominator during the normalization process. These expressions must -be proven different from zero for the correctness of the algorithm. - -The syntax for adding a new field is {\tt Add Field $name$ : $field$ -($mod_1$,\dots,$mod_2$)}. The name is not relevant. It is just used -for error messages. $field$ is a proof that the field signature -satisfies the (semi-)field axioms. The optional list of modifiers is -used to tailor the behavior of the tactic. Since field tactics are -built upon ring tactics, all modifiers of the {\tt Add Ring} -apply. There is only one specific modifier: -\begin{description} -\item[completeness \term] allows the field tactic to prove - automatically that the image of non-zero coefficients are mapped to - non-zero elements of the field. \term is a proof of {\tt forall x y, - [x] == [y] -> x?=!y = true}, which is the completeness of equality - on coefficients w.r.t. the field equality. -\end{description} - -\asection{History of \texttt{ring}} - -First Samuel Boutin designed the tactic \texttt{ACDSimpl}. -This tactic did lot of rewriting. But the proofs -terms generated by rewriting were too big for \Coq's type-checker. -Let us see why: - -\begin{coq_eval} -Require Import ZArith. -Open Scope Z_scope. -\end{coq_eval} -\begin{coq_example} -Goal forall x y z:Z, x + 3 + y + y * z = x + 3 + y + z * y. -\end{coq_example} -\begin{coq_example*} -intros; rewrite (Z.mul_comm y z); reflexivity. -Save toto. -\end{coq_example*} -\begin{coq_example} -Print toto. -\end{coq_example} - -At each step of rewriting, the whole context is duplicated in the proof -term. Then, a tactic that does hundreds of rewriting generates huge proof -terms. Since \texttt{ACDSimpl} was too slow, Samuel Boutin rewrote it -using reflection (see his article in TACS'97 \cite{Bou97}). Later, the -stuff was rewritten by Patrick -Loiseleur: the new tactic does not any more require \texttt{ACDSimpl} -to compile and it makes use of $\beta\delta\iota$-reduction -not only to replace the rewriting steps, but also to achieve the -interleaving of computation and -reasoning (see \ref{DiscussReflection}). He also wrote a -few ML code for the \texttt{Add Ring} command, that allow to register -new rings dynamically. - -Proofs terms generated by \texttt{ring} are quite small, they are -linear in the number of $\oplus$ and $\otimes$ operations in the -normalized terms. Type-checking those terms requires some time because it -makes a large use of the conversion rule, but -memory requirements are much smaller. - -\asection{Discussion} -\label{DiscussReflection} - -Efficiency is not the only motivation to use reflection -here. \texttt{ring} also deals with constants, it rewrites for example the -expression $34 + 2*x -x + 12$ to the expected result $x + 46$. For the -tactic \texttt{ACDSimpl}, the only constants were 0 and 1. So the -expression $34 + 2*(x - 1) + 12$ is interpreted as -$V_0 \oplus V_1 \otimes (V_2 \ominus 1) \oplus V_3$, -with the variables mapping -$\{V_0 \mt 34; V_1 \mt 2; V_2 \mt x; V_3 \mt 12 \}$. Then it is -rewritten to $34 - x + 2*x + 12$, very far from the expected -result. Here rewriting is not sufficient: you have to do some kind of -reduction (some kind of \textit{computation}) to achieve the -normalization. - -The tactic \texttt{ring} is not only faster than a classical one: -using reflection, we get for free integration of computation and -reasoning that would be very complex to implement in the classic fashion. - -Is it the ultimate way to write tactics? The answer is: yes and -no. The \texttt{ring} tactic uses intensively the conversion rule of -\CIC, that is replaces proof by computation the most as it is -possible. It can be useful in all situations where a classical tactic -generates huge proof terms. Symbolic Processing and Tautologies are in -that case. But there are also tactics like \texttt{auto} or -\texttt{linear} that do many complex computations, using side-effects -and backtracking, and generate a small proof term. Clearly, it would -be significantly less efficient to replace them by tactics using -reflection. - -Another idea suggested by Benjamin Werner: reflection could be used to -couple an external tool (a rewriting program or a model checker) with -\Coq. We define (in \Coq) a type of terms, a type of \emph{traces}, -and prove a correction theorem that states that \emph{replaying -traces} is safe w.r.t some interpretation. Then we let the external -tool do every computation (using side-effects, backtracking, -exception, or others features that are not available in pure lambda -calculus) to produce the trace: now we can check in Coq{} that the -trace has the expected semantic by applying the correction lemma. - -%%% Local Variables: -%%% mode: latex -%%% TeX-master: "Reference-Manual" -%%% End: diff --git a/doc/refman/Program.tex b/doc/refman/Program.tex deleted file mode 100644 index 1e204dc83..000000000 --- a/doc/refman/Program.tex +++ /dev/null @@ -1,329 +0,0 @@ -\achapter{\Program{}} -%HEVEA\cutname{program.html} -\label{Program} -\aauthor{Matthieu Sozeau} -\index{Program} - -We present here the \Program\ tactic commands, used to build certified -\Coq\ programs, elaborating them from their algorithmic skeleton and a -rich specification \cite{Sozeau06}. It can be thought of as a dual of extraction -(see Chapter~\ref{Extraction}). The goal of \Program~is to program as in a regular -functional programming language whilst using as rich a specification as -desired and proving that the code meets the specification using the whole \Coq{} proof -apparatus. This is done using a technique originating from the -``Predicate subtyping'' mechanism of \PVS \cite{Rushby98}, which generates type-checking -conditions while typing a term constrained to a particular type. -Here we insert existential variables in the term, which must be filled -with proofs to get a complete \Coq\ term. \Program\ replaces the -\Program\ tactic by Catherine Parent \cite{Parent95b} which had a similar goal but is no longer -maintained. - -The languages available as input are currently restricted to \Coq's term -language, but may be extended to \ocaml{}, \textsc{Haskell} and others -in the future. We use the same syntax as \Coq\ and permit to use implicit -arguments and the existing coercion mechanism. -Input terms and types are typed in an extended system (\Russell) and -interpreted into \Coq\ terms. The interpretation process may produce -some proof obligations which need to be resolved to create the final term. - -\asection{Elaborating programs} -The main difference from \Coq\ is that an object in a type $T : \Set$ -can be considered as an object of type $\{ x : T~|~P\}$ for any -wellformed $P : \Prop$. -If we go from $T$ to the subset of $T$ verifying property $P$, we must -prove that the object under consideration verifies it. \Russell\ will -generate an obligation for every such coercion. In the other direction, -\Russell\ will automatically insert a projection. - -Another distinction is the treatment of pattern-matching. Apart from the -following differences, it is equivalent to the standard {\tt match} -operation (see Section~\ref{Caseexpr}). -\begin{itemize} -\item Generation of equalities. A {\tt match} expression is always - generalized by the corresponding equality. As an example, - the expression: - -\begin{verbatim} - match x with - | 0 => t - | S n => u - end. -\end{verbatim} -will be first rewritten to: -\begin{verbatim} - (match x as y return (x = y -> _) with - | 0 => fun H : x = 0 -> t - | S n => fun H : x = S n -> u - end) (eq_refl n). -\end{verbatim} - - This permits to get the proper equalities in the context of proof - obligations inside clauses, without which reasoning is very limited. - -\item Generation of inequalities. If a pattern intersects with a - previous one, an inequality is added in the context of the second - branch. See for example the definition of {\tt div2} below, where the second - branch is typed in a context where $\forall p, \_ <> S (S p)$. - -\item Coercion. If the object being matched is coercible to an inductive - type, the corresponding coercion will be automatically inserted. This also - works with the previous mechanism. - -\end{itemize} - -There are options to control the generation of equalities -and coercions. - -\begin{itemize} -\item {\tt Unset Program Cases}\optindex{Program Cases} This deactivates - the special treatment of pattern-matching generating equalities and - inequalities when using \Program\ (it is on by default). All - pattern-matchings and let-patterns are handled using the standard - algorithm of Coq (see Section~\ref{Mult-match-full}) when this option is - deactivated. -\item {\tt Unset Program Generalized Coercion}\optindex{Program - Generalized Coercion} This deactivates the coercion of general - inductive types when using \Program\ (the option is on by default). - Coercion of subset types and pairs is still active in this case. -\end{itemize} - -\subsection{Syntactic control over equalities} -\label{ProgramSyntax} -To give more control over the generation of equalities, the typechecker will -fall back directly to \Coq's usual typing of dependent pattern-matching -if a {\tt return} or {\tt in} clause is specified. Likewise, -the {\tt if} construct is not treated specially by \Program{} so boolean -tests in the code are not automatically reflected in the obligations. -One can use the {\tt dec} combinator to get the correct hypotheses as in: - -\begin{coq_eval} -Require Import Program Arith. -\end{coq_eval} -\begin{coq_example} -Program Definition id (n : nat) : { x : nat | x = n } := - if dec (leb n 0) then 0 - else S (pred n). -\end{coq_example} - -The let tupling construct {\tt let (x1, ..., xn) := t in b} -does not produce an equality, contrary to the let pattern construct -{\tt let '(x1, ..., xn) := t in b}. -Also, {\tt {\term}:>} explicitly asks the system to coerce {\tt \term} to its -support type. It can be useful in notations, for example: -\begin{coq_example} -Notation " x `= y " := (@eq _ (x :>) (y :>)) (only parsing). -\end{coq_example} - -This notation denotes equality on subset types using equality on their -support types, avoiding uses of proof-irrelevance that would come up -when reasoning with equality on the subset types themselves. - -The next two commands are similar to their standard counterparts -Definition (see Section~\ref{Basic-definitions}) and Fixpoint (see Section~\ref{Fixpoint}) in that -they define constants. However, they may require the user to prove some -goals to construct the final definitions. - -\subsection{\tt Program Definition {\ident} := {\term}. - \comindex{Program Definition}\label{ProgramDefinition}} - -This command types the value {\term} in \Russell\ and generates proof -obligations. Once solved using the commands shown below, it binds the final -\Coq\ term to the name {\ident} in the environment. - -\begin{ErrMsgs} -\item \errindex{{\ident} already exists} -\end{ErrMsgs} - -\begin{Variants} -\item {\tt Program Definition {\ident} {\tt :}{\term$_1$} := - {\term$_2$}.}\\ - It interprets the type {\term$_1$}, potentially generating proof - obligations to be resolved. Once done with them, we have a \Coq\ type - {\term$_1'$}. It then checks that the type of the interpretation of - {\term$_2$} is coercible to {\term$_1'$}, and registers {\ident} as - being of type {\term$_1'$} once the set of obligations generated - during the interpretation of {\term$_2$} and the aforementioned - coercion derivation are solved. -\item {\tt Program Definition {\ident} {\binder$_1$}\ldots{\binder$_n$} - {\tt :}\term$_1$ {\tt :=} {\term$_2$}.}\\ - This is equivalent to \\ - {\tt Program Definition\,{\ident}\,{\tt :\,forall} % - {\binder$_1$}\ldots{\binder$_n$}{\tt ,}\,\term$_1$\,{\tt :=}} \\ - \qquad {\tt fun}\,{\binder$_1$}\ldots{\binder$_n$}\,{\tt =>}\,{\term$_2$}\,% - {\tt .} -\end{Variants} - -\begin{ErrMsgs} -\item \errindex{In environment {\dots} the term: {\term$_2$} does not have type - {\term$_1$}}.\\ - \texttt{Actually, it has type {\term$_3$}}. -\end{ErrMsgs} - -\SeeAlso Sections \ref{Opaque}, \ref{Transparent}, \ref{unfold} - -\subsection{\tt Program Fixpoint {\ident} {\params} {\tt \{order\}} : type := \term - \comindex{Program Fixpoint} - \label{ProgramFixpoint}} - -The structural fixpoint operator behaves just like the one of Coq -(see Section~\ref{Fixpoint}), except it may also generate obligations. -It works with mutually recursive definitions too. - -\begin{coq_eval} -Admit Obligations. -\end{coq_eval} -\begin{coq_example} -Program Fixpoint div2 (n : nat) : { x : nat | n = 2 * x \/ n = 2 * x + 1 } := - match n with - | S (S p) => S (div2 p) - | _ => O - end. -\end{coq_example} - -Here we have one obligation for each branch (branches for \verb:0: and \verb:(S 0): are -automatically generated by the pattern-matching compilation algorithm). -\begin{coq_example} - Obligation 1. -\end{coq_example} - -One can use a well-founded order or a measure as termination orders using the syntax: -\begin{coq_eval} -Reset Initial. -Require Import Arith. -Require Import Program. -\end{coq_eval} -\begin{coq_example*} -Program Fixpoint div2 (n : nat) {measure n} : - { x : nat | n = 2 * x \/ n = 2 * x + 1 } := - match n with - | S (S p) => S (div2 p) - | _ => O - end. -\end{coq_example*} - -The order annotation can be either: -\begin{itemize} -\item {\tt measure f (R)?} where {\tt f} is a value of type {\tt X} - computed on any subset of the arguments and the optional - (parenthesised) term {\tt (R)} is a relation - on {\tt X}. By default {\tt X} defaults to {\tt nat} and {\tt R} to - {\tt lt}. -\item {\tt wf R x} which is equivalent to {\tt measure x (R)}. -\end{itemize} - -\paragraph{Caution} -When defining structurally recursive functions, the -generated obligations should have the prototype of the currently defined functional -in their context. In this case, the obligations should be transparent -(e.g. defined using {\tt Defined}) so that the guardedness condition on -recursive calls can be checked by the -kernel's type-checker. There is an optimization in the generation of -obligations which gets rid of the hypothesis corresponding to the -functional when it is not necessary, so that the obligation can be -declared opaque (e.g. using {\tt Qed}). However, as soon as it appears in the -context, the proof of the obligation is \emph{required} to be declared transparent. - -No such problems arise when using measures or well-founded recursion. - -\subsection{\tt Program Lemma {\ident} : type. - \comindex{Program Lemma} - \label{ProgramLemma}} - -The \Russell\ language can also be used to type statements of logical -properties. It will generate obligations, try to solve them -automatically and fail if some unsolved obligations remain. -In this case, one can first define the lemma's -statement using {\tt Program Definition} and use it as the goal afterwards. -Otherwise the proof will be started with the elaborated version as a goal. -The {\tt Program} prefix can similarly be used as a prefix for {\tt Variable}, {\tt - Hypothesis}, {\tt Axiom} etc... - -\section{Solving obligations} -The following commands are available to manipulate obligations. The -optional identifier is used when multiple functions have unsolved -obligations (e.g. when defining mutually recursive blocks). The optional -tactic is replaced by the default one if not specified. - -\begin{itemize} -\item {\tt [Local|Global] Obligation Tactic := \tacexpr}\comindex{Obligation Tactic} - Sets the default obligation - solving tactic applied to all obligations automatically, whether to - solve them or when starting to prove one, e.g. using {\tt Next}. - Local makes the setting last only for the current module. Inside - sections, local is the default. -\item {\tt Show Obligation Tactic}\comindex{Show Obligation Tactic} - Displays the current default tactic. -\item {\tt Obligations [of \ident]}\comindex{Obligations} Displays all remaining - obligations. -\item {\tt Obligation num [of \ident]}\comindex{Obligation} Start the proof of - obligation {\tt num}. -\item {\tt Next Obligation [of \ident]}\comindex{Next Obligation} Start the proof of the next - unsolved obligation. -\item {\tt Solve Obligations [of \ident] [with - \tacexpr]}\comindex{Solve Obligations} - Tries to solve - each obligation of \ident using the given tactic or the default one. -\item {\tt Solve All Obligations [with \tacexpr]} Tries to solve - each obligation of every program using the given tactic or the default - one (useful for mutually recursive definitions). -\item {\tt Admit Obligations [of \ident]}\comindex{Admit Obligations} - Admits all obligations (does not work with structurally recursive programs). -\item {\tt Preterm [of \ident]}\comindex{Preterm} - Shows the term that will be fed to - the kernel once the obligations are solved. Useful for debugging. -\item {\tt Set Transparent Obligations}\optindex{Transparent Obligations} - Control whether all obligations should be declared as transparent (the - default), or if the system should infer which obligations can be declared opaque. -\item {\tt Set Hide Obligations}\optindex{Hide Obligations} - Control whether obligations appearing in the term should be hidden - as implicit arguments of the special constant - \texttt{Program.Tactics.obligation}. -\item {\tt Set Shrink Obligations}\optindex{Shrink Obligations} -\emph{Deprecated since 8.7} - This option (on by default) controls whether obligations should have their - context minimized to the set of variables used in the proof of the - obligation, to avoid unnecessary dependencies. -\end{itemize} - -The module {\tt Coq.Program.Tactics} defines the default tactic for solving -obligations called {\tt program\_simpl}. Importing -{\tt Coq.Program.Program} also adds some useful notations, as documented in the file itself. - -\section{Frequently Asked Questions - \label{ProgramFAQ}} - -\begin{itemize} -\item {Ill-formed recursive definitions} - This error can happen when one tries to define a - function by structural recursion on a subset object, which means the Coq - function looks like: - - \verb$Program Fixpoint f (x : A | P) := match x with A b => f b end.$ - - Supposing $b : A$, the argument at the recursive call to f is not a - direct subterm of x as b is wrapped inside an {\tt exist} constructor to build - an object of type \verb${x : A | P}$. Hence the definition is rejected - by the guardedness condition checker. However one can use - wellfounded recursion on subset objects like this: - -\begin{verbatim} -Program Fixpoint f (x : A | P) { measure (size x) } := - match x with A b => f b end. -\end{verbatim} - - One will then just have to prove that the measure decreases at each recursive - call. There are three drawbacks though: - \begin{enumerate} - \item A measure function has to be defined; - \item The reduction is a little more involved, although it works well - using lazy evaluation; - \item Mutual recursion on the underlying inductive type isn't possible - anymore, but nested mutual recursion is always possible. - \end{enumerate} -\end{itemize} - -%%% Local Variables: -%%% mode: latex -%%% TeX-master: "Reference-Manual" -%%% compile-command: "BIBINPUTS=\".\" make QUICK=1 -C ../.. doc/refman/Reference-Manual.pdf" -%%% End: diff --git a/doc/refman/RefMan-oth.tex b/doc/refman/RefMan-oth.tex deleted file mode 100644 index bef31d3fa..000000000 --- a/doc/refman/RefMan-oth.tex +++ /dev/null @@ -1,1224 +0,0 @@ -\chapter[Vernacular commands]{Vernacular commands\label{Vernacular-commands} -\label{Other-commands}} -%HEVEA\cutname{vernacular.html} - -\section{Displaying} - -\subsection[\tt Print {\qualid}.]{\tt Print {\qualid}.\comindex{Print}} -This command displays on the screen information about the declared or -defined object referred by {\qualid}. - -\begin{ErrMsgs} -\item {\qualid} \errindex{not a defined object} -\item \errindex{Universe instance should have length} $n$. -\item \errindex{This object does not support universe names.} -\end{ErrMsgs} - -\begin{Variants} -\item {\tt Print Term {\qualid}.} -\comindex{Print Term}\\ -This is a synonym to {\tt Print {\qualid}} when {\qualid} denotes a -global constant. - -\item {\tt About {\qualid}.} -\label{About} -\comindex{About}\\ -This displays various information about the object denoted by {\qualid}: -its kind (module, constant, assumption, inductive, -constructor, abbreviation, \ldots), long name, type, implicit -arguments and argument scopes. It does not print the body of -definitions or proofs. - -\item {\tt Print {\qualid}@\{names\}.}\\ -This locally renames the polymorphic universes of {\qualid}. -An underscore means the raw universe is printed. -This form can be used with {\tt Print Term} and {\tt About}. - -%\item {\tt Print Proof {\qualid}.}\comindex{Print Proof}\\ -%In case \qualid\ denotes an opaque theorem defined in a section, -%it is stored on a special unprintable form and displayed as -%{\tt <recipe>}. {\tt Print Proof} forces the printable form of \qualid\ -%to be computed and displays it. -\end{Variants} - -\subsection[\tt Print All.]{\tt Print All.\comindex{Print All}} -This command displays information about the current state of the -environment, including sections and modules. - -\begin{Variants} -\item {\tt Inspect \num.}\comindex{Inspect}\\ -This command displays the {\num} last objects of the current -environment, including sections and modules. -\item {\tt Print Section {\ident}.}\comindex{Print Section}\\ -should correspond to a currently open section, this command -displays the objects defined since the beginning of this section. -% Discontinued -%% \item {\tt Print.}\comindex{Print}\\ -%% This command displays the axioms and variables declarations in the -%% environment as well as the constants defined since the last variable -%% was introduced. -\end{Variants} - -\section{Flags, Options and Tables} - -{\Coq} configurability is based on flags (e.g. {\tt Set Printing All} in -Section~\ref{SetPrintingAll}), options (e.g. {\tt Set Printing Width - {\integer}} in Section~\ref{SetPrintingWidth}), or tables (e.g. {\tt - Add Printing Record {\ident}}, in Section~\ref{AddPrintingLet}). The -names of flags, options and tables are made of non-empty sequences of -identifiers (conventionally with capital initial letter). The general -commands handling flags, options and tables are given below. - -\subsection[\tt Set {\rm\sl flag}.]{\tt Set {\rm\sl flag}.\comindex{Set}} -This command switches {\rm\sl flag} on. The original state of -{\rm\sl flag} is restored when the current module ends. - -\begin{Variants} -\item {\tt Local Set {\rm\sl flag}.}\\ -This command switches {\rm\sl flag} on. The original state of -{\rm\sl flag} is restored when the current \emph{section} ends. -\item {\tt Global Set {\rm\sl flag}.}\\ -This command switches {\rm\sl flag} on. The original state of -{\rm\sl flag} is \emph{not} restored at the end of the module. Additionally, -if set in a file, {\rm\sl flag} is switched on when the file is -{\tt Require}-d. -\end{Variants} - -\subsection[\tt Unset {\rm\sl flag}.]{\tt Unset {\rm\sl flag}.\comindex{Unset}} -This command switches {\rm\sl flag} off. The original state of {\rm\sl flag} -is restored when the current module ends. - -\begin{Variants} -\item {\tt Local Unset {\rm\sl flag}.\comindex{Local Unset}}\\ -This command switches {\rm\sl flag} off. The original state of {\rm\sl flag} -is restored when the current \emph{section} ends. -\item {\tt Global Unset {\rm\sl flag}.\comindex{Global Unset}}\\ -This command switches {\rm\sl flag} off. The original state of -{\rm\sl flag} is \emph{not} restored at the end of the module. Additionally, -if set in a file, {\rm\sl flag} is switched off when the file is -{\tt Require}-d. -\end{Variants} - -\subsection[\tt Test {\rm\sl flag}.]{\tt Test {\rm\sl flag}.\comindex{Test}} -This command prints whether {\rm\sl flag} is on or off. - -\subsection[\tt Set {\rm\sl option} {\rm\sl value}.]{\tt Set {\rm\sl option} {\rm\sl value}.\comindex{Set}} -This command sets {\rm\sl option} to {\rm\sl value}. The original value of -{\rm\sl option} is restored when the current module ends. - -\begin{Variants} -\item {\tt Local Set {\rm\sl option} {\rm\sl value}.\comindex{Local Set}} -This command sets {\rm\sl option} to {\rm\sl value}. The original value of -{\rm\sl option} is restored at the end of the module. -\item {\tt Global Set {\rm\sl option} {\rm\sl value}.\comindex{Global Set}} -This command sets {\rm\sl option} to {\rm\sl value}. The original value of -{\rm\sl option} is \emph{not} restored at the end of the module. Additionally, -if set in a file, {\rm\sl option} is set to {\rm\sl value} when the file is -{\tt Require}-d. -\end{Variants} - -\subsection[\tt Unset {\rm\sl option}.]{\tt Unset {\rm\sl option}.\comindex{Unset}} -This command resets {\rm\sl option} to its default value. - -\begin{Variants} -\item {\tt Local Unset {\rm\sl option}.\comindex{Local Unset}}\\ -This command resets {\rm\sl option} to its default value. The original state of {\rm\sl option} -is restored when the current \emph{section} ends. -\item {\tt Global Unset {\rm\sl option}.\comindex{Global Unset}}\\ -This command resets {\rm\sl option} to its default value. The original state of -{\rm\sl option} is \emph{not} restored at the end of the module. Additionally, -if unset in a file, {\rm\sl option} is reset to its default value when the file is -{\tt Require}-d. -\end{Variants} - -\subsection[\tt Test {\rm\sl option}.]{\tt Test {\rm\sl option}.\comindex{Test}} -This command prints the current value of {\rm\sl option}. - -\subsection{Tables} -The general commands for tables are {\tt Add {\rm\sf table} {\rm\sl - value}}, {\tt Remove {\rm\sf table} {\rm\sl value}}, {\tt Test - {\rm\sf table}}, {\tt Test {\rm\sf table} for {\rm\sl value}} and - {\tt Print Table {\rm\sf table}}. - -\subsection[\tt Print Options.]{\tt Print Options.\comindex{Print Options}} -This command lists all available flags, options and tables. - -\begin{Variants} -\item {\tt Print Tables}.\comindex{Print Tables}\\ -This is a synonymous of {\tt Print Options.} -\end{Variants} - -\section{Requests to the environment} - -\subsection[\tt Check {\term}.]{\tt Check {\term}.\label{Check} -\comindex{Check}} -This command displays the type of {\term}. When called in proof mode, -the term is checked in the local context of the current subgoal. - -\begin{Variants} -\item {\tt selector: Check {\term}}.\\ -specifies on which subgoal to perform typing (see - Section~\ref{tactic-syntax}). -\end{Variants} - - -\subsection[\tt Eval {\rm\sl convtactic} in {\term}.]{\tt Eval {\rm\sl convtactic} in {\term}.\comindex{Eval}} - -This command performs the specified reduction on {\term}, and displays -the resulting term with its type. The term to be reduced may depend on -hypothesis introduced in the first subgoal (if a proof is in -progress). - -\SeeAlso Section~\ref{Conversion-tactics}. - -\subsection[\tt Compute {\term}.]{\tt Compute {\term}.\comindex{Compute}} - -This command performs a call-by-value evaluation of {\term} by using -the bytecode-based virtual machine. It is a shortcut for -{\tt Eval vm\_compute in {\term}}. - -\SeeAlso Section~\ref{Conversion-tactics}. - -\subsection[\tt Extraction \term.]{\tt Extraction \term.\label{ExtractionTerm} -\comindex{Extraction}} -This command displays the extracted term from -{\term}. The extraction is processed according to the distinction -between {\Set} and {\Prop}; that is to say, between logical and -computational content (see Section~\ref{Sorts}). The extracted term is -displayed in {\ocaml} syntax, where global identifiers are still -displayed as in \Coq\ terms. - -\begin{Variants} -\item \texttt{Recursive Extraction} {\qualid$_1$} \ldots{} {\qualid$_n$}{\tt .}\\ - Recursively extracts all the material needed for the extraction of - global {\qualid$_1$}, \ldots, {\qualid$_n$}. -\end{Variants} - -\SeeAlso Chapter~\ref{Extraction}. - -\subsection[\tt Print Assumptions {\qualid}.]{\tt Print Assumptions {\qualid}.\comindex{Print Assumptions}} -\label{PrintAssumptions} - -This commands display all the assumptions (axioms, parameters and -variables) a theorem or definition depends on. Especially, it informs -on the assumptions with respect to which the validity of a theorem -relies. - -\begin{Variants} -\item \texttt{\tt Print Opaque Dependencies {\qualid}. - \comindex{Print Opaque Dependencies}}\\ - Displays the set of opaque constants {\qualid} relies on in addition - to the assumptions. -\item \texttt{\tt Print Transparent Dependencies {\qualid}. - \comindex{Print Transparent Dependencies}}\\ - Displays the set of transparent constants {\qualid} relies on in addition - to the assumptions. -\item \texttt{\tt Print All Dependencies {\qualid}. - \comindex{Print All Dependencies}}\\ - Displays all assumptions and constants {\qualid} relies on. -\end{Variants} - -\subsection[\tt Search {\qualid}.]{\tt Search {\qualid}.\comindex{Search}} -This command displays the name and type of all objects (hypothesis of -the current goal, theorems, axioms, etc) of the current context whose -statement contains \qualid. This command is useful to remind the user -of the name of library lemmas. - -\begin{ErrMsgs} -\item \errindex{The reference \qualid\ was not found in the current -environment}\\ - There is no constant in the environment named \qualid. -\end{ErrMsgs} - -\newcommand{\termpatternorstr}{{\termpattern}\textrm{\textsl{-}}{\str}} - -\begin{Variants} -\item {\tt Search {\str}.} - -If {\str} is a valid identifier, this command displays the name and type -of all objects (theorems, axioms, etc) of the current context whose -name contains {\str}. If {\str} is a notation's string denoting some -reference {\qualid} (referred to by its main symbol as in \verb="+"= -or by its notation's string as in \verb="_ + _"= or \verb="_ 'U' _"=, see -Section~\ref{Notation}), the command works like {\tt Search -{\qualid}}. - -\item {\tt Search {\str}\%{\delimkey}.} - -The string {\str} must be a notation or the main symbol of a notation -which is then interpreted in the scope bound to the delimiting key -{\delimkey} (see Section~\ref{scopechange}). - -\item {\tt Search {\termpattern}.} - -This searches for all statements or types of definition that contains -a subterm that matches the pattern {\termpattern} (holes of the -pattern are either denoted by ``{\texttt \_}'' or -by ``{\texttt ?{\ident}}'' when non linear patterns are expected). - -\item {\tt Search \nelist{\zeroone{-}{\termpatternorstr}}{}.}\\ - -\noindent where {\termpatternorstr} is a -{\termpattern} or a {\str}, or a {\str} followed by a scope -delimiting key {\tt \%{\delimkey}}. - -This generalization of {\tt Search} searches for all objects -whose statement or type contains a subterm matching {\termpattern} (or -{\qualid} if {\str} is the notation for a reference {\qualid}) and -whose name contains all {\str} of the request that correspond to valid -identifiers. If a {\termpattern} or a {\str} is prefixed by ``-'', the -search excludes the objects that mention that {\termpattern} or that -{\str}. - -\item - {\tt Search} \nelist{{\termpatternorstr}}{} - {\tt inside} {\module$_1$} \ldots{} {\module$_n$}{\tt .} - -This restricts the search to constructions defined in modules -{\module$_1$} \ldots{} {\module$_n$}. - -\item - {\tt Search \nelist{{\termpatternorstr}}{} - outside {\module$_1$}...{\module$_n$}.} - -This restricts the search to constructions not defined in modules -{\module$_1$} \ldots{} {\module$_n$}. - -\item {\tt selector: Search \nelist{\zeroone{-}{\termpatternorstr}}{}.} - - This specifies the goal on which to search hypothesis (see - Section~\ref{tactic-syntax}). By default the 1st goal is searched. - This variant can be combined with other variants presented here. -\end{Variants} - -\examples - -\begin{coq_example*} -Require Import ZArith. -\end{coq_example*} -\begin{coq_example} -Search Z.mul Z.add "distr". -Search "+"%Z "*"%Z "distr" -positive -Prop. -Search (?x * _ + ?x * _)%Z outside OmegaLemmas. -\end{coq_example} - -\Warning \comindex{SearchAbout} Up to {\Coq} version 8.4, {\tt Search} -had the behavior of current {\tt SearchHead} and the behavior of -current {\tt Search} was obtained with command {\tt SearchAbout}. For -compatibility, the deprecated name {\tt SearchAbout} can still be used -as a synonym of {\tt Search}. For compatibility, the list of objects to -search when using {\tt SearchAbout} may also be enclosed by optional -{\tt [ ]} delimiters. - -\subsection[\tt SearchHead {\term}.]{\tt SearchHead {\term}.\comindex{SearchHead}} -This command displays the name and type of all hypothesis of the -current goal (if any) and theorems of the current context whose -statement's conclusion has the form {\tt ({\term} t1 .. - tn)}. This command is useful to remind the user of the name of -library lemmas. - -\begin{coq_eval} -Reset Initial. -\end{coq_eval} - -\begin{coq_example} -SearchHead le. -SearchHead (@eq bool). -\end{coq_example} - -\begin{Variants} -\item -{\tt SearchHead} {\term} {\tt inside} {\module$_1$} \ldots{} {\module$_n$}{\tt .} - -This restricts the search to constructions defined in modules -{\module$_1$} \ldots{} {\module$_n$}. - -\item {\tt SearchHead} {\term} {\tt outside} {\module$_1$} \ldots{} {\module$_n$}{\tt .} - -This restricts the search to constructions not defined in modules -{\module$_1$} \ldots{} {\module$_n$}. - -\begin{ErrMsgs} -\item \errindex{Module/section \module{} not found} -No module \module{} has been required (see Section~\ref{Require}). -\end{ErrMsgs} - -\item {\tt selector: SearchHead {\term}.} - - This specifies the goal on which to search hypothesis (see - Section~\ref{tactic-syntax}). By default the 1st goal is searched. - This variant can be combined with other variants presented here. - -\end{Variants} - -\Warning Up to {\Coq} version 8.4, {\tt SearchHead} was named {\tt Search}. - -\subsection[\tt SearchPattern {\termpattern}.]{\tt SearchPattern {\term}.\comindex{SearchPattern}} - -This command displays the name and type of all hypothesis of the -current goal (if any) and theorems of the current context whose statement's -conclusion or last hypothesis and conclusion matches the expression -{\term} where holes in the latter are denoted by ``{\texttt \_}''. It -is a variant of {\tt Search - {\termpattern}} that does not look for subterms but searches for -statements whose conclusion has exactly the expected form, or whose -statement finishes by the given series of hypothesis/conclusion. - -\begin{coq_example*} -Require Import Arith. -\end{coq_example*} -\begin{coq_example} -SearchPattern (_ + _ = _ + _). -SearchPattern (nat -> bool). -SearchPattern (forall l : list _, _ l l). -\end{coq_example} - -Patterns need not be linear: you can express that the same expression -must occur in two places by using pattern variables `{\texttt -?{\ident}}''. - -\begin{coq_example} -SearchPattern (?X1 + _ = _ + ?X1). -\end{coq_example} - -\begin{Variants} -\item {\tt SearchPattern {\term} inside -{\module$_1$} \ldots{} {\module$_n$}.} - -This restricts the search to constructions defined in modules -{\module$_1$} \ldots{} {\module$_n$}. - -\item {\tt SearchPattern {\term} outside {\module$_1$} \ldots{} {\module$_n$}.} - -This restricts the search to constructions not defined in modules -{\module$_1$} \ldots{} {\module$_n$}. - -\item {\tt selector: SearchPattern {\term}.} - - This specifies the goal on which to search hypothesis (see - Section~\ref{tactic-syntax}). By default the 1st goal is searched. - This variant can be combined with other variants presented here. - -\end{Variants} - -\subsection[\tt SearchRewrite {\term}.]{\tt SearchRewrite {\term}.\comindex{SearchRewrite}} - -This command displays the name and type of all hypothesis of the -current goal (if any) and theorems of the current context whose -statement's conclusion is an equality of which one side matches the -expression {\term}. Holes in {\term} are denoted by ``{\texttt \_}''. - -\begin{coq_example} -Require Import Arith. -SearchRewrite (_ + _ + _). -\end{coq_example} - -\begin{Variants} -\item {\tt SearchRewrite {\term} inside -{\module$_1$} \ldots{} {\module$_n$}.} - -This restricts the search to constructions defined in modules -{\module$_1$} \ldots{} {\module$_n$}. - -\item {\tt SearchRewrite {\term} outside {\module$_1$} \ldots{} {\module$_n$}.} - -This restricts the search to constructions not defined in modules -{\module$_1$} \ldots{} {\module$_n$}. - -\item {\tt selector: SearchRewrite {\term}.} - - This specifies the goal on which to search hypothesis (see - Section~\ref{tactic-syntax}). By default the 1st goal is searched. - This variant can be combined with other variants presented here. - -\end{Variants} - -\subsubsection{Nota Bene:} -For the {\tt Search}, {\tt SearchHead}, {\tt SearchPattern} and -{\tt SearchRewrite} queries, it is possible to globally filter -the search results via the command -{\tt Add Search Blacklist "substring1"}. -A lemma whose fully-qualified name contains any of the declared substrings -will be removed from the search results. -The default blacklisted substrings are {\tt - "\_subproof" "Private\_"}. The command {\tt Remove Search Blacklist - ...} allows expunging this blacklist. - -% \begin{tabbing} -% \ \ \ \ \=11.\ \=\kill -% \>1.\>$A=B\mx{ if }A\stackrel{\bt{}\io{}}{\lra{}}B$\\ -% \>2.\>$\sa{}x:A.B=\sa{}y:A.B[x\la{}y]\mx{ if }y\not\in{}FV(\sa{}x:A.B)$\\ -% \>3.\>$\Pi{}x:A.B=\Pi{}y:A.B[x\la{}y]\mx{ if }y\not\in{}FV(\Pi{}x:A.B)$\\ -% \>4.\>$\sa{}x:A.B=\sa{}x:B.A\mx{ if }x\not\in{}FV(A,B)$\\ -% \>5.\>$\sa{}x:(\sa{}y:A.B).C=\sa{}x:A.\sa{}y:B[y\la{}x].C[x\la{}(x,y)]$\\ -% \>6.\>$\Pi{}x:(\sa{}y:A.B).C=\Pi{}x:A.\Pi{}y:B[y\la{}x].C[x\la{}(x,y)]$\\ -% \>7.\>$\Pi{}x:A.\sa{}y:B.C=\sa{}y:(\Pi{}x:A.B).(\Pi{}x:A.C[y\la{}(y\sm{}x)]$\\ -% \>8.\>$\sa{}x:A.unit=A$\\ -% \>9.\>$\sa{}x:unit.A=A[x\la{}tt]$\\ -% \>10.\>$\Pi{}x:A.unit=unit$\\ -% \>11.\>$\Pi{}x:unit.A=A[x\la{}tt]$ -% \end{tabbing} - -% For more informations about the exact working of this command, see -% \cite{Del97}. - -\subsection[\tt Locate {\qualid}.]{\tt Locate {\qualid}.\comindex{Locate} -\label{Locate}} -This command displays the full name of objects whose name is a prefix of the -qualified identifier {\qualid}, and consequently the \Coq\ module in which they -are defined. It searches for objects from the different qualified name spaces of -{\Coq}: terms, modules, Ltac, etc. - -\begin{coq_eval} -(*************** The last line should produce **************************) -(*********** Error: I.Dont.Exist not a defined object ******************) -\end{coq_eval} -\begin{coq_eval} -Set Printing Depth 50. -\end{coq_eval} -\begin{coq_example} -Locate nat. -Locate Datatypes.O. -Locate Init.Datatypes.O. -Locate Coq.Init.Datatypes.O. -Locate I.Dont.Exist. -\end{coq_example} - -\begin{Variants} -\item {\tt Locate Term {\qualid}.}\comindex{Locate Term}\\ - As {\tt Locate} but restricted to terms. - -\item {\tt Locate Module {\qualid}.} - As {\tt Locate} but restricted to modules. - -\item {\tt Locate Ltac {\qualid}.}\comindex{Locate Ltac}\\ - As {\tt Locate} but restricted to tactics. -\end{Variants} - - -\SeeAlso Section \ref{LocateSymbol} - -\section{Loading files} - -\Coq\ offers the possibility of loading different -parts of a whole development stored in separate files. Their contents -will be loaded as if they were entered from the keyboard. This means -that the loaded files are ASCII files containing sequences of commands -for \Coq's toplevel. This kind of file is called a {\em script} for -\Coq\index{Script file}. The standard (and default) extension of -\Coq's script files is {\tt .v}. - -\subsection[\tt Load {\ident}.]{\tt Load {\ident}.\comindex{Load}\label{Load}} -This command loads the file named {\ident}{\tt .v}, searching -successively in each of the directories specified in the {\em - loadpath}. (see Section~\ref{loadpath}) - -Files loaded this way cannot leave proofs open, and neither the {\tt - Load} command can be use inside a proof. - -\begin{Variants} -\item {\tt Load {\str}.}\label{Load-str}\\ - Loads the file denoted by the string {\str}, where {\str} is any - complete filename. Then the \verb.~. and {\tt ..} - abbreviations are allowed as well as shell variables. If no - extension is specified, \Coq\ will use the default extension {\tt - .v} -\item {\tt Load Verbose {\ident}.}, - {\tt Load Verbose {\str}}\\ - \comindex{Load Verbose} - Display, while loading, the answers of \Coq\ to each command - (including tactics) contained in the loaded file - \SeeAlso Section~\ref{Begin-Silent} -\end{Variants} - -\begin{ErrMsgs} -\item \errindex{Can't find file {\ident} on loadpath} -\item \errindex{Load is not supported inside proofs} -\item \errindex{Files processed by Load cannot leave open proofs} -\end{ErrMsgs} - -\section[Compiled files]{Compiled files\label{compiled}\index{Compiled files}} - -This section describes the commands used to load compiled files (see -Chapter~\ref{Addoc-coqc} for documentation on how to compile a file). -A compiled file is a particular case of module called {\em library file}. - -%%%%%%%%%%%% -% Import and Export described in RefMan-mod.tex -% the minor difference (to avoid multiple Exporting of libraries) in -% the treatment of normal modules and libraries by Export omitted - -\subsection[\tt Require {\qualid}.]{\tt Require {\qualid}.\label{Require} -\comindex{Require}} - -This command looks in the loadpath for a file containing -module {\qualid} and adds the corresponding module to the environment -of {\Coq}. As library files have dependencies in other library files, -the command {\tt Require {\qualid}} recursively requires all library -files the module {\qualid} depends on and adds the corresponding modules to the -environment of {\Coq} too. {\Coq} assumes that the compiled files have -been produced by a valid {\Coq} compiler and their contents are then not -replayed nor rechecked. - -To locate the file in the file system, {\qualid} is decomposed under -the form {\dirpath}{\tt .}{\textsl{ident}} and the file {\ident}{\tt -.vo} is searched in the physical directory of the file system that is -mapped in {\Coq} loadpath to the logical path {\dirpath} (see -Section~\ref{loadpath}). The mapping between physical directories and -logical names at the time of requiring the file must be consistent -with the mapping used to compile the file. If several files match, one of them -is picked in an unspecified fashion. - -\begin{Variants} -\item {\tt Require Import {\qualid}.} \comindex{Require Import} - - This loads and declares the module {\qualid} and its dependencies - then imports the contents of {\qualid} as described in - Section~\ref{Import}. - - It does not import the modules on which {\qualid} depends unless - these modules were itself required in module {\qualid} using {\tt - Require Export}, as described below, or recursively required through - a sequence of {\tt Require Export}. - - If the module required has already been loaded, {\tt Require Import - {\qualid}} simply imports it, as {\tt Import {\qualid}} would. - -\item {\tt Require Export {\qualid}.} - \comindex{Require Export} - - This command acts as {\tt Require Import} {\qualid}, but if a - further module, say {\it A}, contains a command {\tt Require - Export} {\it B}, then the command {\tt Require Import} {\it A} - also imports the module {\it B}. - -\item {\tt Require \zeroone{Import {\sl |} Export}} {\qualid}$_1$ {\ldots} {\qualid}$_n${\tt .} - - This loads the modules {\qualid}$_1$, \ldots, {\qualid}$_n$ and - their recursive dependencies. If {\tt Import} or {\tt Export} is - given, it also imports {\qualid}$_1$, \ldots, {\qualid}$_n$ and all - the recursive dependencies that were marked or transitively marked - as {\tt Export}. - -\item {\tt From {\dirpath} Require {\qualid}.} - \comindex{From Require} - - This command acts as {\tt Require}, but picks any library whose absolute name - is of the form {\tt{\dirpath}.{\dirpath'}.{\qualid}} for some {\dirpath'}. - This is useful to ensure that the {\qualid} library comes from a given - package by making explicit its absolute root. - -\end{Variants} - -\begin{ErrMsgs} - -\item \errindex{Cannot load {\qualid}: no physical path bound to {\dirpath}} - -\item \errindex{Cannot find library foo in loadpath} - - The command did not find the file {\tt foo.vo}. Either {\tt - foo.v} exists but is not compiled or {\tt foo.vo} is in a directory - which is not in your {\tt LoadPath} (see Section~\ref{loadpath}). - -\item \errindex{Compiled library {\ident}.vo makes inconsistent assumptions over library {\qualid}} - - The command tried to load library file {\ident}.vo that depends on - some specific version of library {\qualid} which is not the one - already loaded in the current {\Coq} session. Probably {\ident}.v - was not properly recompiled with the last version of the file - containing module {\qualid}. - -\item \errindex{Bad magic number} - - \index{Bad-magic-number@{\tt Bad Magic Number}} - The file {\tt{\ident}.vo} was found but either it is not a \Coq\ - compiled module, or it was compiled with an older and incompatible - version of {\Coq}. - -\item \errindex{The file {\ident}.vo contains library {\dirpath} and not - library {\dirpath'}} - - The library file {\dirpath'} is indirectly required by the {\tt - Require} command but it is bound in the current loadpath to the file - {\ident}.vo which was bound to a different library name {\dirpath} - at the time it was compiled. - -\item \errindex{Require is not allowed inside a module or a module type} - - This command is not allowed inside a module or a module type being defined. - It is meant to describe a dependency between compilation units. Note however - that the commands {\tt Import} and {\tt Export} alone can be used inside - modules (see Section~\ref{Import}). - -\end{ErrMsgs} - -\SeeAlso Chapter~\ref{Addoc-coqc} - -\subsection[\tt Print Libraries.]{\tt Print Libraries.\comindex{Print Libraries}} - -This command displays the list of library files loaded in the current -{\Coq} session. For each of these libraries, it also tells if it is -imported. - -\subsection[\tt Declare ML Module {\str$_1$} .. {\str$_n$}.]{\tt Declare ML Module {\str$_1$} .. {\str$_n$}.\comindex{Declare ML Module}} -This commands loads the {\ocaml} compiled files {\str$_1$} {\ldots} -{\str$_n$} (dynamic link). It is mainly used to load tactics -dynamically. -% (see Chapter~\ref{WritingTactics}). - The files are -searched into the current {\ocaml} loadpath (see the command {\tt -Add ML Path} in the Section~\ref{loadpath}). Loading of {\ocaml} -files is only possible under the bytecode version of {\tt coqtop} -(i.e. {\tt coqtop.byte}, see chapter -\ref{Addoc-coqc}), or when {\Coq} has been compiled with a version of -{\ocaml} that supports native {\tt Dynlink} ($\ge$ 3.11). - -\begin{Variants} -\item {\tt Local Declare ML Module {\str$_1$} .. {\str$_n$}.}\\ - This variant is not exported to the modules that import the module - where they occur, even if outside a section. -\end{Variants} - -\begin{ErrMsgs} -\item \errindex{File not found on loadpath : \str} -\item \errindex{Loading of ML object file forbidden in a native {\Coq}} -\end{ErrMsgs} - -\subsection[\tt Print ML Modules.]{\tt Print ML Modules.\comindex{Print ML Modules}} -This print the name of all \ocaml{} modules loaded with \texttt{Declare - ML Module}. To know from where these module were loaded, the user -should use the command \texttt{Locate File} (see Section~\ref{Locate File}) - -\section[Loadpath]{Loadpath} - -Loadpaths are preferably managed using {\Coq} command line options -(see Section~\ref{loadpath}) but there remain vernacular commands to -manage them for practical purposes. Such commands are only meant to be issued in -the toplevel, and using them in source files is discouraged. - -\subsection[\tt Pwd.]{\tt Pwd.\comindex{Pwd}\label{Pwd}} -This command displays the current working directory. - -\subsection[\tt Cd {\str}.]{\tt Cd {\str}.\comindex{Cd}} -This command changes the current directory according to {\str} -which can be any valid path. - -\begin{Variants} -\item {\tt Cd.}\\ - Is equivalent to {\tt Pwd.} -\end{Variants} - -\subsection[\tt Add LoadPath {\str} as {\dirpath}.]{\tt Add LoadPath {\str} as {\dirpath}.\comindex{Add LoadPath}\label{AddLoadPath}} - -This command is equivalent to the command line option {\tt -Q {\str} - {\dirpath}}. It adds the physical directory {\str} to the current {\Coq} -loadpath and maps it to the logical directory {\dirpath}. - -\begin{Variants} -\item {\tt Add LoadPath {\str}.}\\ -Performs as {\tt Add LoadPath {\str} as {\dirpath}} but for the empty directory path. -\end{Variants} - -\subsection[\tt Add Rec LoadPath {\str} as {\dirpath}.]{\tt Add Rec LoadPath {\str} as {\dirpath}.\comindex{Add Rec LoadPath}\label{AddRecLoadPath}} -This command is equivalent to the command line option {\tt -R {\str} - {\dirpath}}. It adds the physical directory {\str} and all its -subdirectories to the current {\Coq} loadpath. - -\begin{Variants} -\item {\tt Add Rec LoadPath {\str}.}\\ -Works as {\tt Add Rec LoadPath {\str} as {\dirpath}} but for the empty logical directory path. -\end{Variants} - -\subsection[\tt Remove LoadPath {\str}.]{\tt Remove LoadPath {\str}.\comindex{Remove LoadPath}} -This command removes the path {\str} from the current \Coq\ loadpath. - -\subsection[\tt Print LoadPath.]{\tt Print LoadPath.\comindex{Print LoadPath}} -This command displays the current \Coq\ loadpath. - -\begin{Variants} -\item {\tt Print LoadPath {\dirpath}.}\\ -Works as {\tt Print LoadPath} but displays only the paths that extend the {\dirpath} prefix. -\end{Variants} - -\subsection[\tt Add ML Path {\str}.]{\tt Add ML Path {\str}.\comindex{Add ML Path}} -This command adds the path {\str} to the current {\ocaml} loadpath (see -the command {\tt Declare ML Module} in the Section~\ref{compiled}). - -\subsection[\tt Add Rec ML Path {\str}.]{\tt Add Rec ML Path {\str}.\comindex{Add Rec ML Path}} -This command adds the directory {\str} and all its subdirectories -to the current {\ocaml} loadpath (see -the command {\tt Declare ML Module} in the Section~\ref{compiled}). - -\subsection[\tt Print ML Path {\str}.]{\tt Print ML Path {\str}.\comindex{Print ML Path}} -This command displays the current {\ocaml} loadpath. -This command makes sense only under the bytecode version of {\tt -coqtop}, i.e. {\tt coqtop.byte} (see the -command {\tt Declare ML Module} in the section -\ref{compiled}). - -\subsection[\tt Locate File {\str}.]{\tt Locate File {\str}.\comindex{Locate - File}\label{Locate File}} -This command displays the location of file {\str} in the current loadpath. -Typically, {\str} is a \texttt{.cmo} or \texttt{.vo} or \texttt{.v} file. - -\subsection[\tt Locate Library {\dirpath}.]{\tt Locate Library {\dirpath}.\comindex{Locate Library}\label{Locate Library}} -This command gives the status of the \Coq\ module {\dirpath}. It tells if the -module is loaded and if not searches in the load path for a module -of logical name {\dirpath}. - -\section{Backtracking} - -The backtracking commands described in this section can only be used -interactively, they cannot be part of a vernacular file loaded via -{\tt Load} or compiled by {\tt coqc}. - -\subsection[\tt Reset \ident.]{\tt Reset \ident.\comindex{Reset}} -This command removes all the objects in the environment since \ident\ -was introduced, including \ident. \ident\ may be the name of a defined -or declared object as well as the name of a section. One cannot reset -over the name of a module or of an object inside a module. - -\begin{ErrMsgs} -\item \ident: \errindex{no such entry} -\end{ErrMsgs} - -\begin{Variants} - \item {\tt Reset Initial.}\comindex{Reset Initial}\\ - Goes back to the initial state, just after the start of the - interactive session. -\end{Variants} - -\subsection[\tt Back.]{\tt Back.\comindex{Back}} - -This commands undoes all the effects of the last vernacular -command. Commands read from a vernacular file via a {\tt Load} are -considered as a single command. Proof management commands -are also handled by this command (see Chapter~\ref{Proof-handling}). -For that, {\tt Back} may have to undo more than one command in order -to reach a state where the proof management information is available. -For instance, when the last command is a {\tt Qed}, the management -information about the closed proof has been discarded. In this case, -{\tt Back} will then undo all the proof steps up to the statement of -this proof. - -\begin{Variants} -\item {\tt Back $n$} \\ - Undoes $n$ vernacular commands. As for {\tt Back}, some extra - commands may be undone in order to reach an adequate state. - For instance {\tt Back n} will not re-enter a closed proof, - but rather go just before that proof. -\end{Variants} - -\begin{ErrMsgs} -\item \errindex{Invalid backtrack} \\ - The user wants to undo more commands than available in the history. -\end{ErrMsgs} - -\subsection[\tt BackTo $\num$.]{\tt BackTo $\num$.\comindex{BackTo}} -\label{sec:statenums} - -This command brings back the system to the state labeled $\num$, -forgetting the effect of all commands executed after this state. -The state label is an integer which grows after each successful command. -It is displayed in the prompt when in \texttt{-emacs} mode. -Just as {\tt Back} (see above), the {\tt BackTo} command now handles -proof states. For that, it may have to undo some -extra commands and end on a state $\num' \leq \num$ if necessary. - -\begin{Variants} -\item {\tt Backtrack $\num_1$ $\num_2$ $\num_3$}.\comindex{Backtrack}\\ - {\tt Backtrack} is a \emph{deprecated} form of {\tt BackTo} which - allows explicitly manipulating the proof environment. The three - numbers $\num_1$, $\num_2$ and $\num_3$ represent the following: -\begin{itemize} -\item $\num_3$: Number of \texttt{Abort} to perform, i.e. the number - of currently opened nested proofs that must be canceled (see - Chapter~\ref{Proof-handling}). -\item $\num_2$: \emph{Proof state number} to unbury once aborts have - been done. {\Coq} will compute the number of \texttt{Undo} to perform - (see Chapter~\ref{Proof-handling}). -\item $\num_1$: State label to reach, as for {\tt BackTo}. -\end{itemize} -\end{Variants} - -\begin{ErrMsgs} -\item \errindex{Invalid backtrack} \\ - The destination state label is unknown. -\end{ErrMsgs} - -\section{Quitting and debugging} - -\subsection[\tt Quit.]{\tt Quit.\comindex{Quit}} -This command permits to quit \Coq. - -\subsection[\tt Drop.]{\tt Drop.\comindex{Drop}\label{Drop}} - -This is used mostly as a debug facility by \Coq's implementors -and does not concern the casual user. -This command permits to leave {\Coq} temporarily and enter the -{\ocaml} toplevel. The {\ocaml} command: - -\begin{flushleft} -\begin{verbatim} -#use "include";; -\end{verbatim} -\end{flushleft} - -\noindent add the right loadpaths and loads some toplevel printers for -all abstract types of \Coq - section\_path, identifiers, terms, judgments, -\dots. You can also use the file \texttt{base\_include} instead, -that loads only the pretty-printers for section\_paths and -identifiers. -% See Section~\ref{test-and-debug} more information on the -% usage of the toplevel. -You can return back to \Coq{} with the command: - -\begin{flushleft} -\begin{verbatim} -go();; -\end{verbatim} -\end{flushleft} - -\begin{Warnings} -\item It only works with the bytecode version of {\Coq} (i.e. {\tt coqtop} called with option {\tt -byte}, see the contents of Section~\ref{binary-images}). -\item You must have compiled {\Coq} from the source package and set the - environment variable \texttt{COQTOP} to the root of your copy of the sources (see Section~\ref{EnvVariables}). -\end{Warnings} - -\subsection[\tt Time \textrm{\textsl{command}}.]{\tt Time \textrm{\textsl{command}}.\comindex{Time} -\label{time}} -This command executes the vernacular command \textrm{\textsl{command}} -and display the time needed to execute it. - -\subsection[\tt Redirect "\textrm{\textsl{file}}" \textrm{\textsl{command}}.]{\tt Redirect "\textrm{\textsl{file}}" \textrm{\textsl{command}}.\comindex{Redirect} -\label{redirect}} -This command executes the vernacular command \textrm{\textsl{command}}, redirecting its output to ``\textrm{\textsl{file}}.out''. - -\subsection[\tt Timeout \textrm{\textsl{int}} \textrm{\textsl{command}}.]{\tt Timeout \textrm{\textsl{int}} \textrm{\textsl{command}}.\comindex{Timeout} -\label{timeout}} - -This command executes the vernacular command \textrm{\textsl{command}}. If -the command has not terminated after the time specified by the integer -(time expressed in seconds), then it is interrupted and an error message -is displayed. - -\subsection[\tt Set Default Timeout \textrm{\textsl{int}}.]{\tt Set - Default Timeout \textrm{\textsl{int}}.\optindex{Default Timeout}} - -After using this command, all subsequent commands behave as if they -were passed to a {\tt Timeout} command. Commands already starting by -a {\tt Timeout} are unaffected. - -\subsection[\tt Unset Default Timeout.]{\tt Unset Default Timeout.\optindex{Default Timeout}} - -This command turns off the use of a default timeout. - -\subsection[\tt Test Default Timeout.]{\tt Test Default Timeout.\optindex{Default Timeout}} - -This command displays whether some default timeout has be set or not. - -\subsection[\tt Fail \textrm{\textsl{command-or-tactic}}.]{\tt Fail \textrm{\textsl{command-or-tactic}}.\comindex{Fail}\label{Fail}} - -For debugging {\Coq} scripts, sometimes it is desirable to know -whether a command or a tactic fails. If the given command or tactic -fails, the {\tt Fail} statement succeeds, without changing the proof -state, and in interactive mode, {\Coq} prints a message confirming the failure. -If the command or tactic succeeds, the statement is an error, and -{\Coq} prints a message indicating that the failure did not occur. - -\section{Controlling display} - -\subsection[\tt Set Silent.]{\tt Set Silent.\optindex{Silent} -\label{Begin-Silent} -\index{Silent mode}} -This command turns off the normal displaying. - -\subsection[\tt Unset Silent.]{\tt Unset Silent.\optindex{Silent}} -This command turns the normal display on. - -\subsection[\tt Set Warnings ``(\nterm{w}$_1$,\ldots,% - \nterm{w}$_n$)''.]{{\tt Set Warnings ``(\nterm{w}$_1$,\ldots,% - \nterm{w}$_n$)''}.\optindex{Warnings}} -\label{SetWarnings} -This command configures the display of warnings. It is experimental, and -expects, between quotes, a comma-separated list of warning names or -categories. Adding~\texttt{-} in front of a warning or category disables it, -adding~\texttt{+} makes it an error. It is possible to use the special -categories \texttt{all} and \texttt{default}, the latter containing the warnings -enabled by default. The flags are interpreted from left to right, so in case of -an overlap, the flags on the right have higher priority, meaning that -\texttt{A,-A} is equivalent to \texttt{-A}. - -\subsection[\tt Set Search Output Name Only.]{\tt Set Search Output Name Only.\optindex{Search Output Name Only} -\label{Search-Output-Name-Only} -\index{Search Output Name Only mode}} -This command restricts the output of search commands to identifier names; turning it on causes invocations of {\tt Search}, {\tt SearchHead}, {\tt SearchPattern}, {\tt SearchRewrite} etc. to omit types from their output, printing only identifiers. - -\subsection[\tt Unset Search Output Name Only.]{\tt Unset Search Output Name Only.\optindex{Search Output Name Only}} -This command turns type display in search results back on. - -\subsection[\tt Set Printing Width {\integer}.]{\tt Set Printing Width {\integer}.\optindex{Printing Width}} -\label{SetPrintingWidth} -This command sets which left-aligned part of the width of the screen -is used for display. - -\subsection[\tt Unset Printing Width.]{\tt Unset Printing Width.\optindex{Printing Width}} -This command resets the width of the screen used for display to its -default value (which is 78 at the time of writing this documentation). - -\subsection[\tt Test Printing Width.]{\tt Test Printing Width.\optindex{Printing Width}} -This command displays the current screen width used for display. - -\subsection[\tt Set Printing Depth {\integer}.]{\tt Set Printing Depth {\integer}.\optindex{Printing Depth}} -This command sets the nesting depth of the formatter used for -pretty-printing. Beyond this depth, display of subterms is replaced by -dots. - -\subsection[\tt Unset Printing Depth.]{\tt Unset Printing Depth.\optindex{Printing Depth}} -This command resets the nesting depth of the formatter used for -pretty-printing to its default value (at the -time of writing this documentation, the default value is 50). - -\subsection[\tt Test Printing Depth.]{\tt Test Printing Depth.\optindex{Printing Depth}} -This command displays the current nesting depth used for display. - -\subsection[\tt Unset Printing Compact Contexts.]{\tt Unset Printing Compact Contexts.\optindex{Printing Compact Contexts}} -This command resets the displaying of goals contexts to non compact -mode (default at the time of writing this documentation). Non compact -means that consecutive variables of different types are printed on -different lines. - -\subsection[\tt Set Printing Compact Contexts.]{\tt Set Printing Compact Contexts.\optindex{Printing Compact Contexts}} -This command sets the displaying of goals contexts to compact mode. -The printer tries to reduce the vertical size of goals contexts by -putting several variables (even if of different types) on the same -line provided it does not exceed the printing width (See {\tt Set - Printing Width} above). - -\subsection[\tt Test Printing Compact Contexts.]{\tt Test Printing Compact Contexts.\optindex{Printing Compact Contexts}} -This command displays the current state of compaction of goal. - - -\subsection[\tt Unset Printing Unfocused.]{\tt Unset Printing Unfocused.\optindex{Printing Unfocused}} -This command resets the displaying of goals to focused goals only -(default). Unfocused goals are created by focusing other goals with -bullets(see~\ref{bullets}) or curly braces (see~\ref{curlybacket}). - -\subsection[\tt Set Printing Unfocused.]{\tt Set Printing Unfocused.\optindex{Printing Unfocused}} -This command enables the displaying of unfocused goals. The goals are -displayed after the focused ones and are distinguished by a separator. - -\subsection[\tt Test Printing Unfocused.]{\tt Test Printing Unfocused.\optindex{Printing Unfocused}} -This command displays the current state of unfocused goals display. - -\subsection[\tt Set Printing Dependent Evars Line.]{\tt Set Printing Dependent Evars Line.\optindex{Printing Dependent Evars Line}} -This command enables the printing of the ``{\tt (dependent evars: \ldots)}'' -line when {\tt -emacs} is passed. - -\subsection[\tt Unset Printing Dependent Evars Line.]{\tt Unset Printing Dependent Evars Line.\optindex{Printing Dependent Evars Line}} -This command disables the printing of the ``{\tt (dependent evars: \ldots)}'' -line when {\tt -emacs} is passed. - -%\subsection{\tt Abstraction ...} -%Not yet documented. - -\section{Controlling the reduction strategies and the conversion algorithm} -\label{Controlling_reduction_strategy} - -{\Coq} provides reduction strategies that the tactics can invoke and -two different algorithms to check the convertibility of types. -The first conversion algorithm lazily -compares applicative terms while the other is a brute-force but efficient -algorithm that first normalizes the terms before comparing them. The -second algorithm is based on a bytecode representation of terms -similar to the bytecode representation used in the ZINC virtual -machine~\cite{Leroy90}. It is especially useful for intensive -computation of algebraic values, such as numbers, and for reflection-based -tactics. The commands to fine-tune the reduction strategies and the -lazy conversion algorithm are described first. - -\subsection[{\tt Opaque} \qualid$_1$ {\ldots} \qualid$_n${\tt .}]{{\tt Opaque} \qualid$_1$ {\ldots} \qualid$_n${\tt .}\comindex{Opaque}\label{Opaque}} -This command has an effect on unfoldable constants, i.e. -on constants defined by {\tt Definition} or {\tt Let} (with an explicit -body), or by a command assimilated to a definition such as {\tt -Fixpoint}, {\tt Program Definition}, etc, or by a proof ended by {\tt -Defined}. The command tells not to unfold -the constants {\qualid$_1$} {\ldots} {\qualid$_n$} in tactics using -$\delta$-conversion (unfolding a constant is replacing it by its -definition). - -{\tt Opaque} has also an effect on the conversion algorithm of {\Coq}, -telling it to delay the unfolding of a constant as much as possible when -{\Coq} has to check the conversion (see Section~\ref{conv-rules}) -of two distinct applied constants. - -The scope of {\tt Opaque} is limited to the current section, or -current file, unless the variant {\tt Global Opaque \qualid$_1$ {\ldots} -\qualid$_n$} is used. - -\SeeAlso sections \ref{Conversion-tactics}, \ref{Automatizing}, -\ref{Theorem} - -\begin{ErrMsgs} -\item \errindex{The reference \qualid\ was not found in the current -environment}\\ - There is no constant referred by {\qualid} in the environment. - Nevertheless, if you asked \texttt{Opaque foo bar} - and if \texttt{bar} does not exist, \texttt{foo} is set opaque. -\end{ErrMsgs} - -\subsection[{\tt Transparent} \qualid$_1$ {\ldots} \qualid$_n${\tt .}]{{\tt Transparent} \qualid$_1$ {\ldots} \qualid$_n${\tt .}\comindex{Transparent}\label{Transparent}} -This command is the converse of {\tt Opaque} and it applies on -unfoldable constants to restore their unfoldability after an {\tt -Opaque} command. - -Note in particular that constants defined by a proof ended by {\tt -Qed} are not unfoldable and {\tt Transparent} has no effect on -them. This is to keep with the usual mathematical practice of {\em -proof irrelevance}: what matters in a mathematical development is the -sequence of lemma statements, not their actual proofs. This -distinguishes lemmas from the usual defined constants, whose actual -values are of course relevant in general. - -The scope of {\tt Transparent} is limited to the current section, or -current file, unless the variant {\tt Global Transparent} \qualid$_1$ -{\ldots} \qualid$_n$ is used. - -\begin{ErrMsgs} -% \item \errindex{Can not set transparent.}\\ -% It is a constant from a required module or a parameter. -\item \errindex{The reference \qualid\ was not found in the current -environment}\\ - There is no constant referred by {\qualid} in the environment. -\end{ErrMsgs} - -\SeeAlso sections \ref{Conversion-tactics}, \ref{Automatizing}, -\ref{Theorem} - -\subsection{{\tt Strategy} {\it level} {\tt [} \qualid$_1$ {\ldots} \qualid$_n$ - {\tt ].}\comindex{Strategy}\comindex{Local Strategy}\label{Strategy}} -This command generalizes the behavior of {\tt Opaque} and {\tt - Transparent} commands. It is used to fine-tune the strategy for -unfolding constants, both at the tactic level and at the kernel -level. This command associates a level to \qualid$_1$ {\ldots} -\qualid$_n$. Whenever two expressions with two distinct head -constants are compared (for instance, this comparison can be triggered -by a type cast), the one with lower level is expanded first. In case -of a tie, the second one (appearing in the cast type) is expanded. - -Levels can be one of the following (higher to lower): -\begin{description} -\item[opaque]: level of opaque constants. They cannot be expanded by - tactics (behaves like $+\infty$, see next item). -\item[\num]: levels indexed by an integer. Level $0$ corresponds - to the default behavior, which corresponds to transparent - constants. This level can also be referred to as {\bf transparent}. - Negative levels correspond to constants to be expanded before normal - transparent constants, while positive levels correspond to constants - to be expanded after normal transparent constants. -\item[expand]: level of constants that should be expanded first - (behaves like $-\infty$) -\end{description} - -These directives survive section and module closure, unless the -command is prefixed by {\tt Local}. In the latter case, the behavior -regarding sections and modules is the same as for the {\tt - Transparent} and {\tt Opaque} commands. - -\subsection{{\tt Print Strategy} \qualid{\tt .}\comindex{Print Strategy}\label{PrintStrategy}} - -This command prints the strategy currently associated to \qualid{}. It fails if -\qualid{} is not an unfoldable reference, that is, neither a variable nor a -constant. - -\begin{ErrMsgs} -\item The reference is not unfoldable. -\end{ErrMsgs} - -\begin{Variants} -\item {\tt Print Strategies}\comindex{Print Strategies}\\ - Print all the currently non-transparent strategies. -\end{Variants} - -\subsection{\tt Declare Reduction \ident\ := {\rm\sl convtactic}.} - -This command allows giving a short name to a reduction expression, -for instance {\tt lazy beta delta [foo bar]}. This short name can -then be used in {\tt Eval \ident\ in ...} or {\tt eval} directives. -This command accepts the {\tt Local} modifier, for discarding -this reduction name at the end of the file or module. For the moment -the name cannot be qualified. In particular declaring the same name -in several modules or in several functor applications will be refused -if these declarations are not local. The name \ident\ cannot be used -directly as an Ltac tactic, but nothing prevent the user to also -perform a {\tt Ltac \ident\ := {\rm\sl convtactic}}. - -\SeeAlso sections \ref{Conversion-tactics} - -\section{Controlling the locality of commands} - -\subsection{{\tt Local}, {\tt Global} -\comindex{Local} -\comindex{Global} -} - -Some commands support a {\tt Local} or {\tt Global} prefix modifier to -control the scope of their effect. There are four kinds of commands: - -\begin{itemize} -\item Commands whose default is to extend their effect both outside the - section and the module or library file they occur in. - - For these commands, the {\tt Local} modifier limits the effect of - the command to the current section or module it occurs in. - - As an example, the {\tt Coercion} (see Section~\ref{Coercions}) - and {\tt Strategy} (see Section~\ref{Strategy}) - commands belong to this category. - -\item Commands whose default behavior is to stop their effect at the - end of the section they occur in but to extent their effect outside - the module or library file they occur in. - - For these commands, the {\tt Local} modifier limits the effect of - the command to the current module if the command does not occur in a - section and the {\tt Global} modifier extends the effect outside the - current sections and current module if the command occurs in a - section. - - As an example, the {\tt Implicit Arguments} (see - Section~\ref{Implicit Arguments}), {\tt Ltac} (see - Chapter~\ref{TacticLanguage}) or {\tt Notation} (see - Section~\ref{Notation}) commands belong to this category. - - Notice that a subclass of these commands do not support extension of - their scope outside sections at all and the {\tt Global} is not - applicable to them. - -\item Commands whose default behavior is to stop their effect at the - end of the section or module they occur in. - - For these commands, the {\tt Global} modifier extends their effect - outside the sections and modules they occurs in. - - The {\tt Transparent} and {\tt Opaque} (see - Section~\ref{Controlling_reduction_strategy}) commands belong to - this category. - -\item Commands whose default behavior is to extend their effect - outside sections but not outside modules when they occur in a - section and to extend their effect outside the module or library - file they occur in when no section contains them. - - For these commands, the {\tt Local} modifier limits the effect to - the current section or module while the {\tt Global} modifier extends - the effect outside the module even when the command occurs in a section. - - The {\tt Set} and {\tt Unset} commands belong to this category. -\end{itemize} - - -%%% Local Variables: -%%% mode: latex -%%% TeX-master: "Reference-Manual" -%%% End: diff --git a/doc/refman/RefMan-pro.tex b/doc/refman/RefMan-pro.tex deleted file mode 100644 index bd74a40d7..000000000 --- a/doc/refman/RefMan-pro.tex +++ /dev/null @@ -1,581 +0,0 @@ -\chapter[Proof handling]{Proof handling\index{Proof editing} -\label{Proof-handling}} -%HEVEA\cutname{proof-handling.html} - -In \Coq's proof editing mode all top-level commands documented in -Chapter~\ref{Vernacular-commands} remain available -and the user has access to specialized commands dealing with proof -development pragmas documented in this section. He can also use some -other specialized commands called {\em tactics}. They are the very -tools allowing the user to deal with logical reasoning. They are -documented in Chapter~\ref{Tactics}.\\ -When switching in editing proof mode, the prompt -\index{Prompt} -{\tt Coq <} is changed into {\tt {\ident} <} where {\ident} is the -declared name of the theorem currently edited. - -At each stage of a proof development, one has a list of goals to -prove. Initially, the list consists only in the theorem itself. After -having applied some tactics, the list of goals contains the subgoals -generated by the tactics. - -To each subgoal is associated a number of -hypotheses called the {\em \index*{local context}} of the goal. -Initially, the local context contains the local variables and -hypotheses of the current section (see Section~\ref{Variable}) and the -local variables and hypotheses of the theorem statement. It is -enriched by the use of certain tactics (see e.g. {\tt intro} in -Section~\ref{intro}). - -When a proof is completed, the message {\tt Proof completed} is -displayed. One can then register this proof as a defined constant in the -environment. Because there exists a correspondence between proofs and -terms of $\lambda$-calculus, known as the {\em Curry-Howard -isomorphism} \cite{How80,Bar91,Gir89,Hue89}, \Coq~ stores proofs as -terms of {\sc Cic}. Those terms are called {\em proof - terms}\index{Proof term}. - -\ErrMsg When one attempts to use a proof editing command out of the -proof editing mode, \Coq~ raises the error message : \errindex{No focused - proof}. - -\section{Switching on/off the proof editing mode} - -The proof editing mode is entered by asserting a statement, which -typically is the assertion of a theorem: - -\begin{quote} -{\tt Theorem {\ident} \zeroone{\binders} : {\form}.\comindex{Theorem} -\label{Theorem}} -\end{quote} - -The list of assertion commands is given in -Section~\ref{Assertions}. The command {\tt Goal} can also be used. - -\subsection[Goal {\form}.]{\tt Goal {\form}.\comindex{Goal}\label{Goal}} - -This is intended for quick assertion of statements, without knowing in -advance which name to give to the assertion, typically for quick -testing of the provability of a statement. If the proof of the -statement is eventually completed and validated, the statement is then -bound to the name {\tt Unnamed\_thm} (or a variant of this name not -already used for another statement). - -\subsection[\tt Qed.]{\tt Qed.\comindex{Qed}\label{Qed}} -This command is available in interactive editing proof mode when the -proof is completed. Then {\tt Qed} extracts a proof term from the -proof script, switches back to {\Coq} top-level and attaches the -extracted proof term to the declared name of the original goal. This -name is added to the environment as an {\tt Opaque} constant. - -\begin{ErrMsgs} -\item \errindex{Attempt to save an incomplete proof} -%\item \ident\ \errindex{already exists}\\ -% The implicit name is already defined. You have then to provide -% explicitly a new name (see variant 3 below). -\item Sometimes an error occurs when building the proof term, -because tactics do not enforce completely the term construction -constraints. - -The user should also be aware of the fact that since the proof term is -completely rechecked at this point, one may have to wait a while when -the proof is large. In some exceptional cases one may even incur a -memory overflow. -\end{ErrMsgs} - -\begin{Variants} - -\item {\tt Defined.} -\comindex{Defined} -\label{Defined} - - Defines the proved term as a transparent constant. - -\item {\tt Save {\ident}.} - - Forces the name of the original goal to be {\ident}. This command - (and the following ones) can only be used if the original goal has - been opened using the {\tt Goal} command. - -\end{Variants} - -\subsection[\tt Admitted.]{\tt Admitted.\comindex{Admitted}\label{Admitted}} -This command is available in interactive editing proof mode to give up -the current proof and declare the initial goal as an axiom. - -\subsection[\tt Proof {\term}.]{\tt Proof {\term}.\comindex{Proof} -\label{BeginProof}} -This command applies in proof editing mode. It is equivalent to {\tt - exact {\term}. Qed.} That is, you have to give the full proof in -one gulp, as a proof term (see Section~\ref{exact}). - -\variant {\tt Proof.} - - Is a noop which is useful to delimit the sequence of tactic commands - which start a proof, after a {\tt Theorem} command. It is a good - practice to use {\tt Proof.} as an opening parenthesis, closed in - the script with a closing {\tt Qed.} - -\SeeAlso {\tt Proof with {\tac}.} in Section~\ref{ProofWith}. - -\subsection[{\tt Proof using} {\ident$_1$} {\ldots} {\ident$_n$}{\tt .}] -{{\tt Proof using} {\ident$_1$} {\ldots} {\ident$_n$}{\tt .} -\comindex{Proof using} \label{ProofUsing}} - -This command applies in proof editing mode. -It declares the set of section variables (see~\ref{Variable}) -used by the proof. At {\tt Qed} time, the system will assert that -the set of section variables actually used in the proof is a subset of -the declared one. - -The set of declared variables is closed under type dependency. -For example if {\tt T} is variable and {\tt a} is a variable of -type {\tt T}, the commands {\tt Proof using a} and -{\tt Proof using T a} are actually equivalent. - -\variant {\tt Proof using} {\ident$_1$} {\ldots} {\ident$_n$} {\tt with} {\tac}{\tt .} -in Section~\ref{ProofWith}. - -\variant {\tt Proof using All.} - - Use all section variables. - -\variant {\tt Proof using Type.} -\variant {\tt Proof using.} - - Use only section variables occurring in the statement. - -\variant {\tt Proof using Type*.} - - The {\tt *} operator computes the forward transitive closure. - E.g. if the variable {\tt H} has type {\tt p < 5} then {\tt H} is - in {\tt p*} since {\tt p} occurs in the type of {\tt H}. - {\tt Type* } is the forward transitive closure of the entire set of - section variables occurring in the statement. - -\variant {\tt Proof using -( \ident$_1$} {\ldots} {\tt \ident$_n$ ).} - - Use all section variables except {\ident$_1$} {\ldots} {\ident$_n$}. - -\variant {\tt Proof using \nterm{collection}$_1$ + \nterm{collection}$_2$ .} - -\variant {\tt Proof using \nterm{collection}$_1$ - \nterm{collection}$_2$ .} - -\variant {\tt Proof using \nterm{collection} - ( \ident$_1$} {\ldots} {\tt \ident$_n$ ).} - -\variant {\tt Proof using \nterm{collection} * .} - - Use section variables being, respectively, in the set union, set difference, - set complement, set forward transitive closure. - See Section~\ref{Collection} to know how to form a named - collection. - The {\tt *} operator binds stronger than {\tt +} and {\tt -}. - -\subsubsection{{\tt Proof using} options} -\optindex{Default Proof Using} -\optindex{Suggest Proof Using} -% \optindex{Proof Using Clear Unused} - -The following options modify the behavior of {\tt Proof using}. - -\variant {\tt Set Default Proof Using "expression".} - - Use {\tt expression} as the default {\tt Proof using} value. - E.g. {\tt Set Default Proof Using "a b".} will complete all {\tt Proof } - commands not followed by a {\tt using} part with {\tt using a b}. - -\variant {\tt Set Suggest Proof Using.} - - When {\tt Qed} is performed, suggest a {\tt using} annotation if - the user did not provide one. - -% \variant{\tt Unset Proof Using Clear Unused.} -% -% When {\tt Proof using a} all section variables but for {\tt a} and -% the variables used in the type of {\tt a} are cleared. -% This option can be used to turn off this behavior. -% -\subsubsection[\tt Collection]{Name a set of section hypotheses for {\tt Proof using}} -\comindex{Collection}\label{Collection} - -The command {\tt Collection} can be used to name a set of section hypotheses, -with the purpose of making {\tt Proof using} annotations more compact. - -\variant {\tt Collection Some := x y z.} - - Define the collection named "Some" containing {\tt x y} and {\tt z} - -\variant {\tt Collection Fewer := Some - x.} - - Define the collection named "Fewer" containing only {\tt x y} - -\variant {\tt Collection Many := Fewer + Some.} -\variant {\tt Collection Many := Fewer - Some.} - - Define the collection named "Many" containing the set union or set difference - of "Fewer" and "Some". - -\variant {\tt Collection Many := Fewer - (x y).} - - Define the collection named "Many" containing the set difference - of "Fewer" and the unnamed collection {\tt x y}. - -\subsection[\tt Abort.]{\tt Abort.\comindex{Abort}} - -This command cancels the current proof development, switching back to -the previous proof development, or to the \Coq\ toplevel if no other -proof was edited. - -\begin{ErrMsgs} -\item \errindex{No focused proof (No proof-editing in progress)} -\end{ErrMsgs} - -\begin{Variants} - -\item {\tt Abort {\ident}.} - - Aborts the editing of the proof named {\ident}. - -\item {\tt Abort All.} - - Aborts all current goals, switching back to the \Coq\ toplevel. - -\end{Variants} - -%%%% -\subsection[\tt Existential {\num} := {\term}.]{\tt Existential {\num} := {\term}.\comindex{Existential} -\label{Existential}} - -This command instantiates an existential variable. {\tt \num} -is an index in the list of uninstantiated existential variables -displayed by {\tt Show Existentials} (described in Section~\ref{Show}). - -This command is intended to be used to instantiate existential -variables when the proof is completed but some uninstantiated -existential variables remain. To instantiate existential variables -during proof edition, you should use the tactic {\tt instantiate}. - -\SeeAlso {\tt instantiate (\num:= \term).} in Section~\ref{instantiate}. -\SeeAlso {\tt Grab Existential Variables.} below. - -\subsection[\tt Grab Existential Variables.]{\tt Grab Existential Variables.\comindex{Grab Existential Variables} -\label{GrabEvars}} - -This command can be run when a proof has no more goal to be solved but has remaining -uninstantiated existential variables. It takes every uninstantiated existential variable -and turns it into a goal. - -%%%%%%%% -\section{Navigation in the proof tree} -%%%%%%%% - -\subsection[\tt Undo.]{\tt Undo.\comindex{Undo}} - -This command cancels the effect of the last command. Thus, it -backtracks one step. - -\begin{Variants} - -\item {\tt Undo {\num}.} - - Repeats {\tt Undo} {\num} times. - -\end{Variants} - -\subsection[\tt Restart.]{\tt Restart.\comindex{Restart}} -This command restores the proof editing process to the original goal. - -\begin{ErrMsgs} -\item \errindex{No focused proof to restart} -\end{ErrMsgs} - -\subsection[\tt Focus.]{\tt Focus.\comindex{Focus}} -This focuses the attention on the first subgoal to prove and the printing -of the other subgoals is suspended until the focused subgoal is -solved or unfocused. This is useful when there are many current -subgoals which clutter your screen. - -\begin{Variant} -\item {\tt Focus {\num}.}\\ -This focuses the attention on the $\num^{th}$ subgoal to prove. -\end{Variant} - -\emph{This command is deprecated since 8.8: prefer the use of bullets or - focusing brackets instead, including {\tt {\num}: \{}}. - -\subsection[\tt Unfocus.]{\tt Unfocus.\comindex{Unfocus}} -This command restores to focus the goal that were suspended by the -last {\tt Focus} command. - -\emph{This command is deprecated since 8.8.} - -\subsection[\tt Unfocused.]{\tt Unfocused.\comindex{Unfocused}} -Succeeds in the proof if fully unfocused, fails if there are some -goals out of focus. - -\subsection[\tt \{ \textrm{and} \}]{\tt \{ \textrm{and} \}\comindex{\{}\comindex{\}}}\label{curlybacket} -The command {\tt \{} (without a terminating period) focuses on the -first goal, much like {\tt Focus.} does, however, the subproof can -only be unfocused when it has been fully solved (\emph{i.e.} when -there is no focused goal left). Unfocusing is then handled by {\tt \}} -(again, without a terminating period). See also example in next section. - -Note that when a focused goal is proved a message is displayed -together with a suggestion about the right bullet or {\tt \}} to -unfocus it or focus the next one. - -\begin{Variants} - -\item {\tt {\num}: \{}\\ -This focuses on the $\num^{th}$ subgoal to prove. - -\end{Variants} - -\begin{ErrMsgs} -\item \errindex{This proof is focused, but cannot be unfocused - this way} You are trying to use {\tt \}} but the current subproof - has not been fully solved. -\item \errindex{No such goal} -\item \errindex{Brackets only support the single numbered goal selector} -\item see also error message about bullets below. -\end{ErrMsgs} - -\subsection[Bullets]{Bullets\comindex{+ (command)} - \comindex{- (command)}\comindex{* (command)}\index{Bullets}}\label{bullets} -Alternatively to {\tt \{} and {\tt \}}, proofs can be structured with -bullets. The use of a bullet $b$ for the first time focuses on the -first goal $g$, the same bullet cannot be used again until the proof -of $g$ is completed, then it is mandatory to focus the next goal with $b$. The -consequence is that $g$ and all goals present when $g$ was focused are -focused with the same bullet $b$. See the example below. - -Different bullets can be used to nest levels. The scope of bullet does -not go beyond enclosing {\tt \{} and {\tt \}}, so bullets can be -reused as further nesting levels provided they are delimited by these. -Available bullets are {\tt -}, {\tt +}, {\tt *}, {\tt --}, {\tt ++}, {\tt **}, -{\tt ---}, {\tt +++}, {\tt ***}, ... (without a -terminating period). - -Note again that when a focused goal is proved a message is displayed -together with a suggestion about the right bullet or {\tt \}} to -unfocus it or focus the next one. - -Remark: In {\ProofGeneral} (Emacs interface to {\Coq}), you must use -bullets with the priority ordering shown above to have a correct -indentation. For example {\tt -} must be the outer bullet and {\tt **} -the inner one in the example below. - -The following example script illustrates all these features: -\begin{coq_example*} -Goal (((True/\True)/\True)/\True)/\True. -Proof. - split. - - split. - + split. - ** { split. - - trivial. - - trivial. - } - ** trivial. - + trivial. - - assert True. - { trivial. } - assumption. -\end{coq_example*} - - -\begin{ErrMsgs} -\item \errindex{Wrong bullet {\abullet}1 : Current bullet - {\abullet}2 is not finished.} - - Before using bullet {\abullet}1 again, you should first finish - proving the current focused goal. Note that {\abullet}1 and - {\abullet}2 may be the same. - -\item \errindex{Wrong bullet {\abullet}1 : Bullet {\abullet}2 - is mandatory here.} You must put {\abullet}2 to focus next goal. - No other bullet is allowed here. - - -\item \errindex{No such goal. Focus next goal with bullet - {\abullet}.} - - You tried to applied a tactic but no goal where under focus. Using - {\abullet} is mandatory here. - -\item \errindex{No such goal. Try unfocusing with {"{\tt \}}"}.} You - just finished a goal focused by {\tt \{}, you must unfocus it with "{\tt \}}". - -\end{ErrMsgs} - -\subsection[\tt Set Bullet Behavior.]{\tt Set Bullet Behavior.\optindex{Bullet Behavior}} - -The bullet behavior can be controlled by the following commands. - -\begin{quote} -Set Bullet Behavior "None". -\end{quote} - -This makes bullets inactive. - -\begin{quote} -Set Bullet Behavior "Strict Subproofs". -\end{quote} - -This makes bullets active (this is the default behavior). - -\section{Requesting information} - -\subsection[\tt Show.]{\tt Show.\comindex{Show}\label{Show}} -This command displays the current goals. - -\begin{Variants} -\item {\tt Show {\num}.}\\ - Displays only the {\num}-th subgoal.\\ -\begin{ErrMsgs} -\item \errindex{No such goal} -\item \errindex{No focused proof} -\end{ErrMsgs} - -\item {\tt Show {\ident}.}\\ - Displays the named goal {\ident}. - This is useful in particular to display a shelved goal but only works - if the corresponding existential variable has been named by the user - (see~\ref{ExistentialVariables}) as in the following example. - -\begin{coq_eval} -Reset Initial. -\end{coq_eval} - -\begin{coq_example*} -Goal exists n, n = 0. - eexists ?[n]. -\end{coq_example*} -\begin{coq_example} - Show n. -\end{coq_example} - -\item {\tt Show Script.}\comindex{Show Script}\\ - Displays the whole list of tactics applied from the beginning - of the current proof. - This tactics script may contain some holes (subgoals not yet proved). - They are printed under the form \verb!<Your Tactic Text here>!. - -\item {\tt Show Proof.}\comindex{Show Proof}\\ -It displays the proof term generated by the -tactics that have been applied. -If the proof is not completed, this term contain holes, -which correspond to the sub-terms which are still to be -constructed. These holes appear as a question mark indexed -by an integer, and applied to the list of variables in -the context, since it may depend on them. -The types obtained by abstracting away the context from the -type of each hole-placer are also printed. - -\item {\tt Show Conjectures.}\comindex{Show Conjectures}\\ -It prints the list of the names of all the theorems that -are currently being proved. -As it is possible to start proving a previous lemma during -the proof of a theorem, this list may contain several -names. - -\item{\tt Show Intro.}\comindex{Show Intro}\\ -If the current goal begins by at least one product, this command -prints the name of the first product, as it would be generated by -an anonymous {\tt intro}. The aim of this command is to ease the -writing of more robust scripts. For example, with an appropriate -{\ProofGeneral} macro, it is possible to transform any anonymous {\tt - intro} into a qualified one such as {\tt intro y13}. -In the case of a non-product goal, it prints nothing. - -\item{\tt Show Intros.}\comindex{Show Intros}\\ -This command is similar to the previous one, it simulates the naming -process of an {\tt intros}. - -\item{\tt Show Existentials.\label{ShowExistentials}}\comindex{Show Existentials} -\\ It displays -the set of all uninstantiated existential variables in the current proof tree, -along with the type and the context of each variable. - -\item{\tt Show Match {\ident}.\label{ShowMatch}}\comindex{Show Match}\\ -This variant displays a template of the Gallina {\tt match} construct -with a branch for each constructor of the type {\ident}. - -Example: - -\begin{coq_example} -Show Match nat. -\end{coq_example} -\begin{ErrMsgs} -\item \errindex{Unknown inductive type} -\end{ErrMsgs} - -\item{\tt Show Universes.\label{ShowUniverses}}\comindex{Show Universes} -\\ It displays the set of all universe constraints and its -normalized form at the current stage of the proof, useful for -debugging universe inconsistencies. - -\end{Variants} - - -\subsection[\tt Guarded.]{\tt Guarded.\comindex{Guarded}\label{Guarded}} - -Some tactics (e.g. refine \ref{refine}) allow to build proofs using -fixpoint or co-fixpoint constructions. Due to the incremental nature -of interactive proof construction, the check of the termination (or -guardedness) of the recursive calls in the fixpoint or cofixpoint -constructions is postponed to the time of the completion of the proof. - -The command \verb!Guarded! allows checking if the guard condition for -fixpoint and cofixpoint is violated at some time of the construction -of the proof without having to wait the completion of the proof." - - -\section{Controlling the effect of proof editing commands} - -\subsection[\tt Set Hyps Limit {\num}.]{\tt Set Hyps Limit {\num}.\optindex{Hyps Limit}} -This command sets the maximum number of hypotheses displayed in -goals after the application of a tactic. -All the hypotheses remains usable in the proof development. - - -\subsection[\tt Unset Hyps Limit.]{\tt Unset Hyps Limit.\optindex{Hyps Limit}} -This command goes back to the default mode which is to print all -available hypotheses. - - -\subsection[\tt Set Automatic Introduction.]{\tt Set Automatic Introduction.\optindex{Automatic Introduction}\label{Set Automatic Introduction}} - -The option {\tt Automatic Introduction} controls the way binders are -handled in assertion commands such as {\tt Theorem {\ident} - \zeroone{\binders} : {\form}}. When the option is set, which is the -default, {\binders} are automatically put in the local context of the -goal to prove. - -The option can be unset by issuing {\tt Unset Automatic Introduction}. -When the option is unset, {\binders} are discharged on the statement -to be proved and a tactic such as {\tt intro} (see -Section~\ref{intro}) has to be used to move the assumptions to the -local context. - -\section{Controlling memory usage\comindex{Optimize Proof}\comindex{Optimize Heap}} - -When experiencing high memory usage the following commands can be -used to force Coq to optimize some of its internal data structures. - -\subsection[\tt Optimize Proof.]{\tt Optimize Proof.} - -This command forces Coq to shrink the data structure used to represent -the ongoing proof. - -\subsection[\tt Optimize Heap.]{\tt Optimize Heap.\label{vernac-optimizeheap}} - -This command forces the OCaml runtime to perform a heap compaction. -This is in general an expensive operation. See: \\ -\ \url{http://caml.inria.fr/pub/docs/manual-ocaml/libref/Gc.html#VALcompact} \\ -There is also an analogous tactic {\tt optimize\_heap} (see~\ref{tactic-optimizeheap}). - -%%% Local Variables: -%%% mode: latex -%%% TeX-master: "Reference-Manual" -%%% End: diff --git a/doc/refman/RefMan-uti.tex b/doc/refman/RefMan-uti.tex deleted file mode 100644 index 962aa98b6..000000000 --- a/doc/refman/RefMan-uti.tex +++ /dev/null @@ -1,482 +0,0 @@ -\chapter[Utilities]{Utilities\label{Utilities}} -%HEVEA\cutname{tools.html} - -The distribution provides utilities to simplify some tedious works -beside proof development, tactics writing or documentation. - -\section[Using Coq as a library]{Using Coq as a library} - -In previous versions, \texttt{coqmktop} was used to build custom -toplevels --- for example for better debugging or custom static -linking. Nowadays, the preferred method is to use \texttt{ocamlfind}. - -The most basic custom toplevel is built using: -\begin{quotation} -\texttt{\% ocamlfind ocamlopt -thread -rectypes -linkall -linkpkg - -package coq.toplevel toplevel/coqtop\_bin.ml -o my\_toplevel.native} -\end{quotation} - -For example, to statically link LTAC, you can just do: -\begin{quotation} -\texttt{\% ocamlfind ocamlopt -thread -rectypes -linkall -linkpkg - -package coq.toplevel -package coq.ltac toplevel/coqtop\_bin.ml -o my\_toplevel.native} -\end{quotation} -and similarly for other plugins. - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\section[Building a \Coq\ project with {\tt coq\_makefile}] -{Building a \Coq\ project with {\tt coq\_makefile} -\label{Makefile} -\ttindex{Makefile} -\ttindex{coq\_Makefile} -\ttindex{\_CoqProject}} - -The majority of \Coq\ projects are very similar: a collection of {\tt .v} -files and eventually some {\tt .ml} ones (a \Coq\ plugin). The main piece -of metadata needed in order to build the project are the command -line options to {\tt coqc} (e.g. {\tt -R, -I}, -\SeeAlso Section~\ref{coqoptions}). Collecting the list of files and -options is the job of the {\tt \_CoqProject} file. - -A simple example of a {\tt \_CoqProject} file follows: - -\begin{verbatim} --R theories/ MyCode -theories/foo.v -theories/bar.v --I src/ -src/baz.ml4 -src/bazaux.ml -src/qux_plugin.mlpack -\end{verbatim} - -Currently, both \CoqIDE{} and Proof General (version $\geq$ 4.3pre) understand -{\tt \_CoqProject} files and invoke \Coq\ with the desired options. - -The {\tt coq\_makefile} utility can be used to set up a build infrastructure -for the \Coq\ project based on makefiles. The recommended way of -invoking {\tt coq\_makefile} is the following one: - -\begin{verbatim} -coq_makefile -f _CoqProject -o CoqMakefile -\end{verbatim} - -Such command generates the following files: -\begin{description} - \item[{\tt CoqMakefile}] is a generic makefile for GNU Make that provides targets to build the project (both {\tt .v} and {\tt .ml*} files), to install it system-wide in the {\tt coq-contrib} directory (i.e. where \Coq\ is installed) as well as to invoke {\tt coqdoc} to generate html documentation. - - \item[{\tt CoqMakefile.conf}] contains make variables assignments that reflect the contents of the {\tt \_CoqProject} file as well as the path relevant to \Coq{}. -\end{description} - -An optional file {\bf {\tt CoqMakefile.local}} can be provided by the user in order to extend {\tt CoqMakefile}. In particular one can declare custom actions to be performed before or after the build process. Similarly one can customize the install target or even provide new targets. Extension points are documented in paragraph \ref{coqmakefile:local}. - -The extensions of the files listed in {\tt \_CoqProject} is -used in order to decide how to build them. In particular: - -\begin{itemize} -\item {\Coq} files must use the \texttt{.v} extension -\item {\ocaml} files must use the \texttt{.ml} or \texttt{.mli} extension -\item {\ocaml} files that require pre processing for syntax extensions (like {\tt VERNAC EXTEND}) must use the \texttt{.ml4} extension -\item In order to generate a plugin one has to list all {\ocaml} modules (i.e. ``Baz'' for ``baz.ml'') in a \texttt{.mlpack} file (or \texttt{.mllib} file). -\end{itemize} - -The use of \texttt{.mlpack} files has to be preferred over \texttt{.mllib} -files, since it results in a ``packed'' plugin: All auxiliary -modules (as {\tt Baz} and {\tt Bazaux}) are hidden inside -the plugin's ``name space'' ({\tt Qux\_plugin}). -This reduces the chances of begin unable to load two distinct plugins -because of a clash in their auxiliary module names. - -\paragraph{CoqMakefile.local} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\label{coqmakefile:local} - -The optional file {\tt CoqMakefile.local} is included by the generated file -{\tt CoqMakefile}. Such can contain two kinds of directives. - -\begin{description} - \item[Variable assignment] to the variables listed in the {\tt Parameters} - section of the generated makefile. Here we describe only few of them. - \begin{description} - \item[CAMLPKGS] can be used to specify third party findlib packages, and is - passed to the OCaml compiler on building or linking of modules. - Eg: {\tt -package yojson}. - \item[CAMLFLAGS] can be used to specify additional flags to the OCaml - compiler, like {\tt -bin-annot} or {\tt -w...}. - \item[COQC, COQDEP, COQDOC] can be set in order to use alternative - binaries (e.g. wrappers) - \item[COQ\_SRC\_SUBDIRS] can be extended by including other paths in which {\tt *.cm*} files are searched. For example {\tt COQ\_SRC\_SUBDIRS+=user-contrib/Unicoq} lets you build a plugin containing OCaml code that depends on the OCaml code of {\tt Unicoq}. - \end{description} -\item[Rule extension] - The following makefile rules can be extended. For example -\begin{verbatim} -pre-all:: - echo "This line is print before making the all target" -install-extra:: - cp ThisExtraFile /there/it/goes -\end{verbatim} - \begin{description} - \item[pre-all::] run before the {\tt all} target. One can use this - to configure the project, or initialize sub modules or check - dependencies are met. - \item[post-all::] run after the {\tt all} target. One can use this - to run a test suite, or compile extracted code. - \item[install-extra::] run after {\tt install}. One can use this - to install extra files. - \item[install-doc::] One can use this to install extra doc. - \item[uninstall::] - \item[uninstall-doc::] - \item[clean::] - \item[cleanall::] - \item[archclean::] - \item[merlin-hook::] One can append lines to the generated {\tt .merlin} - file extending this target. - \end{description} -\end{description} - -\paragraph{Timing targets and performance testing} %%%%%%%%%%%%%%%%%%%%%%%%%%% -The generated \texttt{Makefile} supports the generation of two kinds -of timing data: per-file build-times, and per-line times for an -individual file. - -The following targets and \texttt{Makefile} variables allow collection -of per-file timing data: -\begin{itemize} -\item \texttt{TIMED=1} --- passing this variable will cause - \texttt{make} to emit a line describing the user-space build-time - and peak memory usage for each file built. - - \texttt{Note}: On Mac OS, this works best if you've installed - \texttt{gnu-time}. - - \texttt{Example}: For example, the output of \texttt{make TIMED=1} - may look like this: -\begin{verbatim} -COQDEP Fast.v -COQDEP Slow.v -COQC Slow.v -Slow (user: 0.34 mem: 395448 ko) -COQC Fast.v -Fast (user: 0.01 mem: 45184 ko) -\end{verbatim} -\item \texttt{pretty-timed} --- this target stores the output of - \texttt{make TIMED=1} into \texttt{time-of-build.log}, and displays - a table of the times, sorted from slowest to fastest, which is also - stored in \texttt{time-of-build-pretty.log}. If you want to - construct the log for targets other than the default one, you can - pass them via the variable \texttt{TGTS}, e.g., \texttt{make - pretty-timed TGTS="a.vo b.vo"}. - - \texttt{Note}: This target requires \texttt{python} to build the table. - - \texttt{Note}: This target will \emph{append} to the timing log; if - you want a fresh start, you must remove the file - \texttt{time-of-build.log} or run \texttt{make cleanall}. - - \texttt{Example}: For example, the output of \texttt{make - pretty-timed} may look like this: -\begin{verbatim} -COQDEP Fast.v -COQDEP Slow.v -COQC Slow.v -Slow (user: 0.36 mem: 393912 ko) -COQC Fast.v -Fast (user: 0.05 mem: 45992 ko) -Time | File Name --------------------- -0m00.41s | Total --------------------- -0m00.36s | Slow -0m00.05s | Fast -\end{verbatim} -\item \texttt{print-pretty-timed-diff} --- this target builds a table - of timing changes between two compilations; run \texttt{make - make-pretty-timed-before} to build the log of the ``before'' - times, and run \texttt{make make-pretty-timed-after} to build the - log of the ``after'' times. The table is printed on the command - line, and stored in \texttt{time-of-build-both.log}. This target is - most useful for profiling the difference between two commits to a - repo. - - \texttt{Note}: This target requires \texttt{python} to build the table. - - \texttt{Note}: The \texttt{make-pretty-timed-before} and - \texttt{make-pretty-timed-after} targets will \emph{append} to the - timing log; if you want a fresh start, you must remove the files - \texttt{time-of-build-before.log} and - \texttt{time-of-build-after.log} or run \texttt{make cleanall} - \emph{before} building either the ``before'' or ``after'' targets. - - \texttt{Note}: The table will be sorted first by absolute time - differences rounded towards zero to a whole-number of seconds, then - by times in the ``after'' column, and finally lexicographically by - file name. This will put the biggest changes in either direction - first, and will prefer sorting by build-time over subsecond changes - in build time (which are frequently noise); lexicographic sorting - forces an order on files which take effectively no time to compile. - - \texttt{Example}: For example, the output table from \texttt{make - print-pretty-timed-diff} may look like this: -\begin{verbatim} -After | File Name | Before || Change | % Change --------------------------------------------------------- -0m00.39s | Total | 0m00.35s || +0m00.03s | +11.42% --------------------------------------------------------- -0m00.37s | Slow | 0m00.01s || +0m00.36s | +3600.00% -0m00.02s | Fast | 0m00.34s || -0m00.32s | -94.11% -\end{verbatim} -\end{itemize} - -The following targets and \texttt{Makefile} variables allow collection -of per-line timing data: -\begin{itemize} -\item \texttt{TIMING=1} --- passing this variable will cause - \texttt{make} to use \texttt{coqc -time} to write to a - \texttt{.v.timing} file for each \texttt{.v} file compiled, which - contains line-by-line timing information. - - \texttt{Example}: For example, running \texttt{make all TIMING=1} may - result in a file like this: -\begin{verbatim} -Chars 0 - 26 [Require~Coq.ZArith.BinInt.] 0.157 secs (0.128u,0.028s) -Chars 27 - 68 [Declare~Reduction~comp~:=~vm_c...] 0. secs (0.u,0.s) -Chars 69 - 162 [Definition~foo0~:=~Eval~comp~i...] 0.153 secs (0.136u,0.019s) -Chars 163 - 208 [Definition~foo1~:=~Eval~comp~i...] 0.239 secs (0.236u,0.s) -\end{verbatim} - -\item \texttt{print-pretty-single-time-diff - BEFORE=path/to/file.v.before-timing - AFTER=path/to/file.v.after-timing} --- this target will make a - sorted table of the per-line timing differences between the timing - logs in the \texttt{BEFORE} and \texttt{AFTER} files, display it, - and save it to the file specified by the - \texttt{TIME\_OF\_PRETTY\_BUILD\_FILE} variable, which defaults to - \texttt{time-of-build-pretty.log}. - - To generate the \texttt{.v.before-timing} or - \texttt{.v.after-timing} files, you should pass - \texttt{TIMING=before} or \texttt{TIMING=after} rather than - \texttt{TIMING=1}. - - \texttt{Note}: The sorting used here is the same as in the - \texttt{print-pretty-timed-diff} target. - - \texttt{Note}: This target requires \texttt{python} to build the table. - - \texttt{Example}: For example, running - \texttt{print-pretty-single-time-diff} might give a table like this: -\begin{verbatim} -After | Code | Before || Change | % Change ---------------------------------------------------------------------------------------------------- -0m00.50s | Total | 0m04.17s || -0m03.66s | -87.96% ---------------------------------------------------------------------------------------------------- -0m00.145s | Chars 069 - 162 [Definition~foo0~:=~Eval~comp~i...] | 0m00.192s || -0m00.04s | -24.47% -0m00.126s | Chars 000 - 026 [Require~Coq.ZArith.BinInt.] | 0m00.143s || -0m00.01s | -11.88% - N/A | Chars 027 - 068 [Declare~Reduction~comp~:=~nati...] | 0m00.s || +0m00.00s | N/A -0m00.s | Chars 027 - 068 [Declare~Reduction~comp~:=~vm_c...] | N/A || +0m00.00s | N/A -0m00.231s | Chars 163 - 208 [Definition~foo1~:=~Eval~comp~i...] | 0m03.836s || -0m03.60s | -93.97% -\end{verbatim} - -\item \texttt{all.timing.diff}, \texttt{path/to/file.v.timing.diff} - --- The \texttt{path/to/file.v.timing.diff} target will make a - \texttt{.v.timing.diff} file for the corresponding \texttt{.v} file, - with a table as would be generated by the - \texttt{print-pretty-single-time-diff} target; it depends on having - already made the corresponding \texttt{.v.before-timing} and - \texttt{.v.after-timing} files, which can be made by passing - \texttt{TIMING=before} and \texttt{TIMING=after}. The - \texttt{all.timing.diff} target will make such timing difference - files for all of the \texttt{.v} files that the \texttt{Makefile} - knows about. It will fail if some \texttt{.v.before-timing} or - \texttt{.v.after-timing} files don't exist. - - \texttt{Note}: This target requires \texttt{python} to build the table. -\end{itemize} - -\paragraph{Reusing/extending the generated Makefile} %%%%%%%%%%%%%%%%%%%%%%%%% - -Including the generated makefile with an {\tt include} directive is discouraged. -The contents of this file, including variable names -and status of rules shall change in the future. Users are advised to -include {\tt Makefile.conf} or call a target of the generated Makefile -as in {\tt make -f Makefile target} from another Makefile. - -One way to get access to all targets of the generated -\texttt{CoqMakefile} is to have a generic target for invoking unknown -targets. For example: -\begin{verbatim} -# KNOWNTARGETS will not be passed along to CoqMakefile -KNOWNTARGETS := CoqMakefile extra-stuff extra-stuff2 -# KNOWNFILES will not get implicit targets from the final rule, and so -# depending on them won't invoke the submake -# Warning: These files get declared as PHONY, so any targets depending -# on them always get rebuilt -KNOWNFILES := Makefile _CoqProject - -.DEFAULT_GOAL := invoke-coqmakefile - -CoqMakefile: Makefile _CoqProject - $(COQBIN)coq_makefile -f _CoqProject -o CoqMakefile - -invoke-coqmakefile: CoqMakefile - $(MAKE) --no-print-directory -f CoqMakefile $(filter-out $(KNOWNTARGETS),$(MAKECMDGOALS)) - -.PHONY: invoke-coqmakefile $(KNOWNFILES) - -#################################################################### -## Your targets here ## -#################################################################### - -# This should be the last rule, to handle any targets not declared above -%: invoke-coqmakefile - @true -\end{verbatim} - -\paragraph{Building a subset of the targets with -j} %%%%%%%%%%%%%%%%%%%%%%%%% - -To build, say, two targets \texttt{foo.vo} and \texttt{bar.vo} -in parallel one can use \texttt{make only TGTS="foo.vo bar.vo" -j}. - -Note that \texttt{make foo.vo bar.vo -j} has a different meaning for -the make utility, in particular it may build a shared prerequisite twice. - -\paragraph{Notes for users of {\tt coq\_makefile} with version $<$ 8.7} %%%%%% - -\begin{itemize} -\item Support for ``sub-directory'' is deprecated. To perform actions before - or after the build (like invoking make on a subdirectory) one can - hook in {\tt pre-all} and {\tt post-all} extension points -\item \texttt{-extra-phony} and \texttt{-extra} are deprecated. To provide - additional target ({\tt .PHONY} or not) please use - {\tt CoqMakefile.local} -\end{itemize} - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\section[Modules dependencies]{Modules dependencies\label{Dependencies}\index{Dependencies} - \ttindex{coqdep}} - -In order to compute modules dependencies (so to use {\tt make}), -\Coq\ comes with an appropriate tool, {\tt coqdep}. - -{\tt coqdep} computes inter-module dependencies for \Coq\ and -\ocaml\ programs, and prints the dependencies on the standard -output in a format readable by make. When a directory is given as -argument, it is recursively looked at. - -Dependencies of \Coq\ modules are computed by looking at {\tt Require} -commands ({\tt Require}, {\tt Requi\-re Export}, {\tt Require Import}, -but also at the command {\tt Declare ML Module}. - -Dependencies of \ocaml\ modules are computed by looking at -\verb!open! commands and the dot notation {\em module.value}. However, -this is done approximately and you are advised to use {\tt ocamldep} -instead for the \ocaml\ modules dependencies. - -See the man page of {\tt coqdep} for more details and options. - -The build infrastructure generated by {\tt coq\_makefile} -uses {\tt coqdep} to automatically compute the dependencies -among the files part of the project. - -\section[Documenting \Coq\ files with coqdoc]{Documenting \Coq\ files with coqdoc\label{coqdoc} -\ttindex{coqdoc}} - -\input{./coqdoc} - -\section[Embedded \Coq\ phrases inside \LaTeX\ documents]{Embedded \Coq\ phrases inside \LaTeX\ documents\label{Latex} - \ttindex{coq-tex}\index{Latex@{\LaTeX}}} - -When writing a documentation about a proof development, one may want -to insert \Coq\ phrases inside a \LaTeX\ document, possibly together with -the corresponding answers of the system. We provide a -mechanical way to process such \Coq\ phrases embedded in \LaTeX\ files: the -{\tt coq-tex} filter. This filter extracts Coq phrases embedded in -LaTeX files, evaluates them, and insert the outcome of the evaluation -after each phrase. - -Starting with a file {\em file}{\tt.tex} containing \Coq\ phrases, -the {\tt coq-tex} filter produces a file named {\em file}{\tt.v.tex} with -the \Coq\ outcome. - -There are options to produce the \Coq\ parts in smaller font, italic, -between horizontal rules, etc. -See the man page of {\tt coq-tex} for more details. - -\medskip\noindent {\bf Remark.} This Reference Manual and the Tutorial -have been completely produced with {\tt coq-tex}. - - -\section[\Coq\ and \emacs]{\Coq\ and \emacs\label{Emacs}\index{Emacs}} - -\subsection{The \Coq\ Emacs mode} - -\Coq\ comes with a Major mode for \emacs, {\tt gallina.el}. This mode provides -syntax highlighting -and also a rudimentary indentation facility -in the style of the Caml \emacs\ mode. - -Add the following lines to your \verb!.emacs! file: - -\begin{verbatim} - (setq auto-mode-alist (cons '("\\.v$" . coq-mode) auto-mode-alist)) - (autoload 'coq-mode "gallina" "Major mode for editing Coq vernacular." t) -\end{verbatim} - -The \Coq\ major mode is triggered by visiting a file with extension {\tt .v}, -or manually with the command \verb!M-x coq-mode!. -It gives you the correct syntax table for -the \Coq\ language, and also a rudimentary indentation facility: -\begin{itemize} - \item pressing {\sc Tab} at the beginning of a line indents the line like - the line above; - - \item extra {\sc Tab}s increase the indentation level - (by 2 spaces by default); - - \item M-{\sc Tab} decreases the indentation level. -\end{itemize} - -An inferior mode to run \Coq\ under Emacs, by Marco Maggesi, is also -included in the distribution, in file \texttt{inferior-coq.el}. -Instructions to use it are contained in this file. - -\subsection[{\ProofGeneral}]{{\ProofGeneral}\index{Proof General@{\ProofGeneral}}} - -{\ProofGeneral} is a generic interface for proof assistants based on -Emacs. The main idea is that the \Coq\ commands you are -editing are sent to a \Coq\ toplevel running behind Emacs and the -answers of the system automatically inserted into other Emacs buffers. -Thus you don't need to copy-paste the \Coq\ material from your files -to the \Coq\ toplevel or conversely from the \Coq\ toplevel to some -files. - -{\ProofGeneral} is developed and distributed independently of the -system \Coq. It is freely available at \verb!https://proofgeneral.github.io/!. - - -\section[Module specification]{Module specification\label{gallina}\ttindex{gallina}} - -Given a \Coq\ vernacular file, the {\tt gallina} filter extracts its -specification (inductive types declarations, definitions, type of -lemmas and theorems), removing the proofs parts of the file. The \Coq\ -file {\em file}{\tt.v} gives birth to the specification file -{\em file}{\tt.g} (where the suffix {\tt.g} stands for \gallina). - -See the man page of {\tt gallina} for more details and options. - - -\section[Man pages]{Man pages\label{ManPages}\index{Man pages}} - -There are man pages for the commands {\tt coqdep}, {\tt gallina} and -{\tt coq-tex}. Man pages are installed at installation time -(see installation instructions in file {\tt INSTALL}, step 6). - -%BEGIN LATEX -\RefManCutCommand{ENDREFMAN=\thepage} -%END LATEX - -%%% Local Variables: -%%% mode: latex -%%% TeX-master: t -%%% End: diff --git a/doc/refman/Reference-Manual.tex b/doc/refman/Reference-Manual.tex index 86f123322..061686e12 100644 --- a/doc/refman/Reference-Manual.tex +++ b/doc/refman/Reference-Manual.tex @@ -98,35 +98,18 @@ Options A and B of the licence are {\em not} elected.} \part{The proof engine} -\include{RefMan-oth.v}% Vernacular commands -\include{RefMan-pro.v}% Proof handling \include{RefMan-ltac.v}% Writing tactics \lstset{language=SSR} \lstset{moredelim=[is][]{|*}{*|}} \lstset{moredelim=*[is][\itshape\rmfamily]{/*}{*/}} -\part{User extensions} -%%SUPPRIME \include{RefMan-tus.v}% Writing tactics - -\part{Practical tools} -\include{RefMan-uti}% utilities (gallina, do_Makefile, etc) - %BEGIN LATEX \RefManCutCommand{BEGINADDENDUM=\thepage} %END LATEX \part{Addendum to the Reference Manual} \include{AddRefMan-pre}% -\include{Coercion.v}% -\include{Classes.v}% -\include{Extraction.v}% -\include{Program.v}% -\include{Polynom.v}% = Ring -\include{Nsatz.v}% -\include{Setoid.v}% Tactique pour les setoides -\include{AsyncProofs}% Paral-ITP \include{Universes.v}% Universe polymorphes -\include{Misc.v} %BEGIN LATEX \RefManCutCommand{ENDADDENDUM=\thepage} %END LATEX diff --git a/doc/refman/Setoid.tex b/doc/refman/Setoid.tex deleted file mode 100644 index b7b343112..000000000 --- a/doc/refman/Setoid.tex +++ /dev/null @@ -1,842 +0,0 @@ -\newtheorem{cscexample}{Example} - -\achapter{\protect{Generalized rewriting}} -%HEVEA\cutname{setoid.html} -\aauthor{Matthieu Sozeau} -\label{setoids} - -This chapter presents the extension of several equality related tactics -to work over user-defined structures (called setoids) that are equipped -with ad-hoc equivalence relations meant to behave as equalities. -Actually, the tactics have also been generalized to relations weaker -then equivalences (e.g. rewriting systems). The toolbox also extends the -automatic rewriting capabilities of the system, allowing the specification of -custom strategies for rewriting. - -This documentation is adapted from the previous setoid documentation by -Claudio Sacerdoti Coen (based on previous work by Cl\'ement Renard). -The new implementation is a drop-in replacement for the old one,\footnote{Nicolas -Tabareau helped with the gluing.} hence most of the documentation still applies. - -The work is a complete rewrite of the previous implementation, based on -the type class infrastructure. It also improves on and generalizes -the previous implementation in several ways: -\begin{itemize} -\item User-extensible algorithm. The algorithm is separated in two - parts: generations of the rewriting constraints (done in ML) and - solving of these constraints using type class resolution. As type - class resolution is extensible using tactics, this allows users to define - general ways to solve morphism constraints. -\item Sub-relations. An example extension to the base algorithm is the - ability to define one relation as a subrelation of another so that - morphism declarations on one relation can be used automatically for - the other. This is done purely using tactics and type class search. -\item Rewriting under binders. It is possible to rewrite under binders - in the new implementation, if one provides the proper - morphisms. Again, most of the work is handled in the tactics. -\item First-class morphisms and signatures. Signatures and morphisms are - ordinary Coq terms, hence they can be manipulated inside Coq, put - inside structures and lemmas about them can be proved inside the - system. Higher-order morphisms are also allowed. -\item Performance. The implementation is based on a depth-first search for the first - solution to a set of constraints which can be as fast as linear in the - size of the term, and the size of the proof term is linear - in the size of the original term. Besides, the extensibility allows the - user to customize the proof search if necessary. -\end{itemize} - -\asection{Introduction to generalized rewriting} - -\subsection{Relations and morphisms} - -A parametric \emph{relation} \texttt{R} is any term of type -\texttt{forall ($x_1$:$T_1$) \ldots ($x_n$:$T_n$), relation $A$}. The -expression $A$, which depends on $x_1$ \ldots $x_n$, is called the -\emph{carrier} of the relation and \texttt{R} is -said to be a relation over \texttt{A}; the list $x_1,\ldots,x_n$ -is the (possibly empty) list of parameters of the relation. - -\firstexample -\begin{cscexample}[Parametric relation] -It is possible to implement finite sets of elements of type \texttt{A} -as unordered list of elements of type \texttt{A}. The function -\texttt{set\_eq: forall (A: Type), relation (list A)} satisfied by two lists -with the same elements is a parametric relation over \texttt{(list A)} with -one parameter \texttt{A}. The type of \texttt{set\_eq} is convertible with -\texttt{forall (A: Type), list A -> list A -> Prop}. -\end{cscexample} - -An \emph{instance} of a parametric relation \texttt{R} with $n$ parameters -is any term \texttt{(R $t_1$ \ldots $t_n$)}. - -Let \texttt{R} be a relation over \texttt{A} with $n$ parameters. -A term is a parametric proof of reflexivity for \texttt{R} if it has type -\texttt{forall ($x_1$:$T_1$) \ldots ($x_n$:$T_n$), - reflexive (R $x_1$ \ldots $x_n$)}. Similar definitions are given for -parametric proofs of symmetry and transitivity. - -\begin{cscexample}[Parametric relation (cont.)] -The \texttt{set\_eq} relation of the previous example can be proved to be -reflexive, symmetric and transitive. -\end{cscexample} - -A parametric unary function $f$ of type -\texttt{forall ($x_1$:$T_1$) \ldots ($x_n$:$T_n$), $A_1$ -> $A_2$} -covariantly respects two parametric relation instances $R_1$ and $R_2$ if, -whenever $x, y$ satisfy $R_1~x~y$, their images $(f~x)$ and $(f~y)$ -satisfy $R_2~(f~x)~(f~y)$ . An $f$ that respects its input and output relations -will be called a unary covariant \emph{morphism}. We can also say that $f$ is -a monotone function with respect to $R_1$ and $R_2$. -The sequence $x_1,\ldots x_n$ represents the parameters of the morphism. - -Let $R_1$ and $R_2$ be two parametric relations. -The \emph{signature} of a parametric morphism of type -\texttt{forall ($x_1$:$T_1$) \ldots ($x_n$:$T_n$), $A_1$ -> $A_2$} that -covariantly respects two instances $I_{R_1}$ and $I_{R_2}$ of $R_1$ and $R_2$ is written $I_{R_1} \texttt{++>} I_{R_2}$. -Notice that the special arrow \texttt{++>}, which reminds the reader -of covariance, is placed between the two relation instances, not -between the two carriers. The signature relation instances and morphism will -be typed in a context introducing variables for the parameters. - -The previous definitions are extended straightforwardly to $n$-ary morphisms, -that are required to be simultaneously monotone on every argument. - -Morphisms can also be contravariant in one or more of their arguments. -A morphism is contravariant on an argument associated to the relation instance -$R$ if it is covariant on the same argument when the inverse relation -$R^{-1}$ (\texttt{inverse R} in Coq) is considered. -The special arrow \texttt{-{}->} is used in signatures -for contravariant morphisms. - -Functions having arguments related by symmetric relations instances are both -covariant and contravariant in those arguments. The special arrow -\texttt{==>} is used in signatures for morphisms that are both covariant -and contravariant. - -An instance of a parametric morphism $f$ with $n$ parameters is any term -\texttt{f $t_1$ \ldots $t_n$}. - -\begin{cscexample}[Morphisms] -Continuing the previous example, let -\texttt{union: forall (A: Type), list A -> list A -> list A} perform the union -of two sets by appending one list to the other. \texttt{union} is a binary -morphism parametric over \texttt{A} that respects the relation instance -\texttt{(set\_eq A)}. The latter condition is proved by showing -\texttt{forall (A: Type) (S1 S1' S2 S2': list A), set\_eq A S1 S1' -> - set\_eq A S2 S2' -> set\_eq A (union A S1 S2) (union A S1' S2')}. - -The signature of the function \texttt{union A} is -\texttt{set\_eq A ==> set\_eq A ==> set\_eq A} for all \texttt{A}. -\end{cscexample} - -\begin{cscexample}[Contravariant morphism] -The division function \texttt{Rdiv: R -> R -> R} is a morphism of -signature \texttt{le ++> le -{}-> le} where \texttt{le} is -the usual order relation over real numbers. Notice that division is -covariant in its first argument and contravariant in its second -argument. -\end{cscexample} - -Leibniz equality is a relation and every function is a -morphism that respects Leibniz equality. Unfortunately, Leibniz equality -is not always the intended equality for a given structure. - -In the next section we will describe the commands to register terms as -parametric relations and morphisms. Several tactics that deal with equality -in \Coq\ can also work with the registered relations. -The exact list of tactic will be given in Sect.~\ref{setoidtactics}. -For instance, the -tactic \texttt{reflexivity} can be used to close a goal $R~n~n$ whenever -$R$ is an instance of a registered reflexive relation. However, the tactics -that replace in a context $C[]$ one term with another one related by $R$ -must verify that $C[]$ is a morphism that respects the intended relation. -Currently the verification consists in checking whether $C[]$ is a syntactic -composition of morphism instances that respects some obvious -compatibility constraints. - -\begin{cscexample}[Rewriting] -Continuing the previous examples, suppose that the user must prove -\texttt{set\_eq int (union int (union int S1 S2) S2) (f S1 S2)} under the -hypothesis \texttt{H: set\_eq int S2 (@nil int)}. It is possible to -use the \texttt{rewrite} tactic to replace the first two occurrences of -\texttt{S2} with \texttt{@nil int} in the goal since the context -\texttt{set\_eq int (union int (union int S1 nil) nil) (f S1 S2)}, being -a composition of morphisms instances, is a morphism. However the tactic -will fail replacing the third occurrence of \texttt{S2} unless \texttt{f} -has also been declared as a morphism. -\end{cscexample} - -\subsection{Adding new relations and morphisms} -A parametric relation -\textit{Aeq}\texttt{: forall ($y_1 : \beta_!$ \ldots $y_m : \beta_m$), relation (A $t_1$ \ldots $t_n$)} over -\textit{(A : $\alpha_i$ -> \ldots $\alpha_n$ -> }\texttt{Type}) -can be declared with the following command: - -\comindex{Add Parametric Relation} -\begin{quote} - \texttt{Add Parametric Relation} ($x_1 : T_1$) \ldots ($x_n : T_k$) : - \textit{(A $t_1$ \ldots $t_n$) (Aeq $t'_1$ \ldots $t'_m$)}\\ - ~\zeroone{\texttt{reflexivity proved by} \textit{refl}}\\ - ~\zeroone{\texttt{symmetry proved by} \textit{sym}}\\ - ~\zeroone{\texttt{transitivity proved by} \textit{trans}}\\ - \texttt{~as} \textit{id}. -\end{quote} -after having required the \texttt{Setoid} module with the -\texttt{Require Setoid} command. - -The identifier \textit{id} gives a unique name to the morphism and it is -used by the command to generate fresh names for automatically provided lemmas -used internally. - -Notice that the carrier and relation parameters may refer to the context -of variables introduced at the beginning of the declaration, but the -instances need not be made only of variables. -Also notice that \textit{A} is \emph{not} required to be a term -having the same parameters as \textit{Aeq}, although that is often the -case in practice (this departs from the previous implementation). - -\comindex{Add Relation} -In case the carrier and relations are not parametric, one can use the -command \texttt{Add Relation} instead, whose syntax is the same except -there is no local context. - -The proofs of reflexivity, symmetry and transitivity can be omitted if the -relation is not an equivalence relation. The proofs must be instances of the -corresponding relation definitions: e.g. the proof of reflexivity must -have a type convertible to \texttt{reflexive (A $t_1$ \ldots $t_n$) (Aeq $t'_1$ \ldots - $t'_n$)}. Each proof may refer to the introduced variables as well. - -\begin{cscexample}[Parametric relation] -For Leibniz equality, we may declare: -\texttt{Add Parametric Relation (A : Type) :} \texttt{A (@eq A)}\\ -~\zeroone{\texttt{reflexivity proved by} \texttt{@refl\_equal A}}\\ -\ldots -\end{cscexample} - -Some tactics -(\texttt{reflexivity}, \texttt{symmetry}, \texttt{transitivity}) work only -on relations that respect the expected properties. The remaining tactics -(\texttt{replace}, \texttt{rewrite} and derived tactics such as -\texttt{autorewrite}) do not require any properties over the relation. -However, they are able to replace terms with related ones only in contexts -that are syntactic compositions of parametric morphism instances declared with -the following command. - -\comindex{Add Parametric Morphism} -\begin{quote} - \texttt{Add Parametric Morphism} ($x_1 : \T_1$) \ldots ($x_k : \T_k$) : - (\textit{f $t_1$ \ldots $t_n$})\\ - \texttt{~with signature} \textit{sig}\\ - \texttt{~as id}.\\ - \texttt{Proof}\\ - ~\ldots\\ - \texttt{Qed} -\end{quote} - -The command declares \textit{f} as a parametric morphism of signature -\textit{sig}. The identifier \textit{id} gives a unique name to the morphism -and it is used as the base name of the type class instance definition -and as the name of the lemma that proves the well-definedness of the morphism. -The parameters of the morphism as well as the signature may refer to the -context of variables. -The command asks the user to prove interactively that \textit{f} respects -the relations identified from the signature. - -\begin{cscexample} -We start the example by assuming a small theory over homogeneous sets and -we declare set equality as a parametric equivalence relation and -union of two sets as a parametric morphism. -\begin{coq_example*} -Require Export Setoid. -Require Export Relation_Definitions. -Set Implicit Arguments. -Parameter set: Type -> Type. -Parameter empty: forall A, set A. -Parameter eq_set: forall A, set A -> set A -> Prop. -Parameter union: forall A, set A -> set A -> set A. -Axiom eq_set_refl: forall A, reflexive _ (eq_set (A:=A)). -Axiom eq_set_sym: forall A, symmetric _ (eq_set (A:=A)). -Axiom eq_set_trans: forall A, transitive _ (eq_set (A:=A)). -Axiom empty_neutral: forall A (S: set A), eq_set (union S (empty A)) S. -Axiom union_compat: - forall (A : Type), - forall x x' : set A, eq_set x x' -> - forall y y' : set A, eq_set y y' -> - eq_set (union x y) (union x' y'). -Add Parametric Relation A : (set A) (@eq_set A) - reflexivity proved by (eq_set_refl (A:=A)) - symmetry proved by (eq_set_sym (A:=A)) - transitivity proved by (eq_set_trans (A:=A)) - as eq_set_rel. -Add Parametric Morphism A : (@union A) with -signature (@eq_set A) ==> (@eq_set A) ==> (@eq_set A) as union_mor. -Proof. exact (@union_compat A). Qed. -\end{coq_example*} - -\end{cscexample} - -It is possible to reduce the burden of specifying parameters using -(maximally inserted) implicit arguments. If \texttt{A} is always set as -maximally implicit in the previous example, one can write: - -\begin{coq_eval} -Reset Initial. -Require Export Setoid. -Require Export Relation_Definitions. -Parameter set: Type -> Type. -Parameter empty: forall {A}, set A. -Parameter eq_set: forall {A}, set A -> set A -> Prop. -Parameter union: forall {A}, set A -> set A -> set A. -Axiom eq_set_refl: forall {A}, reflexive (set A) eq_set. -Axiom eq_set_sym: forall {A}, symmetric (set A) eq_set. -Axiom eq_set_trans: forall {A}, transitive (set A) eq_set. -Axiom empty_neutral: forall A (S: set A), eq_set (union S empty) S. -Axiom union_compat: - forall (A : Type), - forall x x' : set A, eq_set x x' -> - forall y y' : set A, eq_set y y' -> - eq_set (union x y) (union x' y'). -\end{coq_eval} - -\begin{coq_example*} -Add Parametric Relation A : (set A) eq_set - reflexivity proved by eq_set_refl - symmetry proved by eq_set_sym - transitivity proved by eq_set_trans - as eq_set_rel. -Add Parametric Morphism A : (@union A) with - signature eq_set ==> eq_set ==> eq_set as union_mor. -Proof. exact (@union_compat A). Qed. -\end{coq_example*} - -We proceed now by proving a simple lemma performing a rewrite step -and then applying reflexivity, as we would do working with Leibniz -equality. Both tactic applications are accepted -since the required properties over \texttt{eq\_set} and -\texttt{union} can be established from the two declarations above. - -\begin{coq_example*} -Goal forall (S: set nat), - eq_set (union (union S empty) S) (union S S). -Proof. intros. rewrite empty_neutral. reflexivity. Qed. -\end{coq_example*} - -The tables of relations and morphisms are managed by the type class -instance mechanism. The behavior on section close is to generalize -the instances by the variables of the section (and possibly hypotheses -used in the proofs of instance declarations) but not to export them in -the rest of the development for proof search. One can use the -\texttt{Existing Instance} command to do so outside the section, -using the name of the declared morphism suffixed by \texttt{\_Morphism}, -or use the \texttt{Global} modifier for the corresponding class instance -declaration (see \S\ref{setoid:first-class}) at definition time. -When loading a compiled file or importing a module, -all the declarations of this module will be loaded. - -\subsection{Rewriting and non reflexive relations} -To replace only one argument of an n-ary morphism it is necessary to prove -that all the other arguments are related to themselves by the respective -relation instances. - -\begin{cscexample} -To replace \texttt{(union S empty)} with \texttt{S} in -\texttt{(union (union S empty) S) (union S S)} the rewrite tactic must -exploit the monotony of \texttt{union} (axiom \texttt{union\_compat} in -the previous example). Applying \texttt{union\_compat} by hand we are left -with the goal \texttt{eq\_set (union S S) (union S S)}. -\end{cscexample} - -When the relations associated to some arguments are not reflexive, the tactic -cannot automatically prove the reflexivity goals, that are left to the user. - -Setoids whose relation are partial equivalence relations (PER) -are useful to deal with partial functions. Let \texttt{R} be a PER. We say -that an element \texttt{x} is defined if \texttt{R x x}. A partial function -whose domain comprises all the defined elements only is declared as a -morphism that respects \texttt{R}. Every time a rewriting step is performed -the user must prove that the argument of the morphism is defined. - -\begin{cscexample} -Let \texttt{eqO} be \texttt{fun x y => x = y $\land$ ~x$\neq$ 0} (the smaller PER over -non zero elements). Division can be declared as a morphism of signature -\texttt{eq ==> eq0 ==> eq}. Replace \texttt{x} with \texttt{y} in -\texttt{div x n = div y n} opens the additional goal \texttt{eq0 n n} that -is equivalent to \texttt{n=n $\land$ n$\neq$0}. -\end{cscexample} - -\subsection{Rewriting and non symmetric relations} -When the user works up to relations that are not symmetric, it is no longer -the case that any covariant morphism argument is also contravariant. As a -result it is no longer possible to replace a term with a related one in -every context, since the obtained goal implies the previous one if and -only if the replacement has been performed in a contravariant position. -In a similar way, replacement in an hypothesis can be performed only if -the replaced term occurs in a covariant position. - -\begin{cscexample}[Covariance and contravariance] -Suppose that division over real numbers has been defined as a -morphism of signature \texttt{Z.div: Z.lt ++> Z.lt -{}-> Z.lt} (i.e. -\texttt{Z.div} is increasing in its first argument, but decreasing on the -second one). Let \texttt{<} denotes \texttt{Z.lt}. -Under the hypothesis \texttt{H: x < y} we have -\texttt{k < x / y -> k < x / x}, but not -\texttt{k < y / x -> k < x / x}. -Dually, under the same hypothesis \texttt{k < x / y -> k < y / y} holds, -but \texttt{k < y / x -> k < y / y} does not. -Thus, if the current goal is \texttt{k < x / x}, it is possible to replace -only the second occurrence of \texttt{x} (in contravariant position) -with \texttt{y} since the obtained goal must imply the current one. -On the contrary, if \texttt{k < x / x} is -an hypothesis, it is possible to replace only the first occurrence of -\texttt{x} (in covariant position) with \texttt{y} since -the current hypothesis must imply the obtained one. -\end{cscexample} - -Contrary to the previous implementation, no specific error message will -be raised when trying to replace a term that occurs in the wrong -position. It will only fail because the rewriting constraints are not -satisfiable. However it is possible to use the \texttt{at} modifier to -specify which occurrences should be rewritten. - -As expected, composing morphisms together propagates the variance annotations by -switching the variance every time a contravariant position is traversed. -\begin{cscexample} -Let us continue the previous example and let us consider the goal -\texttt{x / (x / x) < k}. The first and third occurrences of \texttt{x} are -in a contravariant position, while the second one is in covariant position. -More in detail, the second occurrence of \texttt{x} occurs -covariantly in \texttt{(x / x)} (since division is covariant in its first -argument), and thus contravariantly in \texttt{x / (x / x)} (since division -is contravariant in its second argument), and finally covariantly in -\texttt{x / (x / x) < k} (since \texttt{<}, as every transitive relation, -is contravariant in its first argument with respect to the relation itself). -\end{cscexample} - -\subsection{Rewriting in ambiguous setoid contexts} -One function can respect several different relations and thus it can be -declared as a morphism having multiple signatures. - -\begin{cscexample} -Union over homogeneous lists can be given all the following signatures: -\texttt{eq ==> eq ==> eq} (\texttt{eq} being the equality over ordered lists) -\texttt{set\_eq ==> set\_eq ==> set\_eq} (\texttt{set\_eq} being the equality -over unordered lists up to duplicates), -\texttt{multiset\_eq ==> multiset\_eq ==> multiset\_eq} (\texttt{multiset\_eq} -being the equality over unordered lists). -\end{cscexample} - -To declare multiple signatures for a morphism, repeat the \texttt{Add Morphism} -command. - -When morphisms have multiple signatures it can be the case that a rewrite -request is ambiguous, since it is unclear what relations should be used to -perform the rewriting. Contrary to the previous implementation, the -tactic will always choose the first possible solution to the set of -constraints generated by a rewrite and will not try to find \emph{all} -possible solutions to warn the user about. - -\asection{Commands and tactics} -\subsection{First class setoids and morphisms} -\label{setoid:first-class} - -The implementation is based on a first-class representation of -properties of relations and morphisms as type classes. That is, -the various combinations of properties on relations and morphisms -are represented as records and instances of theses classes are put -in a hint database. -For example, the declaration: - -\begin{quote} - \texttt{Add Parametric Relation} ($x_1 : T_1$) \ldots ($x_n : T_k$) : - \textit{(A $t_1$ \ldots $t_n$) (Aeq $t'_1$ \ldots $t'_m$)}\\ - ~\zeroone{\texttt{reflexivity proved by} \textit{refl}}\\ - ~\zeroone{\texttt{symmetry proved by} \textit{sym}}\\ - ~\zeroone{\texttt{transitivity proved by} \textit{trans}}\\ - \texttt{~as} \textit{id}. -\end{quote} - -is equivalent to an instance declaration: - -\begin{quote} - \texttt{Instance} ($x_1 : T_1$) \ldots ($x_n : T_k$) \texttt{=>} - \textit{id} : \texttt{@Equivalence} \textit{(A $t_1$ \ldots $t_n$) (Aeq - $t'_1$ \ldots $t'_m$)} :=\\ - ~\zeroone{\texttt{Equivalence\_Reflexive :=} \textit{refl}}\\ - ~\zeroone{\texttt{Equivalence\_Symmetric :=} \textit{sym}}\\ - ~\zeroone{\texttt{Equivalence\_Transitive :=} \textit{trans}}. -\end{quote} - -The declaration itself amounts to the definition of an object of the -record type \texttt{Coq.Classes.RelationClasses.Equivalence} and a -hint added to the \texttt{typeclass\_instances} hint database. -Morphism declarations are also instances of a type class defined in -\texttt{Classes.Morphisms}. -See the documentation on type classes \ref{typeclasses} and -the theories files in \texttt{Classes} for further explanations. - -One can inform the rewrite tactic about morphisms and relations just by -using the typeclass mechanism to declare them using \texttt{Instance} -and \texttt{Context} vernacular commands. -Any object of type \texttt{Proper} (the type of morphism declarations) -in the local context will also be automatically used by the rewriting -tactic to solve constraints. - -Other representations of first class setoids and morphisms can also -be handled by encoding them as records. In the following example, -the projections of the setoid relation and of the morphism function -can be registered as parametric relations and morphisms. -\begin{cscexample}[First class setoids] - -\begin{coq_example*} -Require Import Relation_Definitions Setoid. -Record Setoid: Type := -{ car:Type; - eq:car->car->Prop; - refl: reflexive _ eq; - sym: symmetric _ eq; - trans: transitive _ eq -}. -Add Parametric Relation (s : Setoid) : (@car s) (@eq s) - reflexivity proved by (refl s) - symmetry proved by (sym s) - transitivity proved by (trans s) as eq_rel. -Record Morphism (S1 S2:Setoid): Type := -{ f:car S1 ->car S2; - compat: forall (x1 x2: car S1), eq S1 x1 x2 -> eq S2 (f x1) (f x2) }. -Add Parametric Morphism (S1 S2 : Setoid) (M : Morphism S1 S2) : - (@f S1 S2 M) with signature (@eq S1 ==> @eq S2) as apply_mor. -Proof. apply (compat S1 S2 M). Qed. -Lemma test: forall (S1 S2:Setoid) (m: Morphism S1 S2) - (x y: car S1), eq S1 x y -> eq S2 (f _ _ m x) (f _ _ m y). -Proof. intros. rewrite H. reflexivity. Qed. -\end{coq_example*} -\end{cscexample} - -\subsection{Tactics enabled on user provided relations} -\label{setoidtactics} -The following tactics, all prefixed by \texttt{setoid\_}, -deal with arbitrary -registered relations and morphisms. Moreover, all the corresponding unprefixed -tactics (i.e. \texttt{reflexivity}, \texttt{symmetry}, \texttt{transitivity}, -\texttt{replace}, \texttt{rewrite}) -have been extended to fall back to their prefixed counterparts when -the relation involved is not Leibniz equality. Notice, however, that using -the prefixed tactics it is possible to pass additional arguments such as -\texttt{using relation}. -\medskip - -\tacindex{setoid\_reflexivity} -\texttt{setoid\_reflexivity} - -\tacindex{setoid\_symmetry} -\texttt{setoid\_symmetry} \zeroone{\texttt{in} \textit{ident}} - -\tacindex{setoid\_transitivity} -\texttt{setoid\_transitivity} - -\tacindex{setoid\_rewrite} -\texttt{setoid\_rewrite} \zeroone{\textit{orientation}} \textit{term} -~\zeroone{\texttt{at} \textit{occs}} ~\zeroone{\texttt{in} \textit{ident}} - -\tacindex{setoid\_replace} -\texttt{setoid\_replace} \textit{term} \texttt{with} \textit{term} -~\zeroone{\texttt{in} \textit{ident}} -~\zeroone{\texttt{using relation} \textit{term}} -~\zeroone{\texttt{by} \textit{tactic}} -\medskip - -The \texttt{using relation} -arguments cannot be passed to the unprefixed form. The latter argument -tells the tactic what parametric relation should be used to replace -the first tactic argument with the second one. If omitted, it defaults -to the \texttt{DefaultRelation} instance on the type of the objects. -By default, it means the most recent \texttt{Equivalence} instance in -the environment, but it can be customized by declaring new -\texttt{DefaultRelation} instances. As Leibniz equality is a declared -equivalence, it will fall back to it if no other relation is declared on -a given type. - -Every derived tactic that is based on the unprefixed forms of the tactics -considered above will also work up to user defined relations. For instance, -it is possible to register hints for \texttt{autorewrite} that are -not proof of Leibniz equalities. In particular it is possible to exploit -\texttt{autorewrite} to simulate normalization in a term rewriting system -up to user defined equalities. - -\subsection{Printing relations and morphisms} -The \texttt{Print Instances} command can be used to show the list of -currently registered \texttt{Reflexive} (using \texttt{Print Instances Reflexive}), -\texttt{Symmetric} or \texttt{Transitive} relations, -\texttt{Equivalence}s, \texttt{PreOrder}s, \texttt{PER}s, and -Morphisms (implemented as \texttt{Proper} instances). When - the rewriting tactics refuse to replace a term in a context -because the latter is not a composition of morphisms, the \texttt{Print Instances} -commands can be useful to understand what additional morphisms should be -registered. - -\subsection{Deprecated syntax and backward incompatibilities} -Due to backward compatibility reasons, the following syntax for the -declaration of setoids and morphisms is also accepted. - -\comindex{Add Setoid} -\begin{quote} - \texttt{Add Setoid} \textit{A Aeq ST} \texttt{as} \textit{ident} -\end{quote} -where \textit{Aeq} is a congruence relation without parameters, -\textit{A} is its carrier and \textit{ST} is an object of type -\texttt{(Setoid\_Theory A Aeq)} (i.e. a record packing together the reflexivity, -symmetry and transitivity lemmas). Notice that the syntax is not completely -backward compatible since the identifier was not required. - -\comindex{Add Morphism} -\begin{quote} - \texttt{Add Morphism} \textit{f}:\textit{ident}.\\ - Proof.\\ - \ldots\\ - Qed. -\end{quote} - -The latter command also is restricted to the declaration of morphisms without -parameters. It is not fully backward compatible since the property the user -is asked to prove is slightly different: for $n$-ary morphisms the hypotheses -of the property are permuted; moreover, when the morphism returns a -proposition, the property is now stated using a bi-implication in place of -a simple implication. In practice, porting an old development to the new -semantics is usually quite simple. - -Notice that several limitations of the old implementation have been lifted. -In particular, it is now possible to declare several relations with the -same carrier and several signatures for the same morphism. Moreover, it is -now also possible to declare several morphisms having the same signature. -Finally, the replace and rewrite tactics can be used to replace terms in -contexts that were refused by the old implementation. As discussed in -the next section, the semantics of the new \texttt{setoid\_rewrite} -command differs slightly from the old one and \texttt{rewrite}. - -\asection{Extensions} -\subsection{Rewriting under binders} - -\textbf{Warning}: Due to compatibility issues, this feature is enabled only when calling -the \texttt{setoid\_rewrite} tactics directly and not \texttt{rewrite}. - -To be able to rewrite under binding constructs, one must declare -morphisms with respect to pointwise (setoid) equivalence of functions. -Example of such morphisms are the standard \texttt{all} and \texttt{ex} -combinators for universal and existential quantification respectively. -They are declared as morphisms in the \texttt{Classes.Morphisms\_Prop} -module. For example, to declare that universal quantification is a -morphism for logical equivalence: - -\begin{coq_eval} -Reset Initial. -Require Import Setoid Morphisms. -\end{coq_eval} -\begin{coq_example} -Instance all_iff_morphism (A : Type) : - Proper (pointwise_relation A iff ==> iff) (@all A). -Proof. simpl_relation. -\end{coq_example} -\begin{coq_eval} -Admitted. -\end{coq_eval} - -One then has to show that if two predicates are equivalent at every -point, their universal quantifications are equivalent. Once we have -declared such a morphism, it will be used by the setoid rewriting tactic -each time we try to rewrite under an \texttt{all} application (products -in \Prop{} are implicitly translated to such applications). - -Indeed, when rewriting under a lambda, binding variable $x$, say from -$P~x$ to $Q~x$ using the relation \texttt{iff}, the tactic will generate -a proof of \texttt{pointwise\_relation A iff (fun x => P x) (fun x => Q -x)} from the proof of \texttt{iff (P x) (Q x)} and a constraint of the -form \texttt{Proper (pointwise\_relation A iff ==> ?) m} will be -generated for the surrounding morphism \texttt{m}. - -Hence, one can add higher-order combinators as morphisms by providing -signatures using pointwise extension for the relations on the functional -arguments (or whatever subrelation of the pointwise extension). -For example, one could declare the \texttt{map} combinator on lists as -a morphism: -\begin{coq_eval} -Require Import List Setoid Morphisms. -Set Implicit Arguments. -Inductive list_equiv {A:Type} (eqA : relation A) : relation (list A) := -| eq_nil : list_equiv eqA nil nil -| eq_cons : forall x y, eqA x y -> - forall l l', list_equiv eqA l l' -> list_equiv eqA (x :: l) (y :: l'). -Generalizable All Variables. -\end{coq_eval} -\begin{coq_example*} -Instance map_morphism `{Equivalence A eqA, Equivalence B eqB} : - Proper ((eqA ==> eqB) ==> list_equiv eqA ==> list_equiv eqB) (@map A B). -\end{coq_example*} - -where \texttt{list\_equiv} implements an equivalence on lists -parameterized by an equivalence on the elements. - -Note that when one does rewriting with a lemma under a binder -using \texttt{setoid\_rewrite}, the application of the lemma may capture -the bound variable, as the semantics are different from rewrite where -the lemma is first matched on the whole term. With the new -\texttt{setoid\_rewrite}, matching is done on each subterm separately -and in its local environment, and all matches are rewritten -\emph{simultaneously} by default. The semantics of the previous -\texttt{setoid\_rewrite} implementation can almost be recovered using -the \texttt{at 1} modifier. - -\subsection{Sub-relations} - -Sub-relations can be used to specify that one relation is included in -another, so that morphisms signatures for one can be used for the other. -If a signature mentions a relation $R$ on the left of an arrow -\texttt{==>}, then the signature also applies for any relation $S$ that -is smaller than $R$, and the inverse applies on the right of an arrow. -One can then declare only a few morphisms instances that generate the complete set -of signatures for a particular constant. By default, the only declared -subrelation is \texttt{iff}, which is a subrelation of \texttt{impl} -and \texttt{inverse impl} (the dual of implication). That's why we can -declare only two morphisms for conjunction: -\texttt{Proper (impl ==> impl ==> impl) and} and -\texttt{Proper (iff ==> iff ==> iff) and}. This is sufficient to satisfy -any rewriting constraints arising from a rewrite using \texttt{iff}, -\texttt{impl} or \texttt{inverse impl} through \texttt{and}. - -Sub-relations are implemented in \texttt{Classes.Morphisms} and are a -prime example of a mostly user-space extension of the algorithm. - -\subsection{Constant unfolding} - -The resolution tactic is based on type classes and hence regards user-defined -constants as transparent by default. This may slow down the resolution -due to a lot of unifications (all the declared \texttt{Proper} -instances are tried at each node of the search tree). -To speed it up, declare your constant as rigid for proof search -using the command \texttt{Typeclasses Opaque} (see \S -\ref{TypeclassesTransparency}). - -\asection{Strategies for rewriting} - -\subsection{Definitions} -The generalized rewriting tactic is based on a set of strategies that -can be combined to obtain custom rewriting procedures. Its set of -strategies is based on Elan's rewriting strategies -\cite{Luttik97specificationof}. Rewriting strategies are applied using -the tactic \texttt{rewrite\_strat $s$} where $s$ is a strategy -expression. Strategies are defined inductively as described by the -following grammar: - -\def\str#1{\texttt{#1}} - -\def\strline#1#2{& \vert & #1 & \text{#2}} -\def\strlinea#1#2#3{& \vert & \str{#1}~#2 & \text{#3}} - -\[\begin{array}{lcll} - s, t, u & ::= & ( s ) & \text{strategy} \\ - \strline{c}{lemma} \\ - \strline{\str{<-}~c}{lemma, right-to-left} \\ - - \strline{\str{fail}}{failure} \\ - \strline{\str{id}}{identity} \\ - \strline{\str{refl}}{reflexivity} \\ - \strlinea{progress}{s}{progress} \\ - \strlinea{try}{s}{failure catch} \\ - - \strline{s~\str{;}~u}{composition} \\ - \strline{\str{choice}~s~t}{left-biased choice} \\ - - \strlinea{repeat}{s}{iteration (+)} \\ - \strlinea{any}{s}{iteration (*)} \\ - - \strlinea{subterm}{s}{one subterm} \\ - \strlinea{subterms}{s}{all subterms} \\ - \strlinea{innermost}{s}{innermost first} \\ - \strlinea{outermost}{s}{outermost first}\\ - \strlinea{bottomup}{s}{bottom-up} \\ - \strlinea{topdown}{s}{top-down} \\ - - \strlinea{hints}{hintdb}{apply hint} \\ - \strlinea{terms}{c \ldots c}{any of the terms}\\ - \strlinea{eval}{redexpr}{apply reduction}\\ - \strlinea{fold}{c}{fold expression} -\end{array}\] - -Actually a few of these are defined in term of the others using -a primitive fixpoint operator: - -\[\begin{array}{lcl} - \str{try}~s & = & \str{choice}~s~\str{id} \\ - \str{any}~s & = & \str{fix}~u. \str{try}~(s~\str{;}~u) \\ - \str{repeat}~s & = & s~\str{;}~\str{any}~s \\ - \str{bottomup}~s & = & - \str{fix}~bu. (\str{choice}~(\str{progress}~(\str{subterms}~bu))~s)~\str{;}~\str{try}~bu \\ - \str{topdown}~s & = & - \str{fix}~td. (\str{choice}~s~(\str{progress}~(\str{subterms}~td)))~\str{;}~\str{try}~td \\ - \str{innermost}~s & = & \str{fix}~i. (\str{choice}~(\str{subterm}~i)~s) \\ - \str{outermost}~s & = & - \str{fix}~o. (\str{choice}~s~(\str{subterm}~o)) -\end{array}\] - -The basic control strategy semantics are straightforward: strategies are -applied to subterms of the term to rewrite, starting from the root of -the term. The lemma strategies unify the left-hand-side of the -lemma with the current subterm and on success rewrite it to the -right-hand-side. Composition can be used to continue rewriting on the -current subterm. The fail strategy always fails while the identity -strategy succeeds without making progress. The reflexivity strategy -succeeds, making progress using a reflexivity proof of -rewriting. Progress tests progress of the argument strategy and fails if -no progress was made, while \str{try} always succeeds, catching -failures. Choice is left-biased: it will launch the first strategy and -fall back on the second one in case of failure. One can iterate a -strategy at least 1 time using \str{repeat} and at least 0 times using -\str{any}. - -The \str{subterm} and \str{subterms} strategies apply their argument -strategy $s$ to respectively one or all subterms of the current term -under consideration, left-to-right. \str{subterm} stops at the first -subterm for which $s$ made progress. The composite strategies -\str{innermost} and \str{outermost} perform a single innermost our outermost -rewrite using their argument strategy. Their counterparts -\str{bottomup} and \str{topdown} perform as many rewritings as possible, -starting from the bottom or the top of the term. - -Hint databases created for \texttt{autorewrite} can also be used by -\texttt{rewrite\_strat} using the \str{hints} strategy that applies any -of the lemmas at the current subterm. The \str{terms} strategy takes the -lemma names directly as arguments. The \str{eval} strategy expects a -reduction expression (see \S\ref{Conversion-tactics}) and succeeds if it -reduces the subterm under consideration. The \str{fold} strategy takes a -term $c$ and tries to \emph{unify} it to the current subterm, converting -it to $c$ on success, it is stronger than the tactic \texttt{fold}. - - -\subsection{Usage} -\tacindex{rewrite\_strat} - -\texttt{rewrite\_strat}~\textit{s}~\zeroone{\texttt{in} \textit{ident}}: - - Rewrite using the strategy \textit{s} in hypothesis \textit{ident} - or the conclusion. - - \begin{ErrMsgs} - \item \errindex{Nothing to rewrite}. If the strategy failed. - \item \errindex{No progress made}. If the strategy succeeded but - made no progress. - \item \errindex{Unable to satisfy the rewriting constraints}. - If the strategy succeeded and made progress but the corresponding - rewriting constraints are not satisfied. - \end{ErrMsgs} - - -The \texttt{setoid\_rewrite}~c tactic is basically equivalent to -\texttt{rewrite\_strat}~(\str{outermost}~c). - - - - - -%%% Local Variables: -%%% mode: latex -%%% TeX-master: "Reference-Manual" -%%% End: diff --git a/doc/refman/coqdoc.tex b/doc/refman/coqdoc.tex deleted file mode 100644 index 26dbd59e7..000000000 --- a/doc/refman/coqdoc.tex +++ /dev/null @@ -1,573 +0,0 @@ - -%\newcommand{\Coq}{\textsf{Coq}} -\newcommand{\javadoc}{\textsf{javadoc}} -\newcommand{\ocamldoc}{\textsf{ocamldoc}} -\newcommand{\coqdoc}{\textsf{coqdoc}} -\newcommand{\texmacs}{\TeX{}macs} -\newcommand{\monurl}[1]{#1} -%HEVEA\renewcommand{\monurl}[1]{\ahref{#1}{#1}} -%\newcommand{\lnot}{not} % Hevea handles these symbols nicely -%\newcommand{\lor}{or} -%\newcommand{\land}{\&} -%%% Beware : in a \texttt, -- is displayed as a unique - hence -%%% the following macro: -\newcommand{\mm}{\symbol{45}\symbol{45}} - - -\coqdoc\ is a documentation tool for the proof assistant -\Coq, similar to \javadoc\ or \ocamldoc. -The task of \coqdoc\ is -\begin{enumerate} -\item to produce a nice \LaTeX\ and/or HTML document from the \Coq\ - sources, readable for a human and not only for the proof assistant; -\item to help the user navigating in his own (or third-party) sources. -\end{enumerate} - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\subsection{Principles} - -Documentation is inserted into \Coq\ files as \emph{special comments}. -Thus your files will compile as usual, whether you use \coqdoc\ or not. -\coqdoc\ presupposes that the given \Coq\ files are well-formed (at -least lexically). Documentation starts with -\texttt{(**}, followed by a space, and ends with the pending \texttt{*)}. -The documentation format is inspired - by Todd~A.~Coram's \emph{Almost Free Text (AFT)} tool: it is mainly -ASCII text with some syntax-light controls, described below. -\coqdoc\ is robust: it shouldn't fail, whatever the input is. But -remember: ``garbage in, garbage out''. - -\paragraph{\Coq\ material inside documentation.} -\Coq\ material is quoted between the -delimiters \texttt{[} and \texttt{]}. Square brackets may be nested, -the inner ones being understood as being part of the quoted code (thus -you can quote a term like \texttt{fun x => u} by writing -\texttt{[fun x => u]}). Inside quotations, the code is pretty-printed in -the same way as it is in code parts. - -Pre-formatted vernacular is enclosed by \texttt{[[} and -\texttt{]]}. The former must be followed by a newline and the latter -must follow a newline. - -\paragraph{Pretty-printing.} -\coqdoc\ uses different faces for identifiers and keywords. -The pretty-printing of \Coq\ tokens (identifiers or symbols) can be -controlled using one of the following commands: -\begin{alltt} -(** printing \emph{token} %...\LaTeX...% #...HTML...# *) -\end{alltt} -or -\begin{alltt} -(** printing \emph{token} $...\LaTeX\ math...$ #...HTML...# *) -\end{alltt} -It gives the \LaTeX\ and HTML texts to be produced for the given \Coq\ -token. One of the \LaTeX\ or HTML text may be omitted, causing the -default pretty-printing to be used for this token. - -The printing for one token can be removed with -\begin{alltt} -(** remove printing \emph{token} *) -\end{alltt} - -Initially, the pretty-printing table contains the following mapping: -\begin{center} - \begin{tabular}{ll@{\qquad\qquad}ll@{\qquad\qquad}ll@{\qquad\qquad}} - \verb!->! & $\rightarrow$ & - \verb!<-! & $\leftarrow$ & - \verb|*| & $\times$ \\ - \verb|<=| & $\le$ & - \verb|>=| & $\ge$ & - \verb|=>| & $\Rightarrow$ \\ - \verb|<>| & $\not=$ & - \verb|<->| & $\leftrightarrow$ & - \verb!|-! & $\vdash$ \\ - \verb|\/| & $\lor$ & - \verb|/\| & $\land$ & - \verb|~| & $\lnot$ - \end{tabular} -\end{center} -Any of these can be overwritten or suppressed using the -\texttt{printing} commands. - -Important note: the recognition of tokens is done by a (ocaml)lex -automaton and thus applies the longest-match rule. For instance, -\verb!->~! is recognized as a single token, where \Coq\ sees two -tokens. It is the responsibility of the user to insert space between -tokens \emph{or} to give pretty-printing rules for the possible -combinations, e.g. -\begin{verbatim} -(** printing ->~ %\ensuremath{\rightarrow\lnot}% *) -\end{verbatim} - - -\paragraph{Sections.} -Sections are introduced by 1 to 4 leading stars (i.e. at the beginning of the -line) followed by a space. One star is a section, two stars a sub-section, etc. -The section title is given on the remaining of the line. -Example: -\begin{verbatim} - (** * Well-founded relations - - In this section, we introduce... *) -\end{verbatim} - - -%TODO \paragraph{Fonts.} - - -\paragraph{Lists.} -List items are introduced by a leading dash. \coqdoc\ uses whitespace -to determine the depth of a new list item and which text belongs in -which list items. A list ends when a line of text starts at or before -the level of indenting of the list's dash. A list item's dash must -always be the first non-space character on its line (so, in -particular, a list can not begin on the first line of a comment - -start it on the second line instead). - -Example: -\begin{verbatim} - We go by induction on [n]: - - If [n] is 0... - - If [n] is [S n'] we require... - - two paragraphs of reasoning, and two subcases: - - - In the first case... - - In the second case... - - So the theorem holds. -\end{verbatim} - -\paragraph{Rules.} -More than 4 leading dashes produce a horizontal rule. - -\paragraph{Emphasis.} -Text can be italicized by placing it in underscores. A non-identifier -character must precede the leading underscore and follow the trailing -underscore, so that uses of underscores in names aren't mistaken for -emphasis. Usually, these are spaces or punctuation. - -\begin{verbatim} - This sentence contains some _emphasized text_. -\end{verbatim} - -\paragraph{Escaping to \LaTeX\ and HTML.} -Pure \LaTeX\ or HTML material can be inserted using the following -escape sequences: -\begin{itemize} -\item \verb+$...LaTeX stuff...$+ inserts some \LaTeX\ material in math mode. - Simply discarded in HTML output. - -\item \verb+%...LaTeX stuff...%+ inserts some \LaTeX\ material. - Simply discarded in HTML output. - -\item \verb+#...HTML stuff...#+ inserts some HTML material. Simply - discarded in \LaTeX\ output. -\end{itemize} - -Note: to simply output the characters \verb+$+, \verb+%+ and \verb+#+ -and escaping their escaping role, these characters must be doubled. - -\paragraph{Verbatim.} -Verbatim material is introduced by a leading \verb+<<+ and closed by -\verb+>>+ at the beginning of a line. Example: -\begin{verbatim} -Here is the corresponding caml code: -<< - let rec fact n = - if n <= 1 then 1 else n * fact (n-1) ->> -\end{verbatim} - - -\paragraph{Hyperlinks.} -Hyperlinks can be inserted into the HTML output, so that any -identifier is linked to the place of its definition. - -\texttt{coqc \emph{file}.v} automatically dumps localization information -in \texttt{\emph{file}.glob} or appends it to a file specified using option -\texttt{\mm{}dump-glob \emph{file}}. Take care of erasing this global file, if -any, when starting the whole compilation process. - -Then invoke \texttt{coqdoc} or \texttt{coqdoc \mm{}glob-from \emph{file}} to tell -\coqdoc\ to look for name resolutions into the file \texttt{\emph{file}} -(it will look in \texttt{\emph{file}.glob} by default). - -Identifiers from the \Coq\ standard library are linked to the \Coq\ -web site at \url{http://coq.inria.fr/library/}. This behavior can be -changed using command line options \texttt{\mm{}no-externals} and -\texttt{\mm{}coqlib}; see below. - - -\paragraph{Hiding / Showing parts of the source.} -Some parts of the source can be hidden using command line options -\texttt{-g} and \texttt{-l} (see below), or using such comments: -\begin{alltt} -(* begin hide *) -\emph{some Coq material} -(* end hide *) -\end{alltt} -Conversely, some parts of the source which would be hidden can be -shown using such comments: -\begin{alltt} -(* begin show *) -\emph{some Coq material} -(* end show *) -\end{alltt} -The latter cannot be used around some inner parts of a proof, but can -be used around a whole proof. - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\subsection{Usage} - -\coqdoc\ is invoked on a shell command line as follows: -\begin{displaymath} - \texttt{coqdoc }<\textit{options and files}> -\end{displaymath} -Any command line argument which is not an option is considered to be a -file (even if it starts with a \verb!-!). \Coq\ files are identified -by the suffixes \verb!.v! and \verb!.g! and \LaTeX\ files by the -suffix \verb!.tex!. - -\begin{description} -\item[HTML output] ~\par - This is the default output. - One HTML file is created for each \Coq\ file given on the command line, - together with a file \texttt{index.html} (unless option - \texttt{-no-index} is passed). The HTML pages use a style sheet - named \texttt{style.css}. Such a file is distributed with \coqdoc. - -\item[\LaTeX\ output] ~\par - A single \LaTeX\ file is created, on standard output. It can be - redirected to a file with option \texttt{-o}. - The order of files on the command line is kept in the final - document. \LaTeX\ files given on the command line are copied `as is' - in the final document . - DVI and PostScript can be produced directly with the options - \texttt{-dvi} and \texttt{-ps} respectively. - -\item[\texmacs\ output] ~\par - To translate the input files to \texmacs\ format, to be used by - the \texmacs\ Coq interface. - %broken link: - %(see \url{http://www-sop.inria.fr/lemme/Philippe.Audebaud/tmcoq/}). -\end{description} - - -\subsubsection*{Command line options} - - -\paragraph{Overall options} - -\begin{description} - -\item[\texttt{\mm{}html}] ~\par - - Select a HTML output. - -\item[\texttt{\mm{}latex}] ~\par - - Select a \LaTeX\ output. - -\item[\texttt{\mm{}dvi}] ~\par - - Select a DVI output. - -\item[\texttt{\mm{}ps}] ~\par - - Select a PostScript output. - -\item[\texttt{\mm{}texmacs}] ~\par - - Select a \texmacs\ output. - -\item[\texttt{\mm{}stdout}] ~\par - - Write output to stdout. - -\item[\texttt{-o }\textit{file}, \texttt{\mm{}output }\textit{file}] ~\par - - Redirect the output into the file `\textit{file}' (meaningless with - \texttt{-html}). - -\item[\texttt{-d }\textit{dir}, \texttt{\mm{}directory }\textit{dir}] ~\par - - Output files into directory `\textit{dir}' instead of current - directory (option \texttt{-d} does not change the filename specified - with option \texttt{-o}, if any). - -\item[\texttt{\mm{}body-only}] ~\par - - Suppress the header and trailer of the final document. Thus, you can - insert the resulting document into a larger one. - -\item[\texttt{-p} \textit{string}, \texttt{\mm{}preamble} \textit{string}]~\par - - Insert some material in the \LaTeX\ preamble, right before - \verb!\begin{document}! (meaningless with \texttt{-html}). - -\item[\texttt{\mm{}vernac-file }\textit{file}, - \texttt{\mm{}tex-file }\textit{file}] ~\par - - Considers the file `\textit{file}' respectively as a \verb!.v! - (or \verb!.g!) file or a \verb!.tex! file. - -\item[\texttt{\mm{}files-from }\textit{file}] ~\par - - Read file names to process in file `\textit{file}' as if they were - given on the command line. Useful for program sources split up into - several directories. - -\item[\texttt{-q}, \texttt{\mm{}quiet}] ~\par - - Be quiet. Do not print anything except errors. - -\item[\texttt{-h}, \texttt{\mm{}help}] ~\par - - Give a short summary of the options and exit. - -\item[\texttt{-v}, \texttt{\mm{}version}] ~\par - - Print the version and exit. - -\end{description} - -\paragraph{Index options} - -Default behavior is to build an index, for the HTML output only, into -\texttt{index.html}. - -\begin{description} - -\item[\texttt{\mm{}no-index}] ~\par - - Do not output the index. - -\item[\texttt{\mm{}multi-index}] ~\par - - Generate one page for each category and each letter in the index, - together with a top page \texttt{index.html}. - -\item[\texttt{\mm{}index }\textit{string}] ~\par - - Make the filename of the index \textit{string} instead of ``index''. - Useful since ``index.html'' is special. - -\end{description} - -\paragraph{Table of contents option} - -\begin{description} - -\item[\texttt{-toc}, \texttt{\mm{}table-of-contents}] ~\par - - Insert a table of contents. - For a \LaTeX\ output, it inserts a \verb!\tableofcontents! at the - beginning of the document. For a HTML output, it builds a table of - contents into \texttt{toc.html}. - -\item[\texttt{\mm{}toc-depth }\textit{int}] ~\par - - Only include headers up to depth \textit{int} in the table of - contents. - -\end{description} - -\paragraph{Hyperlinks options} -\begin{description} - -\item[\texttt{\mm{}glob-from }\textit{file}] ~\par - - Make references using \Coq\ globalizations from file \textit{file}. - (Such globalizations are obtained with \Coq\ option \texttt{-dump-glob}). - -\item[\texttt{\mm{}no-externals}] ~\par - - Do not insert links to the \Coq\ standard library. - -\item[\texttt{\mm{}external }\textit{url}~\textit{coqdir}] ~\par - - Use given URL for linking references whose name starts with prefix - \textit{coqdir}. - -\item[\texttt{\mm{}coqlib }\textit{url}] ~\par - - Set base URL for the \Coq\ standard library (default is - \url{http://coq.inria.fr/library/}). This is equivalent to - \texttt{\mm{}external }\textit{url}~\texttt{Coq}. - -\item[\texttt{-R }\textit{dir }\textit{coqdir}] ~\par - - Map physical directory \textit{dir} to \Coq\ logical directory - \textit{coqdir} (similarly to \Coq\ option \texttt{-R}). - - Note: option \texttt{-R} only has effect on the files - \emph{following} it on the command line, so you will probably need - to put this option first. - -\end{description} - -\paragraph{Title options} -\begin{description} -\item[\texttt{-s }, \texttt{\mm{}short}] ~\par - - Do not insert titles for the files. The default behavior is to - insert a title like ``Library Foo'' for each file. - -\item[\texttt{\mm{}lib-name }\textit{string}] ~\par - - Print ``\textit{string} Foo'' instead of ``Library Foo'' in titles. - For example ``Chapter'' and ``Module'' are reasonable choices. - -\item[\texttt{\mm{}no-lib-name}] ~\par - - Print just ``Foo'' instead of ``Library Foo'' in titles. - -\item[\texttt{\mm{}lib-subtitles}] ~\par - - Look for library subtitles. When enabled, the beginning of each - file is checked for a comment of the form: -\begin{alltt} -(** * ModuleName : text *) -\end{alltt} - where \texttt{ModuleName} must be the name of the file. If it is - present, the \texttt{text} is used as a subtitle for the module in - appropriate places. - -\item[\texttt{-t }\textit{string}, - \texttt{\mm{}title }\textit{string}] ~\par - - Set the document title. - -\end{description} - -\paragraph{Contents options} -\begin{description} - -\item[\texttt{-g}, \texttt{\mm{}gallina}] ~\par - - Do not print proofs. - -\item[\texttt{-l}, \texttt{\mm{}light}] ~\par - - Light mode. Suppress proofs (as with \texttt{-g}) and the following commands: - \begin{itemize} - \item {}[\texttt{Recursive}] \texttt{Tactic Definition} - \item \texttt{Hint / Hints} - \item \texttt{Require} - \item \texttt{Transparent / Opaque} - \item \texttt{Implicit Argument / Implicits} - \item \texttt{Section / Variable / Hypothesis / End} - \end{itemize} - -\end{description} -The behavior of options \texttt{-g} and \texttt{-l} can be locally -overridden using the \texttt{(* begin show *)} \dots\ \texttt{(* end - show *)} environment (see above). - -There are a few options to drive the parsing of comments: -\begin{description} -\item[\texttt{\mm{}parse-comments}] ~\par - - Parses regular comments delimited by \texttt{(*} and \texttt{*)} as - well. They are typeset inline. - -\item[\texttt{\mm{}plain-comments}] ~\par - - Do not interpret comments, simply copy them as plain-text. - -\item[\texttt{\mm{}interpolate}] ~\par - - Use the globalization information to typeset identifiers appearing in - \Coq{} escapings inside comments. -\end{description} - - -\paragraph{Language options} - -Default behavior is to assume ASCII 7 bits input files. - -\begin{description} - -\item[\texttt{-latin1}, \texttt{\mm{}latin1}] ~\par - - Select ISO-8859-1 input files. It is equivalent to - \texttt{\mm{}inputenc latin1 \mm{}charset iso-8859-1}. - -\item[\texttt{-utf8}, \texttt{\mm{}utf8}] ~\par - - Set \texttt{\mm{}inputenc utf8x} for \LaTeX\ output and - \texttt{\mm{}charset utf-8} for HTML output. Also use Unicode - replacements for a couple of standard plain ASCII notations such - as $\rightarrow$ for \texttt{->} and $\forall$ for - \texttt{forall}. \LaTeX\ UTF-8 support can be found at - \url{http://www.ctan.org/pkg/unicode}. - - For the interpretation of Unicode characters by \LaTeX, extra - packages which {\coqdoc} does not provide by default might be - required, such as \texttt{textgreek} for some Greek letters or - \texttt{stmaryrd} for some mathematical symbols. If a Unicode - character is missing an interpretation in the \texttt{utf8x} input - encoding, add - \verb=\DeclareUnicodeCharacter{=\textit{code}\verb=}{=\textit{latex-interpretation}\verb=}=. Packages - and declarations can be added with option \texttt{-p}. - -\item[\texttt{\mm{}inputenc} \textit{string}] ~\par - - Give a \LaTeX\ input encoding, as an option to \LaTeX\ package - \texttt{inputenc}. - -\item[\texttt{\mm{}charset} \textit{string}] ~\par - - Specify the HTML character set, to be inserted in the HTML header. - -\end{description} - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\subsection[The coqdoc \LaTeX{} style file]{The coqdoc \LaTeX{} style file\label{section:coqdoc.sty}} - -In case you choose to produce a document without the default \LaTeX{} -preamble (by using option \verb|--no-preamble|), then you must insert -into your own preamble the command -\begin{quote} - \verb|\usepackage{coqdoc}| -\end{quote} - -The package optionally takes the argument \verb|[color]| to typeset -identifiers with colors (this requires the \verb|xcolor| package). - -Then you may alter the rendering of the document by -redefining some macros: -\begin{description} - -\item[\texttt{coqdockw}, \texttt{coqdocid}, \ldots] ~ - - The one-argument macros for typesetting keywords and identifiers. - Defaults are sans-serif for keywords and italic for identifiers. - - For example, if you would like a slanted font for keywords, you - may insert -\begin{verbatim} - \renewcommand{\coqdockw}[1]{\textsl{#1}} -\end{verbatim} - anywhere between \verb|\usepackage{coqdoc}| and - \verb|\begin{document}|. - -\item[\texttt{coqdocmodule}] ~ - - One-argument macro for typesetting the title of a \verb|.v| file. - Default is -\begin{verbatim} -\newcommand{\coqdocmodule}[1]{\section*{Module #1}} -\end{verbatim} - and you may redefine it using \verb|\renewcommand|. - -\end{description} - - diff --git a/doc/sphinx/addendum/extraction.rst b/doc/sphinx/addendum/extraction.rst new file mode 100644 index 000000000..d7f97edab --- /dev/null +++ b/doc/sphinx/addendum/extraction.rst @@ -0,0 +1,586 @@ +.. _extraction: + +.. include:: ../replaces.rst + +Extraction of programs in OCaml and Haskell +============================================ + +:Authors: Jean-Christophe Filliâtre and Pierre Letouzey + +We present here the |Coq| extraction commands, used to build certified +and relatively efficient functional programs, extracting them from +either |Coq| functions or |Coq| proofs of specifications. The +functional languages available as output are currently OCaml, Haskell +and Scheme. In the following, "ML" will be used (abusively) to refer +to any of the three. + +Before using any of the commands or options described in this chapter, +the extraction framework should first be loaded explicitly +via ``Require Extraction``, or via the more robust +``From Coq Require Extraction``. +Note that in earlier versions of Coq, these commands and options were +directly available without any preliminary ``Require``. + +.. coqtop:: in + + Require Extraction. + +Generating ML Code +------------------- + +.. note:: + + In the following, a qualified identifier `qualid` + can be used to refer to any kind of |Coq| global "object" : constant, + inductive type, inductive constructor or module name. + +The next two commands are meant to be used for rapid preview of +extraction. They both display extracted term(s) inside |Coq|. + +.. cmd:: Extraction @qualid. + + Extraction of the mentioned object in the |Coq| toplevel. + +.. cmd:: Recursive Extraction @qualid ... @qualid. + + Recursive extraction of all the mentioned objects and + all their dependencies in the |Coq| toplevel. + +All the following commands produce real ML files. User can choose to +produce one monolithic file or one file per |Coq| library. + +.. cmd:: Extraction "@file" @qualid ... @qualid. + + Recursive extraction of all the mentioned objects and all + their dependencies in one monolithic `file`. + Global and local identifiers are renamed according to the chosen ML + language to fulfill its syntactic conventions, keeping original + names as much as possible. + +.. cmd:: Extraction Library @ident. + + Extraction of the whole |Coq| library ``ident.v`` to an ML module + ``ident.ml``. In case of name clash, identifiers are here renamed + using prefixes ``coq_`` or ``Coq_`` to ensure a session-independent + renaming. + +.. cmd:: Recursive Extraction Library @ident. + + Extraction of the |Coq| library ``ident.v`` and all other modules + ``ident.v`` depends on. + +.. cmd:: Separate Extraction @qualid ... @qualid. + + Recursive extraction of all the mentioned objects and all + their dependencies, just as ``Extraction "file"``, + but instead of producing one monolithic file, this command splits + the produced code in separate ML files, one per corresponding Coq + ``.v`` file. This command is hence quite similar to + ``Recursive Extraction Library``, except that only the needed + parts of Coq libraries are extracted instead of the whole. + The naming convention in case of name clash is the same one as + ``Extraction Library``: identifiers are here renamed using prefixes + ``coq_`` or ``Coq_``. + +The following command is meant to help automatic testing of +the extraction, see for instance the ``test-suite`` directory +in the |Coq| sources. + +.. cmd:: Extraction TestCompile @qualid ... @qualid. + + All the mentioned objects and all their dependencies are extracted + to a temporary OCaml file, just as in ``Extraction "file"``. Then + this temporary file and its signature are compiled with the same + OCaml compiler used to built |Coq|. This command succeeds only + if the extraction and the OCaml compilation succeed. It fails + if the current target language of the extraction is not OCaml. + +Extraction Options +------------------- + +Setting the target language +~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +The ability to fix target language is the first and more important +of the extraction options. Default is ``Ocaml``. + +.. cmd:: Extraction Language Ocaml. +.. cmd:: Extraction Language Haskell. +.. cmd:: Extraction Language Scheme. + +Inlining and optimizations +~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +Since OCaml is a strict language, the extracted code has to +be optimized in order to be efficient (for instance, when using +induction principles we do not want to compute all the recursive calls +but only the needed ones). So the extraction mechanism provides an +automatic optimization routine that will be called each time the user +want to generate OCaml programs. The optimizations can be split in two +groups: the type-preserving ones (essentially constant inlining and +reductions) and the non type-preserving ones (some function +abstractions of dummy types are removed when it is deemed safe in order +to have more elegant types). Therefore some constants may not appear in the +resulting monolithic OCaml program. In the case of modular extraction, +even if some inlining is done, the inlined constant are nevertheless +printed, to ensure session-independent programs. + +Concerning Haskell, type-preserving optimizations are less useful +because of laziness. We still make some optimizations, for example in +order to produce more readable code. + +The type-preserving optimizations are controlled by the following |Coq| options: + +.. opt:: Extraction Optimize. + + Default is on. This controls all type-preserving optimizations made on + the ML terms (mostly reduction of dummy beta/iota redexes, but also + simplifications on Cases, etc). Turn this option off if you want a + ML term as close as possible to the Coq term. + +.. opt:: Extraction Conservative Types. + + Default is off. This controls the non type-preserving optimizations + made on ML terms (which try to avoid function abstraction of dummy + types). Turn this option on to make sure that ``e:t`` + implies that ``e':t'`` where ``e'`` and ``t'`` are the extracted + code of ``e`` and ``t`` respectively. + +.. opt:: Extraction KeepSingleton. + + Default is off. Normally, when the extraction of an inductive type + produces a singleton type (i.e. a type with only one constructor, and + only one argument to this constructor), the inductive structure is + removed and this type is seen as an alias to the inner type. + The typical example is ``sig``. This option allows disabling this + optimization when one wishes to preserve the inductive structure of types. + +.. opt:: Extraction AutoInline. + + Default is on. The extraction mechanism inlines the bodies of + some defined constants, according to some heuristics + like size of bodies, uselessness of some arguments, etc. + Those heuristics are not always perfect; if you want to disable + this feature, turn this option off. + +.. cmd:: Extraction Inline @qualid ... @qualid. + + In addition to the automatic inline feature, the constants + mentionned by this command will always be inlined during extraction. + +.. cmd:: Extraction NoInline @qualid ... @qualid. + + Conversely, the constants mentionned by this command will + never be inlined during extraction. + +.. cmd:: Print Extraction Inline. + + Prints the current state of the table recording the custom inlinings + declared by the two previous commands. + +.. cmd:: Reset Extraction Inline. + + Empties the table recording the custom inlinings (see the + previous commands). + +**Inlining and printing of a constant declaration:** + +A user can explicitly ask for a constant to be extracted by two means: + + * by mentioning it on the extraction command line + + * by extracting the whole |Coq| module of this constant. + +In both cases, the declaration of this constant will be present in the +produced file. But this same constant may or may not be inlined in +the following terms, depending on the automatic/custom inlining mechanism. + +For the constants non-explicitly required but needed for dependency +reasons, there are two cases: + + * If an inlining decision is taken, whether automatically or not, + all occurrences of this constant are replaced by its extracted body, + and this constant is not declared in the generated file. + + * If no inlining decision is taken, the constant is normally + declared in the produced file. + +Extra elimination of useless arguments +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +The following command provides some extra manual control on the +code elimination performed during extraction, in a way which +is independent but complementary to the main elimination +principles of extraction (logical parts and types). + +.. cmd:: Extraction Implicit @qualid [ @ident ... @ident ]. + + This experimental command allows declaring some arguments of + `qualid` as implicit, i.e. useless in extracted code and hence to + be removed by extraction. Here `qualid` can be any function or + inductive constructor, and the given `ident` are the names of + the concerned arguments. In fact, an argument can also be referred + by a number indicating its position, starting from 1. + +When an actual extraction takes place, an error is normally raised if the +``Extraction Implicit`` declarations cannot be honored, that is +if any of the implicited variables still occurs in the final code. +This behavior can be relaxed via the following option: + +.. opt:: Extraction SafeImplicits. + + Default is on. When this option is off, a warning is emitted + instead of an error if some implicited variables still occur in the + final code of an extraction. This way, the extracted code may be + obtained nonetheless and reviewed manually to locate the source of the issue + (in the code, some comments mark the location of these remaining + implicited variables). + Note that this extracted code might not compile or run properly, + depending of the use of these remaining implicited variables. + +Realizing axioms +~~~~~~~~~~~~~~~~ + +Extraction will fail if it encounters an informative axiom not realized. +A warning will be issued if it encounters a logical axiom, to remind the +user that inconsistent logical axioms may lead to incorrect or +non-terminating extracted terms. + +It is possible to assume some axioms while developing a proof. Since +these axioms can be any kind of proposition or object or type, they may +perfectly well have some computational content. But a program must be +a closed term, and of course the system cannot guess the program which +realizes an axiom. Therefore, it is possible to tell the system +what ML term corresponds to a given axiom. + +.. cmd:: Extract Constant @qualid => @string. + + Give an ML extraction for the given constant. + The `string` may be an identifier or a quoted string. + +.. cmd:: Extract Inlined Constant @qualid => @string. + + Same as the previous one, except that the given ML terms will + be inlined everywhere instead of being declared via a ``let``. + + .. note:: + + This command is sugar for an ``Extract Constant`` followed + by a ``Extraction Inline``. Hence a ``Reset Extraction Inline`` + will have an effect on the realized and inlined axiom. + +.. caution:: It is the responsibility of the user to ensure that the ML + terms given to realize the axioms do have the expected types. In + fact, the strings containing realizing code are just copied to the + extracted files. The extraction recognizes whether the realized axiom + should become a ML type constant or a ML object declaration. For example: + +.. coqtop:: in + + Axiom X:Set. + Axiom x:X. + Extract Constant X => "int". + Extract Constant x => "0". + +Notice that in the case of type scheme axiom (i.e. whose type is an +arity, that is a sequence of product finished by a sort), then some type +variables have to be given (as quoted strings). The syntax is then: + +.. cmdv:: Extract Constant @qualid @string ... @string => @string. + +The number of type variables is checked by the system. For example: + +.. coqtop:: in + + Axiom Y : Set -> Set -> Set. + Extract Constant Y "'a" "'b" => " 'a * 'b ". + +Realizing an axiom via ``Extract Constant`` is only useful in the +case of an informative axiom (of sort ``Type`` or ``Set``). A logical axiom +have no computational content and hence will not appears in extracted +terms. But a warning is nonetheless issued if extraction encounters a +logical axiom. This warning reminds user that inconsistent logical +axioms may lead to incorrect or non-terminating extracted terms. + +If an informative axiom has not been realized before an extraction, a +warning is also issued and the definition of the axiom is filled with +an exception labeled ``AXIOM TO BE REALIZED``. The user must then +search these exceptions inside the extracted file and replace them by +real code. + +Realizing inductive types +~~~~~~~~~~~~~~~~~~~~~~~~~ + +The system also provides a mechanism to specify ML terms for inductive +types and constructors. For instance, the user may want to use the ML +native boolean type instead of |Coq| one. The syntax is the following: + +.. cmd:: Extract Inductive @qualid => @string [ @string ... @string ]. + + Give an ML extraction for the given inductive type. You must specify + extractions for the type itself (first `string`) and all its + constructors (all the `string` between square brackets). In this form, + the ML extraction must be an ML inductive datatype, and the native + pattern-matching of the language will be used. + +.. cmdv:: Extract Inductive @qualid => @string [ @string ... @string ] @string. + + Same as before, with a final extra `string` that indicates how to + perform pattern-matching over this inductive type. In this form, + the ML extraction could be an arbitrary type. + For an inductive type with `k` constructors, the function used to + emulate the pattern-matching should expect `(k+1)` arguments, first the `k` + branches in functional form, and then the inductive element to + destruct. For instance, the match branch ``| S n => foo`` gives the + functional form ``(fun n -> foo)``. Note that a constructor with no + argument is considered to have one unit argument, in order to block + early evaluation of the branch: ``| O => bar`` leads to the functional + form ``(fun () -> bar)``. For instance, when extracting ``nat`` + into OCaml ``int``, the code to provide has type: + ``(unit->'a)->(int->'a)->int->'a``. + +.. caution:: As for ``Extract Constant``, this command should be used with care: + + * The ML code provided by the user is currently **not** checked at all by + extraction, even for syntax errors. + + * Extracting an inductive type to a pre-existing ML inductive type + is quite sound. But extracting to a general type (by providing an + ad-hoc pattern-matching) will often **not** be fully rigorously + correct. For instance, when extracting ``nat`` to OCaml ``int``, + it is theoretically possible to build ``nat`` values that are + larger than OCaml ``max_int``. It is the user's responsibility to + be sure that no overflow or other bad events occur in practice. + + * Translating an inductive type to an arbitrary ML type does **not** + magically improve the asymptotic complexity of functions, even if the + ML type is an efficient representation. For instance, when extracting + ``nat`` to OCaml ``int``, the function ``Nat.mul`` stays quadratic. + It might be interesting to associate this translation with + some specific ``Extract Constant`` when primitive counterparts exist. + +Typical examples are the following: + +.. coqtop:: in + + Extract Inductive unit => "unit" [ "()" ]. + Extract Inductive bool => "bool" [ "true" "false" ]. + Extract Inductive sumbool => "bool" [ "true" "false" ]. + +.. note:: + + When extracting to Ocaml, if an inductive constructor or type has arity 2 and + the corresponding string is enclosed by parentheses, and the string meets + Ocaml's lexical criteria for an infix symbol, then the rest of the string is + used as infix constructor or type. + +.. coqtop:: in + + Extract Inductive list => "list" [ "[]" "(::)" ]. + Extract Inductive prod => "(*)" [ "(,)" ]. + +As an example of translation to a non-inductive datatype, let's turn +``nat`` into OCaml ``int`` (see caveat above): + +.. coqtop:: in + + Extract Inductive nat => int [ "0" "succ" ] "(fun fO fS n -> if n=0 then fO () else fS (n-1))". + +Avoiding conflicts with existing filenames +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +When using ``Extraction Library``, the names of the extracted files +directly depends from the names of the |Coq| files. It may happen that +these filenames are in conflict with already existing files, +either in the standard library of the target language or in other +code that is meant to be linked with the extracted code. +For instance the module ``List`` exists both in |Coq| and in OCaml. +It is possible to instruct the extraction not to use particular filenames. + +.. cmd:: Extraction Blacklist @ident ... @ident. + + Instruct the extraction to avoid using these names as filenames + for extracted code. + +.. cmd:: Print Extraction Blacklist. + + Show the current list of filenames the extraction should avoid. + +.. cmd:: Reset Extraction Blacklist. + + Allow the extraction to use any filename. + +For OCaml, a typical use of these commands is +``Extraction Blacklist String List``. + +Differences between |Coq| and ML type systems +---------------------------------------------- + +Due to differences between |Coq| and ML type systems, +some extracted programs are not directly typable in ML. +We now solve this problem (at least in OCaml) by adding +when needed some unsafe casting ``Obj.magic``, which give +a generic type ``'a`` to any term. + +First, if some part of the program is *very* polymorphic, there +may be no ML type for it. In that case the extraction to ML works +alright but the generated code may be refused by the ML +type-checker. A very well known example is the ``distr-pair`` +function: + +.. coqtop:: in + + Definition dp {A B:Type}(x:A)(y:B)(f:forall C:Type, C->C) := (f A x, f B y). + +In Ocaml, for instance, the direct extracted term would be:: + + let dp x y f = Pair((f () x),(f () y)) + +and would have type:: + + dp : 'a -> 'a -> (unit -> 'a -> 'b) -> ('b,'b) prod + +which is not its original type, but a restriction. + +We now produce the following correct version:: + + let dp x y f = Pair ((Obj.magic f () x), (Obj.magic f () y)) + +Secondly, some |Coq| definitions may have no counterpart in ML. This +happens when there is a quantification over types inside the type +of a constructor; for example: + +.. coqtop:: in + + Inductive anything : Type := dummy : forall A:Set, A -> anything. + +which corresponds to the definition of an ML dynamic type. +In OCaml, we must cast any argument of the constructor dummy +(no GADT are produced yet by the extraction). + +Even with those unsafe castings, you should never get error like +``segmentation fault``. In fact even if your program may seem +ill-typed to the Ocaml type-checker, it can't go wrong : it comes +from a Coq well-typed terms, so for example inductive types will always +have the correct number of arguments, etc. Of course, when launching +manually some extracted function, you should apply it to arguments +of the right shape (from the |Coq| point-of-view). + +More details about the correctness of the extracted programs can be +found in :cite:`Let02`. + +We have to say, though, that in most "realistic" programs, these problems do not +occur. For example all the programs of Coq library are accepted by the OCaml +type-checker without any ``Obj.magic`` (see examples below). + +Some examples +------------- + +We present here two examples of extractions, taken from the +|Coq| Standard Library. We choose OCaml as target language, +but all can be done in the other dialects with slight modifications. +We then indicate where to find other examples and tests of extraction. + +A detailed example: Euclidean division +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +The file ``Euclid`` contains the proof of Euclidean division. +The natural numbers used there are unary integers of type ``nat``, +defined by two constructors ``O`` and ``S``. +This module contains a theorem ``eucl_dev``, whose type is:: + + forall b:nat, b > 0 -> forall a:nat, diveucl a b + +where ``diveucl`` is a type for the pair of the quotient and the +modulo, plus some logical assertions that disappear during extraction. +We can now extract this program to OCaml: + +.. coqtop:: none + + Reset Initial. + +.. coqtop:: all + + Require Extraction. + Require Import Euclid Wf_nat. + Extraction Inline gt_wf_rec lt_wf_rec induction_ltof2. + Recursive Extraction eucl_dev. + +The inlining of ``gt_wf_rec`` and others is not +mandatory. It only enhances readability of extracted code. +You can then copy-paste the output to a file ``euclid.ml`` or let +|Coq| do it for you with the following command:: + + Extraction "euclid" eucl_dev. + +Let us play the resulting program (in an OCaml toplevel):: + + #use "euclid.ml";; + type nat = O | S of nat + type sumbool = Left | Right + val sub : nat -> nat -> nat = <fun> + val le_lt_dec : nat -> nat -> sumbool = <fun> + val le_gt_dec : nat -> nat -> sumbool = <fun> + type diveucl = Divex of nat * nat + val eucl_dev : nat -> nat -> diveucl = <fun> + + # eucl_dev (S (S O)) (S (S (S (S (S O)))));; + - : diveucl = Divex (S (S O), S O) + +It is easier to test on OCaml integers:: + + # let rec nat_of_int = function 0 -> O | n -> S (nat_of_int (n-1));; + val nat_of_int : int -> nat = <fun> + + # let rec int_of_nat = function O -> 0 | S p -> 1+(int_of_nat p);; + val int_of_nat : nat -> int = <fun> + + # let div a b = + let Divex (q,r) = eucl_dev (nat_of_int b) (nat_of_int a) + in (int_of_nat q, int_of_nat r);; + val div : int -> int -> int * int = <fun> + + # div 173 15;; + - : int * int = (11, 8) + +Note that these ``nat_of_int`` and ``int_of_nat`` are now +available via a mere ``Require Import ExtrOcamlIntConv`` and then +adding these functions to the list of functions to extract. This file +``ExtrOcamlIntConv.v`` and some others in ``plugins/extraction/`` +are meant to help building concrete program via extraction. + +Extraction's horror museum +~~~~~~~~~~~~~~~~~~~~~~~~~~ + +Some pathological examples of extraction are grouped in the file +``test-suite/success/extraction.v`` of the sources of |Coq|. + +Users' Contributions +~~~~~~~~~~~~~~~~~~~~ + +Several of the |Coq| Users' Contributions use extraction to produce +certified programs. In particular the following ones have an automatic +extraction test: + + * ``additions`` : https://github.com/coq-contribs/additions + * ``bdds`` : https://github.com/coq-contribs/bdds + * ``canon-bdds`` : https://github.com/coq-contribs/canon-bdds + * ``chinese`` : https://github.com/coq-contribs/chinese + * ``continuations`` : https://github.com/coq-contribs/continuations + * ``coq-in-coq`` : https://github.com/coq-contribs/coq-in-coq + * ``exceptions`` : https://github.com/coq-contribs/exceptions + * ``firing-squad`` : https://github.com/coq-contribs/firing-squad + * ``founify`` : https://github.com/coq-contribs/founify + * ``graphs`` : https://github.com/coq-contribs/graphs + * ``higman-cf`` : https://github.com/coq-contribs/higman-cf + * ``higman-nw`` : https://github.com/coq-contribs/higman-nw + * ``hardware`` : https://github.com/coq-contribs/hardware + * ``multiplier`` : https://github.com/coq-contribs/multiplier + * ``search-trees`` : https://github.com/coq-contribs/search-trees + * ``stalmarck`` : https://github.com/coq-contribs/stalmarck + +Note that ``continuations`` and ``multiplier`` are a bit particular. They are +examples of developments where ``Obj.magic`` are needed. This is +probably due to an heavy use of impredicativity. After compilation, those +two examples run nonetheless, thanks to the correction of the +extraction :cite:`Let02`. diff --git a/doc/sphinx/addendum/generalized-rewriting.rst b/doc/sphinx/addendum/generalized-rewriting.rst new file mode 100644 index 000000000..da9e97e6f --- /dev/null +++ b/doc/sphinx/addendum/generalized-rewriting.rst @@ -0,0 +1,845 @@ +.. _generalizedrewriting: + +----------------------- + Generalized rewriting +----------------------- + +:Author: Matthieu Sozeau + +Generalized rewriting +===================== + + +This chapter presents the extension of several equality related +tactics to work over user-defined structures (called setoids) that are +equipped with ad-hoc equivalence relations meant to behave as +equalities. Actually, the tactics have also been generalized to +relations weaker then equivalences (e.g. rewriting systems). The +toolbox also extends the automatic rewriting capabilities of the +system, allowing the specification of custom strategies for rewriting. + +This documentation is adapted from the previous setoid documentation +by Claudio Sacerdoti Coen (based on previous work by Clément Renard). +The new implementation is a drop-in replacement for the old one +[#tabareau]_, hence most of the documentation still applies. + +The work is a complete rewrite of the previous implementation, based +on the type class infrastructure. It also improves on and generalizes +the previous implementation in several ways: + + ++ User-extensible algorithm. The algorithm is separated in two parts: + generations of the rewriting constraints (done in ML) and solving of + these constraints using type class resolution. As type class + resolution is extensible using tactics, this allows users to define + general ways to solve morphism constraints. ++ Sub-relations. An example extension to the base algorithm is the + ability to define one relation as a subrelation of another so that + morphism declarations on one relation can be used automatically for + the other. This is done purely using tactics and type class search. ++ Rewriting under binders. It is possible to rewrite under binders in + the new implementation, if one provides the proper morphisms. Again, + most of the work is handled in the tactics. ++ First-class morphisms and signatures. Signatures and morphisms are + ordinary Coq terms, hence they can be manipulated inside Coq, put + inside structures and lemmas about them can be proved inside the + system. Higher-order morphisms are also allowed. ++ Performance. The implementation is based on a depth-first search for + the first solution to a set of constraints which can be as fast as + linear in the size of the term, and the size of the proof term is + linear in the size of the original term. Besides, the extensibility + allows the user to customize the proof search if necessary. + +.. [#tabareau] Nicolas Tabareau helped with the gluing. + +Introduction to generalized rewriting +------------------------------------- + + +Relations and morphisms +~~~~~~~~~~~~~~~~~~~~~~~ + +A parametric *relation* ``R`` is any term of type +``forall (x1 :T1 ) ... (xn :Tn ), relation A``. +The expression ``A``, which depends on ``x1 ... xn`` , is called the *carrier* +of the relation and ``R`` is said to be a relation over ``A``; the list +``x1,...,xn`` is the (possibly empty) list of parameters of the relation. + +**Example 1 (Parametric relation):** + +It is possible to implement finite sets of elements of type ``A`` as +unordered list of elements of type ``A``. +The function ``set_eq: forall (A: Type), relation (list A)`` +satisfied by two lists with the same elements is a parametric relation +over ``(list A)`` with one parameter ``A``. The type of ``set_eq`` +is convertible with ``forall (A: Type), list A -> list A -> Prop.`` + +An *instance* of a parametric relation ``R`` with n parameters is any term +``(R t1 ... tn )``. + +Let ``R`` be a relation over ``A`` with ``n`` parameters. A term is a parametric +proof of reflexivity for ``R`` if it has type +``forall (x1 :T1 ) ... (xn :Tn), reflexive (R x1 ... xn )``. +Similar definitions are given for parametric proofs of symmetry and transitivity. + +**Example 2 (Parametric relation (cont.)):** + +The ``set_eq`` relation of the previous example can be proved to be +reflexive, symmetric and transitive. A parametric unary function ``f`` of type +``forall (x1 :T1 ) ... (xn :Tn ), A1 -> A2`` covariantly respects two parametric relation instances +``R1`` and ``R2`` if, whenever ``x``, ``y`` satisfy ``R1 x y``, their images (``f x``) and (``f y``) +satisfy ``R2 (f x) (f y)``. An ``f`` that respects its input and output +relations will be called a unary covariant *morphism*. We can also say +that ``f`` is a monotone function with respect to ``R1`` and ``R2`` . The +sequence ``x1 ... xn`` represents the parameters of the morphism. + +Let ``R1`` and ``R2`` be two parametric relations. The *signature* of a +parametric morphism of type ``forall (x1 :T1 ) ... (xn :Tn ), A1 -> A2`` +that covariantly respects two instances :math:`I_{R_1}` and :math:`I_{R_2}` of ``R1`` and ``R2`` +is written :math:`I_{R_1} ++> I_{R_2}`. Notice that the special arrow ++>, which +reminds the reader of covariance, is placed between the two relation +instances, not between the two carriers. The signature relation +instances and morphism will be typed in a context introducing +variables for the parameters. + +The previous definitions are extended straightforwardly to n-ary +morphisms, that are required to be simultaneously monotone on every +argument. + +Morphisms can also be contravariant in one or more of their arguments. +A morphism is contravariant on an argument associated to the relation +instance :math`R` if it is covariant on the same argument when the inverse +relation :math:`R^{−1}` (``inverse R`` in Coq) is considered. The special arrow ``-->`` +is used in signatures for contravariant morphisms. + +Functions having arguments related by symmetric relations instances +are both covariant and contravariant in those arguments. The special +arrow ``==>`` is used in signatures for morphisms that are both +covariant and contravariant. + +An instance of a parametric morphism :math:`f` with :math:`n` +parameters is any term :math:`f \, t_1 \ldots t_n`. + +**Example 3 (Morphisms):** + +Continuing the previous example, let ``union: forall (A: Type), list A -> list A -> list A`` +perform the union of two sets by appending one list to the other. ``union` is a binary +morphism parametric over ``A`` that respects the relation instance +``(set_eq A)``. The latter condition is proved by showing: + +.. coqtop:: in + + forall (A: Type) (S1 S1’ S2 S2’: list A), + set_eq A S1 S1’ -> + set_eq A S2 S2’ -> + set_eq A (union A S1 S2) (union A S1’ S2’). + +The signature of the function ``union A`` is ``set_eq A ==> set_eq A ==> set_eq A`` +for all ``A``. + +**Example 4 (Contravariant morphism):** + +The division function ``Rdiv: R -> R -> R`` is a morphism of signature +``le ++> le --> le`` where ``le`` is the usual order relation over +real numbers. Notice that division is covariant in its first argument +and contravariant in its second argument. + +Leibniz equality is a relation and every function is a morphism that +respects Leibniz equality. Unfortunately, Leibniz equality is not +always the intended equality for a given structure. + +In the next section we will describe the commands to register terms as +parametric relations and morphisms. Several tactics that deal with +equality in Coq can also work with the registered relations. The exact +list of tactic will be given :ref:`in this section <tactics-enabled-on-user-provided-relations>`. +For instance, the tactic reflexivity can be used to close a goal ``R n n`` whenever ``R`` +is an instance of a registered reflexive relation. However, the +tactics that replace in a context ``C[]`` one term with another one +related by ``R`` must verify that ``C[]`` is a morphism that respects the +intended relation. Currently the verification consists in checking +whether ``C[]`` is a syntactic composition of morphism instances that respects some obvious +compatibility constraints. + + +**Example 5 (Rewriting):** + +Continuing the previous examples, suppose that the user must prove +``set_eq int (union int (union int S1 S2) S2) (f S1 S2)`` under the +hypothesis ``H: set_eq int S2 (@nil int)``. It +is possible to use the ``rewrite`` tactic to replace the first two +occurrences of ``S2`` with ``@nil int`` in the goal since the +context ``set_eq int (union int (union int S1 nil) nil) (f S1 S2)``, +being a composition of morphisms instances, is a morphism. However the +tactic will fail replacing the third occurrence of ``S2`` unless ``f`` +has also been declared as a morphism. + + +Adding new relations and morphisms +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +A parametric relation :g:`Aeq: forall (y1 : β1 ... ym : βm )`, +:g:`relation (A t1 ... tn)` over :g:`(A : αi -> ... αn -> Type)` can be +declared with the following command: + +.. cmd:: Add Parametric Relation (x1 : T1) ... (xn : Tk) : (A t1 ... tn) (Aeq t′1 ... t′m ) {? reflexivity proved by refl} {? symmetry proved by sym} {? transitivity proved by trans} as @ident. + +after having required the ``Setoid`` module with the ``Require Setoid`` +command. + +The :g:`@ident` gives a unique name to the morphism and it is used +by the command to generate fresh names for automatically provided +lemmas used internally. + +Notice that the carrier and relation parameters may refer to the +context of variables introduced at the beginning of the declaration, +but the instances need not be made only of variables. Also notice that +``A`` is *not* required to be a term having the same parameters as ``Aeq``, +although that is often the case in practice (this departs from the +previous implementation). + + +.. cmd:: Add Relation + +In case the carrier and relations are not parametric, one can use this command +instead, whose syntax is the same except there is no local context. + +The proofs of reflexivity, symmetry and transitivity can be omitted if +the relation is not an equivalence relation. The proofs must be +instances of the corresponding relation definitions: e.g. the proof of +reflexivity must have a type convertible to +:g:`reflexive (A t1 ... tn) (Aeq t′ 1 …t′ n )`. +Each proof may refer to the introduced variables as well. + +**Example 6 (Parametric relation):** + +For Leibniz equality, we may declare: + +.. coqtop:: in + + Add Parametric Relation (A : Type) : A (@eq A) + [reflexivity proved by @refl_equal A] + ... + +Some tactics (``reflexivity``, ``symmetry``, ``transitivity``) work only on +relations that respect the expected properties. The remaining tactics +(``replace``, ``rewrite`` and derived tactics such as ``autorewrite``) do not +require any properties over the relation. However, they are able to +replace terms with related ones only in contexts that are syntactic +compositions of parametric morphism instances declared with the +following command. + +.. cmd:: Add Parametric Morphism (x1 : T1 ) ... (xk : Tk ) : (f t1 ... tn ) with signature sig as @ident. + +The command declares ``f`` as a parametric morphism of signature ``sig``. The +identifier ``id`` gives a unique name to the morphism and it is used as +the base name of the type class instance definition and as the name of +the lemma that proves the well-definedness of the morphism. The +parameters of the morphism as well as the signature may refer to the +context of variables. The command asks the user to prove interactively +that ``f`` respects the relations identified from the signature. + +**Example 7:** + +We start the example by assuming a small theory over +homogeneous sets and we declare set equality as a parametric +equivalence relation and union of two sets as a parametric morphism. + +.. coqtop:: in + + Require Export Setoid. + Require Export Relation_Definitions. + + Set Implicit Arguments. + + Parameter set: Type -> Type. + Parameter empty: forall A, set A. + Parameter eq_set: forall A, set A -> set A -> Prop. + Parameter union: forall A, set A -> set A -> set A. + + Axiom eq_set_refl: forall A, reflexive _ (eq_set (A:=A)). + Axiom eq_set_sym: forall A, symmetric _ (eq_set (A:=A)). + Axiom eq_set_trans: forall A, transitive _ (eq_set (A:=A)). + Axiom empty_neutral: forall A (S: set A), eq_set (union S (empty A)) S. + + Axiom union_compat: forall (A : Type), + forall x x' : set A, eq_set x x' -> + forall y y' : set A, eq_set y y' -> + eq_set (union x y) (union x' y'). + + Add Parametric Relation A : (set A) (@eq_set A) + reflexivity proved by (eq_set_refl (A:=A)) + symmetry proved by (eq_set_sym (A:=A)) + transitivity proved by (eq_set_trans (A:=A)) + as eq_set_rel. + + Add Parametric Morphism A : (@union A) with + signature (@eq_set A) ==> (@eq_set A) ==> (@eq_set A) as union_mor. + Proof. + exact (@union_compat A). + Qed. + +It is possible to reduce the burden of specifying parameters using +(maximally inserted) implicit arguments. If ``A`` is always set as +maximally implicit in the previous example, one can write: + +.. coqtop:: in + + Add Parametric Relation A : (set A) eq_set + reflexivity proved by eq_set_refl + symmetry proved by eq_set_sym + transitivity proved by eq_set_trans + as eq_set_rel. + +.. coqtop:: in + + Add Parametric Morphism A : (@union A) with + signature eq_set ==> eq_set ==> eq_set as union_mor. + +.. coqtop:: in + + Proof. exact (@union_compat A). Qed. + +We proceed now by proving a simple lemma performing a rewrite step and +then applying reflexivity, as we would do working with Leibniz +equality. Both tactic applications are accepted since the required +properties over ``eq_set`` and ``union`` can be established from the two +declarations above. + +.. coqtop:: in + + Goal forall (S: set nat), + eq_set (union (union S empty) S) (union S S). + +.. coqtop:: in + + Proof. intros. rewrite empty_neutral. reflexivity. Qed. + +The tables of relations and morphisms are managed by the type class +instance mechanism. The behavior on section close is to generalize the +instances by the variables of the section (and possibly hypotheses +used in the proofs of instance declarations) but not to export them in +the rest of the development for proof search. One can use the +``Existing Instance`` command to do so outside the section, using the name of the +declared morphism suffixed by ``_Morphism``, or use the ``Global`` modifier +for the corresponding class instance declaration +(see :ref:`First Class Setoids and Morphisms <first-class-setoids-and-morphisms>`) at +definition time. When loading a compiled file or importing a module, +all the declarations of this module will be loaded. + + +Rewriting and non reflexive relations +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +To replace only one argument of an n-ary morphism it is necessary to +prove that all the other arguments are related to themselves by the +respective relation instances. + +**Example 8:** + +To replace ``(union S empty)`` with ``S`` in ``(union (union S empty) S) (union S S)`` +the rewrite tactic must exploit the monotony of ``union`` (axiom ``union_compat`` +in the previous example). Applying ``union_compat`` by hand we are left with the +goal ``eq_set (union S S) (union S S)``. + +When the relations associated to some arguments are not reflexive, the +tactic cannot automatically prove the reflexivity goals, that are left +to the user. + +Setoids whose relation are partial equivalence relations (PER) are +useful to deal with partial functions. Let ``R`` be a PER. We say that an +element ``x`` is defined if ``R x x``. A partial function whose domain +comprises all the defined elements only is declared as a morphism that +respects ``R``. Every time a rewriting step is performed the user must +prove that the argument of the morphism is defined. + +**Example 9:** + +Let ``eqO`` be ``fun x y => x = y /\ x <> 0`` (the +smaller PER over non zero elements). Division can be declared as a +morphism of signature ``eq ==> eq0 ==> eq``. Replace ``x`` with +``y`` in ``div x n = div y n`` opens the additional goal ``eq0 n n`` +that is equivalent to ``n = n /\ n <> 0``. + + +Rewriting and non symmetric relations +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +When the user works up to relations that are not symmetric, it is no +longer the case that any covariant morphism argument is also +contravariant. As a result it is no longer possible to replace a term +with a related one in every context, since the obtained goal implies +the previous one if and only if the replacement has been performed in +a contravariant position. In a similar way, replacement in an +hypothesis can be performed only if the replaced term occurs in a +covariant position. + +**Example 10 (Covariance and contravariance):** + +Suppose that division over real numbers has been defined as a morphism of signature +``Z.div: Z.lt ++> Z.lt --> Z.lt`` (i.e. ``Z.div`` is increasing in +its first argument, but decreasing on the second one). Let ``<`` +denotes ``Z.lt``. Under the hypothesis ``H: x < y`` we have +``k < x / y -> k < x / x``, but not ``k < y / x -> k < x / x``. Dually, +under the same hypothesis ``k < x / y -> k < y / y`` holds, but +``k < y / x -> k < y / y`` does not. Thus, if the current goal is +``k < x / x``, it is possible to replace only the second occurrence of +``x`` (in contravariant position) with ``y`` since the obtained goal +must imply the current one. On the contrary, if ``k < x / x`` is an +hypothesis, it is possible to replace only the first occurrence of +``x`` (in covariant position) with ``y`` since the current +hypothesis must imply the obtained one. + +Contrary to the previous implementation, no specific error message +will be raised when trying to replace a term that occurs in the wrong +position. It will only fail because the rewriting constraints are not +satisfiable. However it is possible to use the at modifier to specify +which occurrences should be rewritten. + +As expected, composing morphisms together propagates the variance +annotations by switching the variance every time a contravariant +position is traversed. + +**Example 11:** + +Let us continue the previous example and let us consider +the goal ``x / (x / x) < k``. The first and third occurrences of +``x`` are in a contravariant position, while the second one is in +covariant position. More in detail, the second occurrence of ``x`` +occurs covariantly in ``(x / x)`` (since division is covariant in +its first argument), and thus contravariantly in ``x / (x / x)`` +(since division is contravariant in its second argument), and finally +covariantly in ``x / (x / x) < k`` (since ``<``, as every +transitive relation, is contravariant in its first argument with +respect to the relation itself). + + +Rewriting in ambiguous setoid contexts +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +One function can respect several different relations and thus it can +be declared as a morphism having multiple signatures. + +**Example 12:** + + +Union over homogeneous lists can be given all the +following signatures: ``eq ==> eq ==> eq`` (``eq`` being the +equality over ordered lists) ``set_eq ==> set_eq ==> set_eq`` +(``set_eq`` being the equality over unordered lists up to duplicates), +``multiset_eq ==> multiset_eq ==> multiset_eq`` (``multiset_eq`` +being the equality over unordered lists). + +To declare multiple signatures for a morphism, repeat the ``Add Morphism`` +command. + +When morphisms have multiple signatures it can be the case that a +rewrite request is ambiguous, since it is unclear what relations +should be used to perform the rewriting. Contrary to the previous +implementation, the tactic will always choose the first possible +solution to the set of constraints generated by a rewrite and will not +try to find *all* possible solutions to warn the user about. + + +Commands and tactics +-------------------- + + +.. _first-class-setoids-and-morphisms: + +First class setoids and morphisms +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + + + +The implementation is based on a first-class representation of +properties of relations and morphisms as type classes. That is, the +various combinations of properties on relations and morphisms are +represented as records and instances of theses classes are put in a +hint database. For example, the declaration: + +.. coqtop:: in + + Add Parametric Relation (x1 : T1) ... (xn : Tk) : (A t1 ... tn) (Aeq t′1 ... t′m) + [reflexivity proved by refl] + [symmetry proved by sym] + [transitivity proved by trans] + as id. + + +is equivalent to an instance declaration: + +.. coqtop:: in + + Instance (x1 : T1) ... (xn : Tk) => id : @Equivalence (A t1 ... tn) (Aeq t′1 ... t′m) := + [Equivalence_Reflexive := refl] + [Equivalence_Symmetric := sym] + [Equivalence_Transitive := trans]. + +The declaration itself amounts to the definition of an object of the +record type ``Coq.Classes.RelationClasses.Equivalence`` and a hint added +to the ``typeclass_instances`` hint database. Morphism declarations are +also instances of a type class defined in ``Classes.Morphisms``. See the +documentation on type classes :ref:`TODO-chapter-20-type-classes` +and the theories files in Classes for further explanations. + +One can inform the rewrite tactic about morphisms and relations just +by using the typeclass mechanism to declare them using Instance and +Context vernacular commands. Any object of type Proper (the type of +morphism declarations) in the local context will also be automatically +used by the rewriting tactic to solve constraints. + +Other representations of first class setoids and morphisms can also be +handled by encoding them as records. In the following example, the +projections of the setoid relation and of the morphism function can be +registered as parametric relations and morphisms. + +**Example 13 (First class setoids):** + +.. coqtop:: in + + Require Import Relation_Definitions Setoid. + + Record Setoid: Type := + { car: Type; + eq: car -> car -> Prop; + refl: reflexive _ eq; + sym: symmetric _ eq; + trans: transitive _ eq + }. + + Add Parametric Relation (s : Setoid) : (@car s) (@eq s) + reflexivity proved by (refl s) + symmetry proved by (sym s) + transitivity proved by (trans s) as eq_rel. + + Record Morphism (S1 S2:Setoid): Type := + { f: car S1 -> car S2; + compat: forall (x1 x2: car S1), eq S1 x1 x2 -> eq S2 (f x1) (f x2) + }. + + Add Parametric Morphism (S1 S2 : Setoid) (M : Morphism S1 S2) : + (@f S1 S2 M) with signature (@eq S1 ==> @eq S2) as apply_mor. + Proof. apply (compat S1 S2 M). Qed. + + Lemma test: forall (S1 S2:Setoid) (m: Morphism S1 S2) + (x y: car S1), eq S1 x y -> eq S2 (f _ _ m x) (f _ _ m y). + Proof. intros. rewrite H. reflexivity. Qed. + +.. _tactics-enabled-on-user-provided-relations: + +Tactics enabled on user provided relations +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +The following tactics, all prefixed by ``setoid_``, deal with arbitrary +registered relations and morphisms. Moreover, all the corresponding +unprefixed tactics (i.e. ``reflexivity``, ``symmetry``, ``transitivity``, +``replace``, ``rewrite``) have been extended to fall back to their prefixed +counterparts when the relation involved is not Leibniz equality. +Notice, however, that using the prefixed tactics it is possible to +pass additional arguments such as ``using relation``. + +.. tacv:: setoid_reflexivity + +.. tacv:: setoid_symmetry [in @ident] + +.. tacv:: setoid_transitivity + +.. tacv:: setoid_rewrite [@orientation] @term [at @occs] [in @ident] + +.. tacv:: setoid_replace @term with @term [in @ident] [using relation @term] [by @tactic] + + +The ``using relation`` arguments cannot be passed to the unprefixed form. +The latter argument tells the tactic what parametric relation should +be used to replace the first tactic argument with the second one. If +omitted, it defaults to the ``DefaultRelation`` instance on the type of +the objects. By default, it means the most recent ``Equivalence`` instance +in the environment, but it can be customized by declaring +new ``DefaultRelation`` instances. As Leibniz equality is a declared +equivalence, it will fall back to it if no other relation is declared +on a given type. + +Every derived tactic that is based on the unprefixed forms of the +tactics considered above will also work up to user defined relations. +For instance, it is possible to register hints for ``autorewrite`` that +are not proof of Leibniz equalities. In particular it is possible to +exploit ``autorewrite`` to simulate normalization in a term rewriting +system up to user defined equalities. + + +Printing relations and morphisms +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +The ``Print Instances`` command can be used to show the list of currently +registered ``Reflexive`` (using ``Print Instances Reflexive``), ``Symmetric`` +or ``Transitive`` relations, Equivalences, PreOrders, PERs, and Morphisms +(implemented as ``Proper`` instances). When the rewriting tactics refuse +to replace a term in a context because the latter is not a composition +of morphisms, the ``Print Instances`` commands can be useful to understand +what additional morphisms should be registered. + + +Deprecated syntax and backward incompatibilities +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +Due to backward compatibility reasons, the following syntax for the +declaration of setoids and morphisms is also accepted. + +.. tacv:: Add Setoid @A @Aeq @ST as @ident + +where ``Aeq`` is a congruence relation without parameters, ``A`` is its carrier +and ``ST`` is an object of type (``Setoid_Theory A Aeq``) (i.e. a record +packing together the reflexivity, symmetry and transitivity lemmas). +Notice that the syntax is not completely backward compatible since the +identifier was not required. + +.. cmd:: Add Morphism f : @ident. + +The latter command also is restricted to the declaration of morphisms +without parameters. It is not fully backward compatible since the +property the user is asked to prove is slightly different: for n-ary +morphisms the hypotheses of the property are permuted; moreover, when +the morphism returns a proposition, the property is now stated using a +bi-implication in place of a simple implication. In practice, porting +an old development to the new semantics is usually quite simple. + +Notice that several limitations of the old implementation have been +lifted. In particular, it is now possible to declare several relations +with the same carrier and several signatures for the same morphism. +Moreover, it is now also possible to declare several morphisms having +the same signature. Finally, the replace and rewrite tactics can be +used to replace terms in contexts that were refused by the old +implementation. As discussed in the next section, the semantics of the +new ``setoid_rewrite`` command differs slightly from the old one and +``rewrite``. + + +Extensions +---------- + + +Rewriting under binders +~~~~~~~~~~~~~~~~~~~~~~~ + +warning:: Due to compatibility issues, this feature is enabled only +when calling the ``setoid_rewrite`` tactics directly and not ``rewrite``. + +To be able to rewrite under binding constructs, one must declare +morphisms with respect to pointwise (setoid) equivalence of functions. +Example of such morphisms are the standard ``all`` and ``ex`` combinators for +universal and existential quantification respectively. They are +declared as morphisms in the ``Classes.Morphisms_Prop`` module. For +example, to declare that universal quantification is a morphism for +logical equivalence: + +.. coqtop:: in + + Instance all_iff_morphism (A : Type) : + Proper (pointwise_relation A iff ==> iff) (@all A). + +.. coqtop:: all + + Proof. simpl_relation. + +One then has to show that if two predicates are equivalent at every +point, their universal quantifications are equivalent. Once we have +declared such a morphism, it will be used by the setoid rewriting +tactic each time we try to rewrite under an ``all`` application (products +in ``Prop`` are implicitly translated to such applications). + +Indeed, when rewriting under a lambda, binding variable ``x``, say from ``P x`` +to ``Q x`` using the relation iff, the tactic will generate a proof of +``pointwise_relation A iff (fun x => P x) (fun x => Q x)`` from the proof +of ``iff (P x) (Q x)`` and a constraint of the form Proper +``(pointwise_relation A iff ==> ?) m`` will be generated for the +surrounding morphism ``m``. + +Hence, one can add higher-order combinators as morphisms by providing +signatures using pointwise extension for the relations on the +functional arguments (or whatever subrelation of the pointwise +extension). For example, one could declare the ``map`` combinator on lists +as a morphism: + +.. coqtop:: in + + Instance map_morphism `{Equivalence A eqA, Equivalence B eqB} : + Proper ((eqA ==> eqB) ==> list_equiv eqA ==> list_equiv eqB) (@map A B). + +where ``list_equiv`` implements an equivalence on lists parameterized by +an equivalence on the elements. + +Note that when one does rewriting with a lemma under a binder using +``setoid_rewrite``, the application of the lemma may capture the bound +variable, as the semantics are different from rewrite where the lemma +is first matched on the whole term. With the new ``setoid_rewrite``, +matching is done on each subterm separately and in its local +environment, and all matches are rewritten *simultaneously* by +default. The semantics of the previous ``setoid_rewrite`` implementation +can almost be recovered using the ``at 1`` modifier. + + +Sub-relations +~~~~~~~~~~~~~ + +Sub-relations can be used to specify that one relation is included in +another, so that morphisms signatures for one can be used for the +other. If a signature mentions a relation ``R`` on the left of an +arrow ``==>``, then the signature also applies for any relation ``S`` that is +smaller than ``R``, and the inverse applies on the right of an arrow. One +can then declare only a few morphisms instances that generate the +complete set of signatures for a particular constant. By default, the +only declared subrelation is ``iff``, which is a subrelation of ``impl`` and +``inverse impl`` (the dual of implication). That’s why we can declare only +two morphisms for conjunction: ``Proper (impl ==> impl ==> impl) and`` and +``Proper (iff ==> iff ==> iff) and``. This is sufficient to satisfy any +rewriting constraints arising from a rewrite using ``iff``, ``impl`` or +``inverse impl`` through ``and``. + +Sub-relations are implemented in ``Classes.Morphisms`` and are a prime +example of a mostly user-space extension of the algorithm. + + +Constant unfolding +~~~~~~~~~~~~~~~~~~ + +The resolution tactic is based on type classes and hence regards user- +defined constants as transparent by default. This may slow down the +resolution due to a lot of unifications (all the declared ``Proper`` +instances are tried at each node of the search tree). To speed it up, +declare your constant as rigid for proof search using the command +``Typeclasses Opaque`` (see :ref:`TODO-20.6.7-typeclasses-transparency`). + + +Strategies for rewriting +------------------------ + + +Definitions +~~~~~~~~~~~ + +The generalized rewriting tactic is based on a set of strategies that +can be combined to obtain custom rewriting procedures. Its set of +strategies is based on Elan’s rewriting strategies :ref:`TODO-102-biblio`. Rewriting +strategies are applied using the tactic ``rewrite_strat s`` where ``s`` is a +strategy expression. Strategies are defined inductively as described +by the following grammar: + +.. productionlist:: rewriting + s, t, u : `strategy` + : | `lemma` + : | `lemma_right_to_left` + : | `failure` + : | `identity` + : | `reflexivity` + : | `progress` + : | `failure_catch` + : | `composition` + : | `left_biased_choice` + : | `iteration_one_or_more` + : | `iteration_zero_or_more` + : | `one_subterm` + : | `all_subterms` + : | `innermost_first` + : | `outermost_first` + : | `bottom_up` + : | `top_down` + : | `apply_hint` + : | `any_of_the_terms` + : | `apply_reduction` + : | `fold_expression` + +.. productionlist:: rewriting + strategy : "(" `s` ")" + lemma : `c` + lemma_right_to_left : "<-" `c` + failure : `fail` + identity : `id` + reflexivity : `refl` + progress : `progress` `s` + failure_catch : `try` `s` + composition : `s` ";" `u` + left_biased_choice : choice `s` `t` + iteration_one_or_more : `repeat` `s` + iteration_zero_or_more : `any` `s` + one_subterm : subterm `s` + all_subterms : subterms `s` + innermost_first : `innermost` `s` + outermost_first : `outermost` `s` + bottom_up : `bottomup` `s` + top_down : `topdown` `s` + apply_hint : hints `hintdb` + any_of_the_terms : terms (`c`)+ + apply_reduction : eval `redexpr` + fold_expression : fold `c` + + +Actually a few of these are defined in term of the others using a +primitive fixpoint operator: + +.. productionlist:: rewriting + try `s` : choice `s` `id` + any `s` : fix `u`. try (`s` ; `u`) + repeat `s` : `s` ; `any` `s` + bottomup s : fix `bu`. (choice (progress (subterms bu)) s) ; try bu + topdown s : fix `td`. (choice s (progress (subterms td))) ; try td + innermost s : fix `i`. (choice (subterm i) s) + outermost s : fix `o`. (choice s (subterm o)) + +The basic control strategy semantics are straightforward: strategies +are applied to subterms of the term to rewrite, starting from the root +of the term. The lemma strategies unify the left-hand-side of the +lemma with the current subterm and on success rewrite it to the right- +hand-side. Composition can be used to continue rewriting on the +current subterm. The fail strategy always fails while the identity +strategy succeeds without making progress. The reflexivity strategy +succeeds, making progress using a reflexivity proof of rewriting. +Progress tests progress of the argument strategy and fails if no +progress was made, while ``try`` always succeeds, catching failures. +Choice is left-biased: it will launch the first strategy and fall back +on the second one in case of failure. One can iterate a strategy at +least 1 time using ``repeat`` and at least 0 times using ``any``. + +The ``subterm`` and ``subterms`` strategies apply their argument strategy ``s`` to +respectively one or all subterms of the current term under +consideration, left-to-right. ``subterm`` stops at the first subterm for +which ``s`` made progress. The composite strategies ``innermost`` and ``outermost`` +perform a single innermost or outermost rewrite using their argument +strategy. Their counterparts ``bottomup`` and ``topdown`` perform as many +rewritings as possible, starting from the bottom or the top of the +term. + +Hint databases created for ``autorewrite`` can also be used +by ``rewrite_strat`` using the ``hints`` strategy that applies any of the +lemmas at the current subterm. The ``terms`` strategy takes the lemma +names directly as arguments. The ``eval`` strategy expects a reduction +expression (see :ref:`TODO-8.7-performing-computations`) and succeeds +if it reduces the subterm under consideration. The ``fold`` strategy takes +a term ``c`` and tries to *unify* it to the current subterm, converting it to ``c`` +on success, it is stronger than the tactic ``fold``. + + +Usage +~~~~~ + + +.. tacv:: rewrite_strat @s [in @ident] + + Rewrite using the strategy s in hypothesis ident or the conclusion. + + .. exn:: Nothing to rewrite. + + If the strategy failed. + + .. exn:: No progress made. + + If the strategy succeeded but made no progress. + + .. exn:: Unable to satisfy the rewriting constraints. + + If the strategy succeeded and made progress but the + corresponding rewriting constraints are not satisfied. + + + The ``setoid_rewrite c`` tactic is basically equivalent to + ``rewrite_strat (outermost c)``. + diff --git a/doc/sphinx/addendum/implicit-coercions.rst b/doc/sphinx/addendum/implicit-coercions.rst new file mode 100644 index 000000000..f5ca5be44 --- /dev/null +++ b/doc/sphinx/addendum/implicit-coercions.rst @@ -0,0 +1,469 @@ +.. _implicitcoercions: + +.. include:: ../replaces.rst + +Implicit Coercions +==================== + +:Author: Amokrane Saïbi + +General Presentation +--------------------- + +This section describes the inheritance mechanism of |Coq|. In |Coq| with +inheritance, we are not interested in adding any expressive power to +our theory, but only convenience. Given a term, possibly not typable, +we are interested in the problem of determining if it can be well +typed modulo insertion of appropriate coercions. We allow to write: + + * :g:`f a` where :g:`f:(forall x:A,B)` and :g:`a:A'` when ``A'`` can + be seen in some sense as a subtype of ``A``. + * :g:`x:A` when ``A`` is not a type, but can be seen in + a certain sense as a type: set, group, category etc. + * :g:`f a` when ``f`` is not a function, but can be seen in a certain sense + as a function: bijection, functor, any structure morphism etc. + + +Classes +------- + +A class with `n` parameters is any defined name with a type +:g:`forall (x₁:A₁)..(xₙ:Aₙ),s` where ``s`` is a sort. Thus a class with +parameters is considered as a single class and not as a family of +classes. An object of a class ``C`` is any term of type :g:`C t₁ .. tₙ`. +In addition to these user-classes, we have two abstract classes: + + + * ``Sortclass``, the class of sorts; its objects are the terms whose type is a + sort (e.g. :g:`Prop` or :g:`Type`). + * ``Funclass``, the class of functions; its objects are all the terms with a functional + type, i.e. of form :g:`forall x:A,B`. + +Formally, the syntax of a classes is defined as: + +.. productionlist:: + class: qualid + : | `Sortclass` + : | `Funclass` + + +Coercions +--------- + +A name ``f`` can be declared as a coercion between a source user-class +``C`` with `n` parameters and a target class ``D`` if one of these +conditions holds: + + * ``D`` is a user-class, then the type of ``f`` must have the form + :g:`forall (x₁:A₁)..(xₙ:Aₙ)(y:C x₁..xₙ), D u₁..uₘ` where `m` + is the number of parameters of ``D``. + * ``D`` is ``Funclass``, then the type of ``f`` must have the form + :g:`forall (x₁:A₁)..(xₙ:Aₙ)(y:C x₁..xₙ)(x:A), B`. + * ``D`` is ``Sortclass``, then the type of ``f`` must have the form + :g:`forall (x₁:A₁)..(xₙ:Aₙ)(y:C x₁..xₙ), s` with ``s`` a sort. + +We then write :g:`f : C >-> D`. The restriction on the type +of coercions is called *the uniform inheritance condition*. + +.. note:: The abstract classe ``Sortclass`` can be used as a source class, but + the abstract class ``Funclass`` cannot. + +To coerce an object :g:`t:C t₁..tₙ` of ``C`` towards ``D``, we have to +apply the coercion ``f`` to it; the obtained term :g:`f t₁..tₙ t` is +then an object of ``D``. + + +Identity Coercions +------------------- + +Identity coercions are special cases of coercions used to go around +the uniform inheritance condition. Let ``C`` and ``D`` be two classes +with respectively `n` and `m` parameters and +:g:`f:forall (x₁:T₁)..(xₖ:Tₖ)(y:C u₁..uₙ), D v₁..vₘ` a function which +does not verify the uniform inheritance condition. To declare ``f`` as +coercion, one has first to declare a subclass ``C'`` of ``C``: + + :g:`C' := fun (x₁:T₁)..(xₖ:Tₖ) => C u₁..uₙ` + +We then define an *identity coercion* between ``C'`` and ``C``: + + :g:`Id_C'_C := fun (x₁:T₁)..(xₖ:Tₖ)(y:C' x₁..xₖ) => (y:C u₁..uₙ)` + +We can now declare ``f`` as coercion from ``C'`` to ``D``, since we can +"cast" its type as +:g:`forall (x₁:T₁)..(xₖ:Tₖ)(y:C' x₁..xₖ),D v₁..vₘ`. + +The identity coercions have a special status: to coerce an object +:g:`t:C' t₁..tₖ` +of ``C'`` towards ``C``, we does not have to insert explicitly ``Id_C'_C`` +since :g:`Id_C'_C t₁..tₖ t` is convertible with ``t``. However we +"rewrite" the type of ``t`` to become an object of ``C``; in this case, +it becomes :g:`C uₙ'..uₖ'` where each ``uᵢ'`` is the result of the +substitution in ``uᵢ`` of the variables ``xⱼ`` by ``tⱼ``. + +Inheritance Graph +------------------ + +Coercions form an inheritance graph with classes as nodes. We call +*coercion path* an ordered list of coercions between two nodes of +the graph. A class ``C`` is said to be a subclass of ``D`` if there is a +coercion path in the graph from ``C`` to ``D``; we also say that ``C`` +inherits from ``D``. Our mechanism supports multiple inheritance since a +class may inherit from several classes, contrary to simple inheritance +where a class inherits from at most one class. However there must be +at most one path between two classes. If this is not the case, only +the *oldest* one is valid and the others are ignored. So the order +of declaration of coercions is important. + +We extend notations for coercions to coercion paths. For instance +:g:`[f₁;..;fₖ] : C >-> D` is the coercion path composed +by the coercions ``f₁..fₖ``. The application of a coercion path to a +term consists of the successive application of its coercions. + + +Declaration of Coercions +------------------------- + +.. cmd:: Coercion @qualid : @class >-> @class. + + Declares the construction denoted by `qualid` as a coercion between + the two given classes. + + .. exn:: @qualid not declared + .. exn:: @qualid is already a coercion + .. exn:: Funclass cannot be a source class + .. exn:: @qualid is not a function + .. exn:: Cannot find the source class of @qualid + .. exn:: Cannot recognize @class as a source class of @qualid + .. exn:: @qualid does not respect the uniform inheritance condition + .. exn:: Found target class ... instead of ... + + .. warn:: Ambigous path: + + When the coercion `qualid` is added to the inheritance graph, non + valid coercion paths are ignored; they are signaled by a warning + displaying these paths of the form :g:`[f₁;..;fₙ] : C >-> D`. + + .. cmdv:: Local Coercion @qualid : @class >-> @class. + + Declares the construction denoted by `qualid` as a coercion local to + the current section. + + .. cmdv:: Coercion @ident := @term. + + This defines `ident` just like ``Definition`` `ident` ``:=`` `term`, + and then declares `ident` as a coercion between it source and its target. + + .. cmdv:: Coercion @ident := @term : @type. + + This defines `ident` just like ``Definition`` `ident` : `type` ``:=`` `term`, + and then declares `ident` as a coercion between it source and its target. + + .. cmdv:: Local Coercion @ident := @term. + + This defines `ident` just like ``Let`` `ident` ``:=`` `term`, + and then declares `ident` as a coercion between it source and its target. + +Assumptions can be declared as coercions at declaration time. +This extends the grammar of assumptions from +Figure :ref:`TODO-1.3-sentences-syntax` as follows: + +.. + FIXME: + \comindex{Variable \mbox{\rm (and coercions)}} + \comindex{Axiom \mbox{\rm (and coercions)}} + \comindex{Parameter \mbox{\rm (and coercions)}} + \comindex{Hypothesis \mbox{\rm (and coercions)}} + +.. productionlist:: + assumption : assumption_keyword assums . + assums : simple_assums + : | (simple_assums) ... (simple_assums) + simple_assums : ident ... ident :[>] term + +If the extra ``>`` is present before the type of some assumptions, these +assumptions are declared as coercions. + +Similarly, constructors of inductive types can be declared as coercions at +definition time of the inductive type. This extends and modifies the +grammar of inductive types from Figure :ref:`TODO-1.3-sentences-syntax` as follows: + +.. + FIXME: + \comindex{Inductive \mbox{\rm (and coercions)}} + \comindex{CoInductive \mbox{\rm (and coercions)}} + +.. productionlist:: + inductive : `Inductive` ind_body `with` ... `with` ind_body + : | `CoInductive` ind_body `with` ... `with` ind_body + ind_body : ident [binders] : term := [[|] constructor | ... | constructor] + constructor : ident [binders] [:[>] term] + +Especially, if the extra ``>`` is present in a constructor +declaration, this constructor is declared as a coercion. + +.. cmd:: Identity Coercion @ident : @class >-> @class. + + If ``C`` is the source `class` and ``D`` the destination, we check + that ``C`` is a constant with a body of the form + :g:`fun (x₁:T₁)..(xₙ:Tₙ) => D t₁..tₘ` where `m` is the + number of parameters of ``D``. Then we define an identity + function with type :g:`forall (x₁:T₁)..(xₙ:Tₙ)(y:C x₁..xₙ),D t₁..tₘ`, + and we declare it as an identity coercion between ``C`` and ``D``. + + .. exn:: @class must be a transparent constant + + .. cmdv:: Local Identity Coercion @ident : @ident >-> @ident. + + Idem but locally to the current section. + + .. cmdv:: SubClass @ident := @type. + + If `type` is a class `ident'` applied to some arguments then + `ident` is defined and an identity coercion of name + `Id_ident_ident'` is + declared. Otherwise said, this is an abbreviation for + + ``Definition`` `ident` ``:=`` `type`. + + ``Identity Coercion`` `Id_ident_ident'` : `ident` ``>->`` `ident'`. + + .. cmdv:: Local SubClass @ident := @type. + + Same as before but locally to the current section. + + +Displaying Available Coercions +------------------------------- + +.. cmd:: Print Classes. + + Print the list of declared classes in the current context. + +.. cmd:: Print Coercions. + + Print the list of declared coercions in the current context. + +.. cmd:: Print Graph. + + Print the list of valid coercion paths in the current context. + +.. cmd:: Print Coercion Paths @class @class. + + Print the list of valid coercion paths between the two given classes. + +Activating the Printing of Coercions +------------------------------------- + +.. cmd:: Set Printing Coercions. + + This command forces all the coercions to be printed. + Conversely, to skip the printing of coercions, use + ``Unset Printing Coercions``. By default, coercions are not printed. + +.. cmd:: Add Printing Coercion @qualid. + + This command forces coercion denoted by `qualid` to be printed. + To skip the printing of coercion `qualid`, use + ``Remove Printing Coercion`` `qualid`. By default, a coercion is never printed. + + +Classes as Records +------------------ + +We allow the definition of *Structures with Inheritance* (or +classes as records) by extending the existing ``Record`` macro +(see Section :ref:`TODO-2.1-Record`). Its new syntax is: + +.. cmd:: Record {? >} @ident {? @binders} : @sort := {? @ident} { {+; @ident :{? >} @term } }. + + The first identifier `ident` is the name of the defined record and + `sort` is its type. The optional identifier after ``:=`` is the name + of the constuctor (it will be ``Build_``\ `ident` if not given). + The other identifiers are the names of the fields, and the `term` + are their respective types. If ``:>`` is used instead of ``:`` in + the declaration of a field, then the name of this field is automatically + declared as a coercion from the record name to the class of this + field type. Remark that the fields always verify the uniform + inheritance condition. If the optional ``>`` is given before the + record name, then the constructor name is automatically declared as + a coercion from the class of the last field type to the record name + (this may fail if the uniform inheritance condition is not + satisfied). + +.. note:: + + The keyword ``Structure`` is a synonym of ``Record``. + +.. + FIXME: \comindex{Structure} + + +Coercions and Sections +---------------------- + +The inheritance mechanism is compatible with the section +mechanism. The global classes and coercions defined inside a section +are redefined after its closing, using their new value and new +type. The classes and coercions which are local to the section are +simply forgotten. +Coercions with a local source class or a local target class, and +coercions which do not verify the uniform inheritance condition any longer +are also forgotten. + +Coercions and Modules +--------------------= + +From |Coq| version 8.3, the coercions present in a module are activated +only when the module is explicitly imported. Formerly, the coercions +were activated as soon as the module was required, whatever it was +imported or not. + +To recover the behavior of the versions of |Coq| prior to 8.3, use the +following command: + +.. cmd:: Set Automatic Coercions Import. + +To cancel the effect of the option, use instead ``Unset Automatic Coercions Import``. + + +Examples +-------- + +There are three situations: + +Coercion at function application +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +:g:`f a` is ill-typed where :g:`f:forall x:A,B` and :g:`a:A'`. If there is a +coercion path between ``A'`` and ``A``, then :g:`f a` is transformed into +:g:`f a'` where ``a'`` is the result of the application of this +coercion path to ``a``. + +We first give an example of coercion between atomic inductive types + +.. coqtop:: all + + Definition bool_in_nat (b:bool) := if b then 0 else 1. + Coercion bool_in_nat : bool >-> nat. + Check (0 = true). + Set Printing Coercions. + Check (0 = true). + Unset Printing Coercions. + + +.. warning:: + + Note that ``Check true=O`` would fail. This is "normal" behaviour of + coercions. To validate ``true=O``, the coercion is searched from + ``nat`` to ``bool``. There is none. + +We give an example of coercion between classes with parameters. + +.. coqtop:: all + + Parameters (C : nat -> Set) (D : nat -> bool -> Set) (E : bool -> Set). + Parameter f : forall n:nat, C n -> D (S n) true. + Coercion f : C >-> D. + Parameter g : forall (n:nat) (b:bool), D n b -> E b. + Coercion g : D >-> E. + Parameter c : C 0. + Parameter T : E true -> nat. + Check (T c). + Set Printing Coercions. + Check (T c). + Unset Printing Coercions. + +We give now an example using identity coercions. + +.. coqtop:: all + + Definition D' (b:bool) := D 1 b. + Identity Coercion IdD'D : D' >-> D. + Print IdD'D. + Parameter d' : D' true. + Check (T d'). + Set Printing Coercions. + Check (T d'). + Unset Printing Coercions. + + +In the case of functional arguments, we use the monotonic rule of +sub-typing. Approximatively, to coerce :g:`t:forall x:A,B` towards +:g:`forall x:A',B'`, one have to coerce ``A'`` towards ``A`` and ``B`` +towards ``B'``. An example is given below: + +.. coqtop:: all + + Parameters (A B : Set) (h : A -> B). + Coercion h : A >-> B. + Parameter U : (A -> E true) -> nat. + Parameter t : B -> C 0. + Check (U t). + Set Printing Coercions. + Check (U t). + Unset Printing Coercions. + +Remark the changes in the result following the modification of the +previous example. + +.. coqtop:: all + + Parameter U' : (C 0 -> B) -> nat. + Parameter t' : E true -> A. + Check (U' t'). + Set Printing Coercions. + Check (U' t'). + Unset Printing Coercions. + + +Coercion to a type +~~~~~~~~~~~~~~~~~~ + +An assumption ``x:A`` when ``A`` is not a type, is ill-typed. It is +replaced by ``x:A'`` where ``A'`` is the result of the application to +``A`` of the coercion path between the class of ``A`` and +``Sortclass`` if it exists. This case occurs in the abstraction +:g:`fun x:A => t`, universal quantification :g:`forall x:A,B`, global +variables and parameters of (co-)inductive definitions and +functions. In :g:`forall x:A,B`, such a coercion path may be applied +to ``B`` also if necessary. + +.. coqtop:: all + + Parameter Graph : Type. + Parameter Node : Graph -> Type. + Coercion Node : Graph >-> Sortclass. + Parameter G : Graph. + Parameter Arrows : G -> G -> Type. + Check Arrows. + Parameter fg : G -> G. + Check fg. + Set Printing Coercions. + Check fg. + Unset Printing Coercions. + + +Coercion to a function +~~~~~~~~~~~~~~~~~~~~~~ + +``f a`` is ill-typed because ``f:A`` is not a function. The term +``f`` is replaced by the term obtained by applying to ``f`` the +coercion path between ``A`` and ``Funclass`` if it exists. + +.. coqtop:: all + + Parameter bij : Set -> Set -> Set. + Parameter ap : forall A B:Set, bij A B -> A -> B. + Coercion ap : bij >-> Funclass. + Parameter b : bij nat nat. + Check (b 0). + Set Printing Coercions. + Check (b 0). + Unset Printing Coercions. + +Let us see the resulting graph after all these examples. + +.. coqtop:: all + + Print Graph. diff --git a/doc/sphinx/addendum/miscellaneous-extensions.rst b/doc/sphinx/addendum/miscellaneous-extensions.rst new file mode 100644 index 000000000..b0343a8f0 --- /dev/null +++ b/doc/sphinx/addendum/miscellaneous-extensions.rst @@ -0,0 +1,67 @@ +.. include:: ../replaces.rst + +.. _miscellaneousextensions: + +Miscellaneous extensions +======================= + +:Source: https://coq.inria.fr/distrib/current/refman/miscellaneous.html +:Converted by: Paul Steckler + +.. contents:: + :local: + :depth: 1 +---- + +Program derivation +----------------- + +|Coq| comes with an extension called ``Derive``, which supports program +derivation. Typically in the style of Bird and Meertens or derivations +of program refinements. To use the Derive extension it must first be +required with ``Require Coq.Derive.Derive``. When the extension is loaded, +it provides the following command: + +.. cmd:: Derive @ident SuchThat @term As @ident + +The first `ident` can appear in `term`. This command opens a new proof +presenting the user with a goal for term in which the name `ident` is +bound to an existential variable `?x` (formally, there are other goals +standing for the existential variables but they are shelved, as +described in Section :ref:`TODO-8.17.4`). + +When the proof ends two constants are defined: + ++ The first one is named using the first `ident` and is defined as the proof of the + shelved goal (which is also the value of `?x`). It is always + transparent. ++ The second one is named using the second `ident`. It has type `term`, and its body is + the proof of the initially visible goal. It is opaque if the proof + ends with ``Qed``, and transparent if the proof ends with ``Defined``. + +.. example:: + .. coqtop:: all + + Require Coq.derive.Derive. + Require Import Coq.Numbers.Natural.Peano.NPeano. + + Section P. + + Variables (n m k:nat). + + Derive p SuchThat ((k*n)+(k*m) = p) As h. + Proof. + rewrite <- Nat.mul_add_distr_l. + subst p. + reflexivity. + Qed. + + End P. + + Print p. + Check h. + +Any property can be used as `term`, not only an equation. In particular, +it could be an order relation specifying some form of program +refinement or a non-executable property from which deriving a program +is convenient. diff --git a/doc/sphinx/addendum/nsatz.rst b/doc/sphinx/addendum/nsatz.rst new file mode 100644 index 000000000..ef9b3505d --- /dev/null +++ b/doc/sphinx/addendum/nsatz.rst @@ -0,0 +1,101 @@ +.. include:: ../preamble.rst + +.. _nsatz: + +Nsatz: tactics for proving equalities in integral domains +=========================================================== + +:Author: Loïc Pottier + +The tactic `nsatz` proves goals of the form + +:math:`\begin{array}{l} +\forall X_1,\ldots,X_n \in A,\\ +P_1(X_1,\ldots,X_n) = Q_1(X_1,\ldots,X_n) , \ldots , P_s(X_1,\ldots,X_n) =Q_s(X_1,\ldots,X_n)\\ +\vdash P(X_1,\ldots,X_n) = Q(X_1,\ldots,X_n)\\ +\end{array}` + +where :math:`P, Q, P₁,Q₁,\ldots,Pₛ, Qₛ` are polynomials and :math:`A` is an integral +domain, i.e. a commutative ring with no zero divisor. For example, :math:`A` +can be :math:`\mathbb{R}`, :math:`\mathbb{Z}`, or :math:`\mathbb{Q}`. +Note that the equality :math:`=` used in these goals can be +any setoid equality (see :ref:`TODO-27.2.2`) , not only Leibnitz equality. + +It also proves formulas + +:math:`\begin{array}{l} +\forall X_1,\ldots,X_n \in A,\\ +P_1(X_1,\ldots,X_n) = Q_1(X_1,\ldots,X_n) \wedge \ldots \wedge P_s(X_1,\ldots,X_n) =Q_s(X_1,\ldots,X_n)\\ +\rightarrow P(X_1,\ldots,X_n) = Q(X_1,\ldots,X_n)\\ +\end{array}` + +doing automatic introductions. + + +Using the basic tactic `nsatz` +------------------------------ + + +Load the Nsatz module: + +.. coqtop:: all + + Require Import Nsatz. + +and use the tactic `nsatz`. + +More about `nsatz` +--------------------- + +Hilbert’s Nullstellensatz theorem shows how to reduce proofs of +equalities on polynomials on a commutative ring :math:`A` with no zero divisor +to algebraic computations: it is easy to see that if a polynomial :math:`P` in +:math:`A[X_1,\ldots,X_n]` verifies :math:`c P^r = \sum_{i=1}^{s} S_i P_i`, with +:math:`c \in A`, :math:`c \not = 0`, +:math:`r` a positive integer, and the :math:`S_i` s in :math:`A[X_1,\ldots,X_n ]`, +then :math:`P` is zero whenever polynomials :math:`P_1,\ldots,P_s` are zero +(the converse is also true when :math:`A` is an algebraic closed field: the method is +complete). + +So, proving our initial problem can reduce into finding :math:`S_1,\ldots,S_s`, +:math:`c` and :math:`r` such that :math:`c (P-Q)^r = \sum_{i} S_i (P_i-Q_i)`, +which will be proved by the tactic ring. + +This is achieved by the computation of a Gröbner basis of the ideal +generated by :math:`P_1-Q_1,...,P_s-Q_s`, with an adapted version of the +Buchberger algorithm. + +This computation is done after a step of *reification*, which is +performed using :ref:`typeclasses`. + +The ``Nsatz`` module defines the tactic `nsatz`, which can be used without +arguments, or with the syntax: + +| nsatz with radicalmax:=num%N strategy:=num%Z parameters:= :n:`{* var}` variables:= :n:`{* var}` + +where: + +* `radicalmax` is a bound when for searching r s.t. + :math:`c (P−Q) r = \sum_{i=1..s} S_i (P i − Q i)` + +* `strategy` gives the order on variables :math:`X_1,\ldots,X_n` and the strategy + used in Buchberger algorithm (see :cite:`sugar` for details): + + * strategy = 0: reverse lexicographic order and newest s-polynomial. + * strategy = 1: reverse lexicographic order and sugar strategy. + * strategy = 2: pure lexicographic order and newest s-polynomial. + * strategy = 3: pure lexicographic order and sugar strategy. + +* `parameters` is the list of variables :math:`X_{i_1},\ldots,X_{i_k}` among + :math:`X_1,\ldots,X_n` which are considered as parameters: computation will be performed with + rational fractions in these variables, i.e. polynomials are considered + with coefficients in :math:`R(X_{i_1},\ldots,X_{i_k})`. In this case, the coefficient + :math:`c` can be a non constant polynomial in :math:`X_{i_1},\ldots,X_{i_k}`, and the tactic + produces a goal which states that :math:`c` is not zero. + +* `variables` is the list of the variables in the decreasing order in + which they will be used in Buchberger algorithm. If `variables` = `(@nil R)`, + then `lvar` is replaced by all the variables which are not in + `parameters`. + +See file `Nsatz.v` for many examples, especially in geometry. diff --git a/doc/sphinx/addendum/parallel-proof-processing.rst b/doc/sphinx/addendum/parallel-proof-processing.rst new file mode 100644 index 000000000..8c1b9d152 --- /dev/null +++ b/doc/sphinx/addendum/parallel-proof-processing.rst @@ -0,0 +1,229 @@ +.. include:: ../replaces.rst + +.. _asynchronousandparallelproofprocessing: + +Asynchronous and Parallel Proof Processing +========================================== + +:Author: Enrico Tassi + +This chapter explains how proofs can be asynchronously processed by +|Coq|. This feature improves the reactivity of the system when used in +interactive mode via |CoqIDE|. In addition, it allows |Coq| to take +advantage of parallel hardware when used as a batch compiler by +decoupling the checking of statements and definitions from the +construction and checking of proofs objects. + +This feature is designed to help dealing with huge libraries of +theorems characterized by long proofs. In the current state, it may +not be beneficial on small sets of short files. + +This feature has some technical limitations that may make it +unsuitable for some use cases. + +For example, in interactive mode, some errors coming from the kernel +of |Coq| are signaled late. The type of errors belonging to this +category are universe inconsistencies. + +At the time of writing, only opaque proofs (ending with ``Qed`` or +``Admitted``) can be processed asynchronously. + +Finally, asynchronous processing is disabled when running |CoqIDE| in +Windows. The current implementation of the feature is not stable on +Windows. It can be enabled, as described below at :ref:`interactive-mode`, +though doing so is not recommended. + +Proof annotations +---------------------- + +To process a proof asynchronously |Coq| needs to know the precise +statement of the theorem without looking at the proof. This requires +some annotations if the theorem is proved inside a Section (see +Section :ref:`TODO-2.4`). + +When a section ends, |Coq| looks at the proof object to decide which +section variables are actually used and hence have to be quantified in +the statement of the theorem. To avoid making the construction of +proofs mandatory when ending a section, one can start each proof with +the ``Proof using`` command (Section :ref:`TODO-7.1.5`) that declares which section +variables the theorem uses. + +The presence of ``Proof`` using is needed to process proofs asynchronously +in interactive mode. + +It is not strictly mandatory in batch mode if it is not the first time +the file is compiled and if the file itself did not change. When the +proof does not begin with Proof using, the system records in an +auxiliary file, produced along with the `.vo` file, the list of section +variables used. + +Automatic suggestion of proof annotations +````````````````````````````````````````` + +The command ``Set Suggest Proof Using`` makes |Coq| suggest, when a ``Qed`` +command is processed, a correct proof annotation. It is up to the user +to modify the proof script accordingly. + + +Proof blocks and error resilience +-------------------------------------- + +|Coq| 8.6 introduced a mechanism for error resiliency: in interactive +mode |Coq| is able to completely check a document containing errors +instead of bailing out at the first failure. + +Two kind of errors are supported: errors occurring in vernacular +commands and errors occurring in proofs. + +To properly recover from a failing tactic, |Coq| needs to recognize the +structure of the proof in order to confine the error to a sub proof. +Proof block detection is performed by looking at the syntax of the +proof script (i.e. also looking at indentation). |Coq| comes with four +kind of proof blocks, and an ML API to add new ones. + +:curly: blocks are delimited by { and }, see Chapter :ref:`proofhandling` +:par: blocks are atomic, i.e. just one tactic introduced by the `par:` + goal selector +:indent: blocks end with a tactic indented less than the previous one +:bullet: blocks are delimited by two equal bullet signs at the same + indentation level + +Caveats +```````` + +When a vernacular command fails the subsequent error messages may be +bogus, i.e. caused by the first error. Error resiliency for vernacular +commands can be switched off by passing ``-async-proofs-command-error-resilience off`` +to |CoqIDE|. + +An incorrect proof block detection can result into an incorrect error +recovery and hence in bogus errors. Proof block detection cannot be +precise for bullets or any other non well parenthesized proof +structure. Error resiliency can be turned off or selectively activated +for any set of block kind passing to |CoqIDE| one of the following +options: + +- ``-async-proofs-tactic-error-resilience off`` +- ``-async-proofs-tactic-error-resilience all`` +- ``-async-proofs-tactic-error-resilience`` :n:`{*, blocktype}` + +Valid proof block types are: “curly”, “par”, “indent”, and “bullet”. + +.. _interactive-mode: + +Interactive mode +--------------------- + +At the time of writing the only user interface supporting asynchronous +proof processing is |CoqIDE|. + +When |CoqIDE| is started, two |Coq| processes are created. The master one +follows the user, giving feedback as soon as possible by skipping +proofs, which are delegated to the worker process. The worker process, +whose state can be seen by clicking on the button in the lower right +corner of the main |CoqIDE| window, asynchronously processes the proofs. +If a proof contains an error, it is reported in red in the label of +the very same button, that can also be used to see the list of errors +and jump to the corresponding line. + +If a proof is processed asynchronously the corresponding Qed command +is colored using a lighter color that usual. This signals that the +proof has been delegated to a worker process (or will be processed +lazily if the ``-async-proofs lazy`` option is used). Once finished, the +worker process will provide the proof object, but this will not be +automatically checked by the kernel of the main process. To force the +kernel to check all the proof objects, one has to click the button +with the gears. Only then are all the universe constraints checked. + +Caveats +``````` + +The number of worker processes can be increased by passing |CoqIDE| +the ``-async-proofs-j n`` flag. Note that the memory consumption increases too, +since each worker requires the same amount of memory as the master +process. Also note that increasing the number of workers may reduce +the reactivity of the master process to user commands. + +To disable this feature, one can pass the ``-async-proofs off`` flag to +|CoqIDE|. Conversely, on Windows, where the feature is disabled by +default, pass the ``-async-proofs on`` flag to enable it. + +Proofs that are known to take little time to process are not delegated +to a worker process. The threshold can be configure with +``-async-proofs-delegation-threshold``. Default is 0.03 seconds. + +Batch mode +--------------- + +When |Coq| is used as a batch compiler by running `coqc` or `coqtop` +-compile, it produces a `.vo` file for each `.v` file. A `.vo` file contains, +among other things, theorems statements and proofs. Hence to produce a +.vo |Coq| need to process all the proofs of the `.v` file. + +The asynchronous processing of proofs can decouple the generation of a +compiled file (like the `.vo` one) that can be loaded by ``Require`` from the +generation and checking of the proof objects. The ``-quick`` flag can be +passed to `coqc` or `coqtop` to produce, quickly, `.vio` files. +Alternatively, when using a Makefile produced by `coq_makefile`, +the ``quick`` target can be used to compile all files using the ``-quick`` flag. + +A `.vio` file can be loaded using ``Require`` exactly as a `.vo` file but +proofs will not be available (the Print command produces an error). +Moreover, some universe constraints might be missing, so universes +inconsistencies might go unnoticed. A `.vio` file does not contain proof +objects, but proof tasks, i.e. what a worker process can transform +into a proof object. + +Compiling a set of files with the ``-quick`` flag allows one to work, +interactively, on any file without waiting for all the proofs to be +checked. + +When working interactively, one can fully check all the `.v` files by +running `coqc` as usual. + +Alternatively one can turn each `.vio` into the corresponding `.vo`. All +.vio files can be processed in parallel, hence this alternative might +be faster. The command ``coqtop -schedule-vio2vo 2 a b c`` can be used to +obtain a good scheduling for two workers to produce `a.vo`, `b.vo`, and +`c.vo`. When using a Makefile produced by `coq_makefile`, the ``vio2vo`` target +can be used for that purpose. Variable `J` should be set to the number +of workers, e.g. ``make vio2vo J=2``. The only caveat is that, while the +.vo files obtained from `.vio` files are complete (they contain all proof +terms and universe constraints), the satisfiability of all universe +constraints has not been checked globally (they are checked to be +consistent for every single proof). Constraints will be checked when +these `.vo` files are (recursively) loaded with ``Require``. + +There is an extra, possibly even faster, alternative: just check the +proof tasks stored in `.vio` files without producing the `.vo` files. This +is possibly faster because all the proof tasks are independent, hence +one can further partition the job to be done between workers. The +``coqtop -schedule-vio-checking 6 a b c`` command can be used to obtain a +good scheduling for 6 workers to check all the proof tasks of `a.vio`, +`b.vio`, and `c.vio`. Auxiliary files are used to predict how long a proof +task will take, assuming it will take the same amount of time it took +last time. When using a Makefile produced by coq_makefile, the +``checkproofs`` target can be used to check all `.vio` files. Variable `J` +should be set to the number of workers, e.g. ``make checkproofs J=6``. As +when converting `.vio` files to `.vo` files, universe constraints are not +checked to be globally consistent. Hence this compilation mode is only +useful for quick regression testing and on developments not making +heavy use of the `Type` hierarchy. + +Limiting the number of parallel workers +-------------------------------------------- + +Many |Coq| processes may run on the same computer, and each of them may +start many additional worker processes. The `coqworkmgr` utility lets +one limit the number of workers, globally. + +The utility accepts the ``-j`` argument to specify the maximum number of +workers (defaults to 2). `coqworkmgr` automatically starts in the +background and prints an environment variable assignment +like ``COQWORKMGR_SOCKET=localhost:45634``. The user must set this variable +in all the shells from which |Coq| processes will be started. If one +uses just one terminal running the bash shell, then +``export ‘coqworkmgr -j 4‘`` will do the job. + +After that, all |Coq| processes, e.g. `coqide` and `coqc`, will honor the +limit, globally. diff --git a/doc/sphinx/addendum/program.rst b/doc/sphinx/addendum/program.rst new file mode 100644 index 000000000..eb50e52dc --- /dev/null +++ b/doc/sphinx/addendum/program.rst @@ -0,0 +1,381 @@ +.. include:: ../preamble.rst +.. include:: ../replaces.rst + +.. this should be just "_program", but refs to it don't work + +.. _programs: + +Program +======== + +:Author: Matthieu Sozeau + +We present here the |Program| tactic commands, used to build +certified |Coq| programs, elaborating them from their algorithmic +skeleton and a rich specification :cite:`sozeau06`. It can be thought of as a +dual of :ref:`Extraction <extraction>`. The goal of |Program| is to +program as in a regular functional programming language whilst using +as rich a specification as desired and proving that the code meets the +specification using the whole |Coq| proof apparatus. This is done using +a technique originating from the “Predicate subtyping” mechanism of +PVS :cite:`Rushby98`, which generates type-checking conditions while typing a +term constrained to a particular type. Here we insert existential +variables in the term, which must be filled with proofs to get a +complete |Coq| term. |Program| replaces the |Program| tactic by Catherine +Parent :cite:`Parent95b` which had a similar goal but is no longer maintained. + +The languages available as input are currently restricted to |Coq|’s +term language, but may be extended to OCaml, Haskell and +others in the future. We use the same syntax as |Coq| and permit to use +implicit arguments and the existing coercion mechanism. Input terms +and types are typed in an extended system (Russell) and interpreted +into |Coq| terms. The interpretation process may produce some proof +obligations which need to be resolved to create the final term. + + +.. _elaborating-programs: + +Elaborating programs +--------------------- + +The main difference from |Coq| is that an object in a type T : Set can +be considered as an object of type { x : T | P} for any wellformed P : +Prop. If we go from T to the subset of T verifying property P, we must +prove that the object under consideration verifies it. Russell will +generate an obligation for every such coercion. In the other +direction, Russell will automatically insert a projection. + +Another distinction is the treatment of pattern-matching. Apart from +the following differences, it is equivalent to the standard match +operation (see :ref:`extendedpatternmatching`). + + ++ Generation of equalities. A match expression is always generalized + by the corresponding equality. As an example, the expression: + + :: + + match x with + | 0 => t + | S n => u + end. + + will be first rewritten to: + + :: + + (match x as y return (x = y -> _) with + | 0 => fun H : x = 0 -> t + | S n => fun H : x = S n -> u + end) (eq_refl n). + + This permits to get the proper equalities in the context of proof + obligations inside clauses, without which reasoning is very limited. + ++ Generation of inequalities. If a pattern intersects with a previous + one, an inequality is added in the context of the second branch. See + for example the definition of div2 below, where the second branch is + typed in a context where ∀ p, _ <> S (S p). ++ Coercion. If the object being matched is coercible to an inductive + type, the corresponding coercion will be automatically inserted. This + also works with the previous mechanism. + + +There are options to control the generation of equalities and +coercions. + +.. opt:: Program Cases + + This controls the special treatment of pattern-matching generating equalities + and inequalities when using |Program| (it is on by default). All + pattern-matchings and let-patterns are handled using the standard algorithm + of |Coq| (see :ref:`extendedpatternmatching`) when this option is + deactivated. + +.. opt:: Program Generalized Coercion + + This controls the coercion of general inductive types when using |Program| + (the option is on by default). Coercion of subset types and pairs is still + active in this case. + +.. _syntactic_control: + +Syntactic control over equalities +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +To give more control over the generation of equalities, the +typechecker will fall back directly to |Coq|’s usual typing of dependent +pattern-matching if a return or in clause is specified. Likewise, the +if construct is not treated specially by |Program| so boolean tests in +the code are not automatically reflected in the obligations. One can +use the dec combinator to get the correct hypotheses as in: + +.. coqtop:: none + + Require Import Program Arith. + +.. coqtop:: all + + Program Definition id (n : nat) : { x : nat | x = n } := + if dec (leb n 0) then 0 + else S (pred n). + +The let tupling construct :g:`let (x1, ..., xn) := t in b` does not +produce an equality, contrary to the let pattern construct :g:`let ’(x1, +..., xn) := t in b`. Also, :g:`term :>` explicitly asks the system to +coerce term to its support type. It can be useful in notations, for +example: + +.. coqtop:: all + + Notation " x `= y " := (@eq _ (x :>) (y :>)) (only parsing). + +This notation denotes equality on subset types using equality on their +support types, avoiding uses of proof-irrelevance that would come up +when reasoning with equality on the subset types themselves. + +The next two commands are similar to their standard counterparts +Definition (see Section `TODO-1.3.2-Definition`_) and Fixpoint (see Section `TODO-1.3.4-Fixpoint`_) +in that they define constants. However, they may require the user to +prove some goals to construct the final definitions. + + +.. _program_definition: + +Program Definition +~~~~~~~~~~~~~~~~~~ + +.. cmd:: Program Definition @ident := @term. + + This command types the value term in Russell and generates proof + obligations. Once solved using the commands shown below, it binds the + final |Coq| term to the name ``ident`` in the environment. + + .. exn:: ident already exists + + .. cmdv:: Program Definition @ident : @type := @term + + It interprets the type ``type``, potentially generating proof + obligations to be resolved. Once done with them, we have a |Coq| + type |type_0|. It then elaborates the preterm ``term`` into a |Coq| + term |term_0|, checking that the type of |term_0| is coercible to + |type_0|, and registers ``ident`` as being of type |type_0| once the + set of obligations generated during the interpretation of |term_0| + and the aforementioned coercion derivation are solved. + + .. exn:: In environment … the term: @term does not have type @type. Actually, it has type ... + + + .. cmdv:: Program Definition @ident @binders : @type := @term. + + This is equivalent to: + + :g:`Program Definition ident : forall binders, type := fun binders => term`. + + .. TODO refer to production in alias + +See also: Sections `TODO-6.10.1-Opaque`_, `TODO-6.10.2-Transparent`_, `TODO-8.7.5-unfold`_ + +.. _program_fixpoint: + +Program Fixpoint +~~~~~~~~~~~~~~~~ + +.. cmd:: Program Fixpoint @ident @params {? {@order}} : @type := @term. + +The optional order annotation follows the grammar: + +.. productionlist:: orderannot + order : measure `term` (`term`)? | wf `term` `term` + ++ :g:`measure f ( R )` where :g:`f` is a value of type :g:`X` computed on + any subset of the arguments and the optional (parenthesised) term + ``(R)`` is a relation on ``X``. By default ``X`` defaults to ``nat`` and ``R`` + to ``lt``. + ++ :g:`wf R x` which is equivalent to :g:`measure x (R)`. + +The structural fixpoint operator behaves just like the one of |Coq| (see +Section `TODO-1.3.4-Fixpoint`_), except it may also generate obligations. It works +with mutually recursive definitions too. + +.. coqtop:: reset none + + Require Import Program Arith. + +.. coqtop:: all + + Program Fixpoint div2 (n : nat) : { x : nat | n = 2 * x \/ n = 2 * x + 1 } := + match n with + | S (S p) => S (div2 p) + | _ => O + end. + +Here we have one obligation for each branch (branches for :g:`0` and +``(S 0)`` are automatically generated by the pattern-matching +compilation algorithm). + +.. coqtop:: all + + Obligation 1. + +.. coqtop:: reset none + + Require Import Program Arith. + +One can use a well-founded order or a measure as termination orders +using the syntax: + +.. coqtop:: in + + Program Fixpoint div2 (n : nat) {measure n} : { x : nat | n = 2 * x \/ n = 2 * x + 1 } := + match n with + | S (S p) => S (div2 p) + | _ => O + end. + + + +.. caution:: When defining structurally recursive functions, the generated + obligations should have the prototype of the currently defined + functional in their context. In this case, the obligations should be + transparent (e.g. defined using :g:`Defined`) so that the guardedness + condition on recursive calls can be checked by the kernel’s type- + checker. There is an optimization in the generation of obligations + which gets rid of the hypothesis corresponding to the functional when + it is not necessary, so that the obligation can be declared opaque + (e.g. using :g:`Qed`). However, as soon as it appears in the context, the + proof of the obligation is *required* to be declared transparent. + + No such problems arise when using measures or well-founded recursion. + +.. _program_lemma: + +Program Lemma +~~~~~~~~~~~~~ + +.. cmd:: Program Lemma @ident : @type. + + The Russell language can also be used to type statements of logical + properties. It will generate obligations, try to solve them + automatically and fail if some unsolved obligations remain. In this + case, one can first define the lemma’s statement using :g:`Program + Definition` and use it as the goal afterwards. Otherwise the proof + will be started with the elaborated version as a goal. The + :g:`Program` prefix can similarly be used as a prefix for + :g:`Variable`, :g:`Hypothesis`, :g:`Axiom` etc... + +.. _solving_obligations: + +Solving obligations +-------------------- + +The following commands are available to manipulate obligations. The +optional identifier is used when multiple functions have unsolved +obligations (e.g. when defining mutually recursive blocks). The +optional tactic is replaced by the default one if not specified. + +.. cmd:: {? Local|Global} Obligation Tactic := @tactic + + Sets the default obligation solving tactic applied to all obligations + automatically, whether to solve them or when starting to prove one, + e.g. using :g:`Next`. :g:`Local` makes the setting last only for the current + module. Inside sections, local is the default. + +.. cmd:: Show Obligation Tactic + + Displays the current default tactic. + +.. cmd:: Obligations {? of @ident} + + Displays all remaining obligations. + +.. cmd:: Obligation num {? of @ident} + + Start the proof of obligation num. + +.. cmd:: Next Obligation {? of @ident} + + Start the proof of the next unsolved obligation. + +.. cmd:: Solve Obligations {? of @ident} {? with @tactic} + + Tries to solve each obligation of ``ident`` using the given ``tactic`` or the default one. + +.. cmd:: Solve All Obligations {? with @tactic} + + Tries to solve each obligation of every program using the given + tactic or the default one (useful for mutually recursive definitions). + +.. cmd:: Admit Obligations {? of @ident} + + Admits all obligations (of ``ident``). + + .. note:: Does not work with structurally recursive programs. + +.. cmd:: Preterm {? of @ident} + + Shows the term that will be fed to the kernel once the obligations + are solved. Useful for debugging. + +.. opt:: Transparent Obligations + + Control whether all obligations should be declared as transparent + (the default), or if the system should infer which obligations can be + declared opaque. + +.. opt:: Hide Obligations + + Control whether obligations appearing in the + term should be hidden as implicit arguments of the special + constantProgram.Tactics.obligation. + +.. opt:: Shrink Obligations + + *Deprecated since 8.7* + + This option (on by default) controls whether obligations should have + their context minimized to the set of variables used in the proof of + the obligation, to avoid unnecessary dependencies. + +The module :g:`Coq.Program.Tactics` defines the default tactic for solving +obligations called :g:`program_simpl`. Importing :g:`Coq.Program.Program` also +adds some useful notations, as documented in the file itself. + +.. _program-faq: + +Frequently Asked Questions +--------------------------- + + +.. exn:: Ill-formed recursive definition + + This error can happen when one tries to define a function by structural + recursion on a subset object, which means the |Coq| function looks like: + + :: + + Program Fixpoint f (x : A | P) := match x with A b => f b end. + + Supposing ``b : A``, the argument at the recursive call to ``f`` is not a + direct subterm of ``x`` as ``b`` is wrapped inside an ``exist`` constructor to + build an object of type ``{x : A | P}``. Hence the definition is + rejected by the guardedness condition checker. However one can use + wellfounded recursion on subset objects like this: + + :: + + Program Fixpoint f (x : A | P) { measure (size x) } := + match x with A b => f b end. + + One will then just have to prove that the measure decreases at each + recursive call. There are three drawbacks though: + + #. A measure function has to be defined; + #. The reduction is a little more involved, although it works well + using lazy evaluation; + #. Mutual recursion on the underlying inductive type isn’t possible + anymore, but nested mutual recursion is always possible. + +.. bibliography:: ../biblio.bib + :keyprefix: p- diff --git a/doc/sphinx/addendum/ring.rst b/doc/sphinx/addendum/ring.rst new file mode 100644 index 000000000..b861892cb --- /dev/null +++ b/doc/sphinx/addendum/ring.rst @@ -0,0 +1,770 @@ +.. include:: ../replaces.rst +.. |ra| replace:: :math:`\rightarrow_{\beta\delta\iota}` +.. |la| replace:: :math:`\leftarrow_{\beta\delta\iota}` +.. |eq| replace:: `=`:sub:`(by the main correctness theorem)` +.. |re| replace:: ``(PEeval`` `v` `ap`\ ``)`` +.. |le| replace:: ``(Pphi_dev`` `v` ``(norm`` `ap`\ ``))`` + + +.. _theringandfieldtacticfamilies: + +The ring and field tactic families +==================================== + +:Author: Bruno Barras, Benjamin Grégoire, Assia Mahboubi, Laurent Théry [#f1]_ + +This chapter presents the tactics dedicated to deal with ring and +field equations. + +What does this tactic do? +------------------------------ + +``ring`` does associative-commutative rewriting in ring and semi-ring +structures. Assume you have two binary functions :math:`\oplus` and +:math:`\otimes` that are associative and commutative, with :math:`\oplus` +distributive on :math:`\otimes`, and two constants 0 and 1 that are unities for +:math:`\oplus` and :math:`\otimes`. A polynomial is an expression built on +variables :math:`V_0`, :math:`V_1`, :math:`\dots` and constants by application +of :math:`\oplus` and :math:`\otimes`. + +Let an ordered product be a product of variables :math:`V_{i_1} \otimes \dots +\otimes V_{i_n}` verifying :math:`i_1 ≤ i_2 ≤ \dots ≤ i_n` . Let a monomial be +the product of a constant and an ordered product. We can order the monomials by +the lexicographic order on products of variables. Let a canonical sum be an +ordered sum of monomials that are all different, i.e. each monomial in the sum +is strictly less than the following monomial according to the lexicographic +order. It is an easy theorem to show that every polynomial is equivalent (modulo +the ring properties) to exactly one canonical sum. This canonical sum is called +the normal form of the polynomial. In fact, the actual representation shares +monomials with same prefixes. So what does ring? It normalizes polynomials over +any ring or semi-ring structure. The basic use of ``ring`` is to simplify ring +expressions, so that the user does not have to deal manually with the theorems +of associativity and commutativity. + + +.. example:: + + In the ring of integers, the normal form of + :math:`x (3 + yx + 25(1 − z)) + zx` + is + :math:`28x + (−24)xz + xxy`. + + +``ring`` is also able to compute a normal form modulo monomial equalities. +For example, under the hypothesis that :math:`2x^2 = yz+1`, the normal form of +:math:`2(x + 1)x − x − zy` is :math:`x+1`. + +The variables map +---------------------- + +It is frequent to have an expression built with :math:`+` and :math:`\times`, +but rarely on variables only. Let us associate a number to each subterm of a +ring expression in the Gallina language. For example in the ring |nat|, consider +the expression: + + +:: + + (plus (mult (plus (f (5)) x) x) + (mult (if b then (4) else (f (3))) (2))) + + +As a ring expression, it has 3 subterms. Give each subterm a number in +an arbitrary order: + +===== =============== ========================= +0 :math:`\mapsto` if b then (4) else (f (3)) +1 :math:`\mapsto` (f (5)) +2 :math:`\mapsto` x +===== =============== ========================= + +Then normalize the “abstract” polynomial +:math:`((V_1 \otimes V_2 ) \oplus V_2) \oplus (V_0 \otimes 2)` +In our example the normal form is: +:math:`(2 \otimes V_0 ) \oplus (V_1 \otimes V_2) \oplus (V_2 \otimes V_2 )`. +Then substitute the variables by their values in the variables map to +get the concrete normal polynomial: + +:: + + (plus (mult (2) (if b then (4) else (f (3)))) + (plus (mult (f (5)) x) (mult x x))) + + +Is it automatic? +--------------------- + +Yes, building the variables map and doing the substitution after +normalizing is automatically done by the tactic. So you can just +forget this paragraph and use the tactic according to your intuition. + +Concrete usage in Coq +-------------------------- + +.. tacn:: ring + +The ``ring`` tactic solves equations upon polynomial expressions of a ring +(or semi-ring) structure. It proceeds by normalizing both hand sides +of the equation (w.r.t. associativity, commutativity and +distributivity, constant propagation, rewriting of monomials) and +comparing syntactically the results. + +.. tacn:: ring_simplify + +``ring_simplify`` applies the normalization procedure described above to +the terms given. The tactic then replaces all occurrences of the terms +given in the conclusion of the goal by their normal forms. If no term +is given, then the conclusion should be an equation and both hand +sides are normalized. The tactic can also be applied in a hypothesis. + +The tactic must be loaded by ``Require Import Ring``. The ring structures +must be declared with the ``Add Ring`` command (see below). The ring of +booleans is predefined; if one wants to use the tactic on |nat| one must +first require the module ``ArithRing`` exported by ``Arith``); for |Z|, do +``Require Import ZArithRing`` or simply ``Require Import ZArith``; for |N|, do +``Require Import NArithRing`` or ``Require Import NArith``. + + +.. example:: + + .. coqtop:: all + + Require Import ZArith. + Open Scope Z_scope. + Goal forall a b c:Z, + (a + b + c) ^ 2 = + a * a + b ^ 2 + c * c + 2 * a * b + 2 * a * c + 2 * b * c. + intros; ring. + Abort. + Goal forall a b:Z, + 2 * a * b = 30 -> (a + b) ^ 2 = a ^ 2 + b ^ 2 + 30. + intros a b H; ring [H]. + Abort. + + +.. tacv:: ring [{* @term }] + +decides the equality of two terms modulo ring operations and +the equalities defined by the :n:`@term`\ s. +Each :n:`@term` has to be a proof of some equality `m = p`, where `m` is a monomial (after “abstraction”), `p` a polynomial and `=` the corresponding equality of the ring structure. + +.. tacv:: ring_simplify [{* @term }] {* @term } in @ident + +performs the simplification in the hypothesis named :n:`@ident`. + + +.. note:: + + .. tacn:: ring_simplify @term1; ring_simplify @term2 + + is not equivalent to + + .. tacn:: ring_simplify @term1 @term2 + + In the latter case the variables map + is shared between the two terms, and common subterm `t` of :n:`@term1` and :n:`@term2` + will have the same associated variable number. So the first + alternative should be avoided for terms belonging to the same ring + theory. + + +Error messages: + + +.. exn:: not a valid ring equation + + The conclusion of the goal is not provable in the corresponding ring theory. + +.. exn:: arguments of ring_simplify do not have all the same type + + ``ring_simplify`` cannot simplify terms of several rings at the same + time. Invoke the tactic once per ring structure. + +.. exn:: cannot find a declared ring structure over @term + + No ring has been declared for the type of the terms to be simplified. + Use ``Add Ring`` first. + +.. exn:: cannot find a declared ring structure for equality @term + + Same as above is the case of the ``ring`` tactic. + + +Adding a ring structure +---------------------------- + +Declaring a new ring consists in proving that a ring signature (a +carrier set, an equality, and ring operations: ``Ring_theory.ring_theory`` +and ``Ring_theory.semi_ring_theory``) satisfies the ring axioms. Semi- +rings (rings without + inverse) are also supported. The equality can +be either Leibniz equality, or any relation declared as a setoid (see +:ref:`tactics-enabled-on-user-provided-relations`). The definition of ring and semi-rings (see module +``Ring_theory``) is: + +.. coqtop:: in + + Record ring_theory : Prop := mk_rt { + Radd_0_l : forall x, 0 + x == x; + Radd_sym : forall x y, x + y == y + x; + Radd_assoc : forall x y z, x + (y + z) == (x + y) + z; + Rmul_1_l : forall x, 1 * x == x; + Rmul_sym : forall x y, x * y == y * x; + Rmul_assoc : forall x y z, x * (y * z) == (x * y) * z; + Rdistr_l : forall x y z, (x + y) * z == (x * z) + (y * z); + Rsub_def : forall x y, x - y == x + -y; + Ropp_def : forall x, x + (- x) == 0 + }. + + Record semi_ring_theory : Prop := mk_srt { + SRadd_0_l : forall n, 0 + n == n; + SRadd_sym : forall n m, n + m == m + n ; + SRadd_assoc : forall n m p, n + (m + p) == (n + m) + p; + SRmul_1_l : forall n, 1*n == n; + SRmul_0_l : forall n, 0*n == 0; + SRmul_sym : forall n m, n*m == m*n; + SRmul_assoc : forall n m p, n*(m*p) == (n*m)*p; + SRdistr_l : forall n m p, (n + m)*p == n*p + m*p + }. + + +This implementation of ``ring`` also features a notion of constant that +can be parameterized. This can be used to improve the handling of +closed expressions when operations are effective. It consists in +introducing a type of *coefficients* and an implementation of the ring +operations, and a morphism from the coefficient type to the ring +carrier type. The morphism needs not be injective, nor surjective. + +As an example, one can consider the real numbers. The set of +coefficients could be the rational numbers, upon which the ring +operations can be implemented. The fact that there exists a morphism +is defined by the following properties: + +.. coqtop:: in + + Record ring_morph : Prop := mkmorph { + morph0 : [cO] == 0; + morph1 : [cI] == 1; + morph_add : forall x y, [x +! y] == [x]+[y]; + morph_sub : forall x y, [x -! y] == [x]-[y]; + morph_mul : forall x y, [x *! y] == [x]*[y]; + morph_opp : forall x, [-!x] == -[x]; + morph_eq : forall x y, x?=!y = true -> [x] == [y] + }. + + Record semi_morph : Prop := mkRmorph { + Smorph0 : [cO] == 0; + Smorph1 : [cI] == 1; + Smorph_add : forall x y, [x +! y] == [x]+[y]; + Smorph_mul : forall x y, [x *! y] == [x]*[y]; + Smorph_eq : forall x y, x?=!y = true -> [x] == [y] + }. + + +where ``c0`` and ``cI`` denote the 0 and 1 of the coefficient set, ``+!``, ``*!``, ``-!`` +are the implementations of the ring operations, ``==`` is the equality of +the coefficients, ``?+!`` is an implementation of this equality, and ``[x]`` +is a notation for the image of ``x`` by the ring morphism. + +Since |Z| is an initial ring (and |N| is an initial semi-ring), it can +always be considered as a set of coefficients. There are basically +three kinds of (semi-)rings: + +abstract rings + to be used when operations are not effective. The set + of coefficients is |Z| (or |N| for semi-rings). + +computational rings + to be used when operations are effective. The + set of coefficients is the ring itself. The user only has to provide + an implementation for the equality. + +customized ring + for other cases. The user has to provide the + coefficient set and the morphism. + + +This implementation of ring can also recognize simple power +expressions as ring expressions. A power function is specified by the +following property: + +.. coqtop:: in + + Section POWER. + Variable Cpow : Set. + Variable Cp_phi : N -> Cpow. + Variable rpow : R -> Cpow -> R. + + Record power_theory : Prop := mkpow_th { + rpow_pow_N : forall r n, req (rpow r (Cp_phi n)) (pow_N rI rmul r n) + }. + + End POWER. + + +The syntax for adding a new ring is + +.. cmd:: Add Ring @ident : @term {? ( @ring_mod {* , @ring_mod } )}. + +The :n:`@ident` is not relevant. It is just used for error messages. The +:n:`@term` is a proof that the ring signature satisfies the (semi-)ring +axioms. The optional list of modifiers is used to tailor the behavior +of the tactic. The following list describes their syntax and effects: + +.. prodn:: + ring_mod ::= abstract %| decidable @term %| morphism @term + %| setoid @term @term + %| constants [@ltac] + %| preprocess [@ltac] + %| postprocess [@ltac] + %| power_tac @term [@ltac] + %| sign @term + %| div @term + + +abstract + declares the ring as abstract. This is the default. + +decidable :n:`@term` + declares the ring as computational. The expression + :n:`@term` is the correctness proof of an equality test ``?=!`` + (which hould be evaluable). Its type should be of the form + ``forall x y, x ?=! y = true → x == y``. + +morphism :n:`@term` + declares the ring as a customized one. The expression + :n:`@term` is a proof that there exists a morphism between a set of + coefficient and the ring carrier (see ``Ring_theory.ring_morph`` and + ``Ring_theory.semi_morph``). + +setoid :n:`@term` :n:`@term` + forces the use of given setoid. The first + :n:`@term` is a proof that the equality is indeed a setoid (see + ``Setoid.Setoid_Theory``), and the second :n:`@term` a proof that the + ring operations are morphisms (see ``Ring_theory.ring_eq_ext`` and + ``Ring_theory.sring_eq_ext``). + This modifier needs not be used if the setoid and morphisms have been + declared. + +constants [:n:`@ltac`] + specifies a tactic expression :n:`@ltac` that, given a + term, returns either an object of the coefficient set that is mapped + to the expression via the morphism, or returns + ``InitialRing.NotConstant``. The default behavior is to map only 0 and 1 + to their counterpart in the coefficient set. This is generally not + desirable for non trivial computational rings. + +preprocess [:n:`@ltac`] + specifies a tactic :n:`@ltac` that is applied as a + preliminary step for ``ring`` and ``ring_simplify``. It can be used to + transform a goal so that it is better recognized. For instance, ``S n`` + can be changed to ``plus 1 n``. + +postprocess [:n:`@ltac`] + specifies a tactic :n:`@ltac` that is applied as a final + step for ``ring_simplify``. For instance, it can be used to undo + modifications of the preprocessor. + +power_tac :n:`@term` [:n:`@ltac`] + allows ``ring`` and ``ring_simplify`` to recognize + power expressions with a constant positive integer exponent (example: + ::math:`x^2` ). The term :n:`@term` is a proof that a given power function satisfies + the specification of a power function (term has to be a proof of + ``Ring_theory.power_theory``) and :n:`@ltac` specifies a tactic expression + that, given a term, “abstracts” it into an object of type |N| whose + interpretation via ``Cp_phi`` (the evaluation function of power + coefficient) is the original term, or returns ``InitialRing.NotConstant`` + if not a constant coefficient (i.e. |L_tac| is the inverse function of + ``Cp_phi``). See files ``plugins/setoid_ring/ZArithRing.v`` + and ``plugins/setoid_ring/RealField.v`` for examples. By default the tactic + does not recognize power expressions as ring expressions. + +sign :n:`@term` + allows ``ring_simplify`` to use a minus operation when + outputting its normal form, i.e writing ``x − y`` instead of ``x + (− y)``. The + term `:n:`@term` is a proof that a given sign function indicates expressions + that are signed (`term` has to be a proof of ``Ring_theory.get_sign``). See + ``plugins/setoid_ring/InitialRing.v`` for examples of sign function. + +div :n:`@term` + allows ``ring`` and ``ring_simplify`` to use monomials with + coefficient other than 1 in the rewriting. The term :n:`@term` is a proof + that a given division function satisfies the specification of an + euclidean division function (:n:`@term` has to be a proof of + ``Ring_theory.div_theory``). For example, this function is called when + trying to rewrite :math:`7x` by :math:`2x = z` to tell that :math:`7 = 3 \times 2 + 1`. See + ``plugins/setoid_ring/InitialRing.v`` for examples of div function. + +Error messages: + +.. exn:: bad ring structure + + The proof of the ring structure provided is not + of the expected type. + +.. exn:: bad lemma for decidability of equality + + The equality function + provided in the case of a computational ring has not the expected + type. + +.. exn:: ring operation should be declared as a morphism + + A setoid associated to the carrier of the ring structure has been found, + but the ring operation should be declared as morphism. See :ref:`tactics-enabled-on-user-provided-relations`. + +How does it work? +---------------------- + +The code of ring is a good example of tactic written using *reflection*. +What is reflection? Basically, it is writing |Coq| tactics in |Coq|, rather +than in |OCaml|. From the philosophical point of view, it is +using the ability of the Calculus of Constructions to speak and reason +about itself. For the ring tactic we used Coq as a programming +language and also as a proof environment to build a tactic and to +prove it correctness. + +The interested reader is strongly advised to have a look at the +file ``Ring_polynom.v``. Here a type for polynomials is defined: + + +.. coqtop:: in + + Inductive PExpr : Type := + | PEc : C -> PExpr + | PEX : positive -> PExpr + | PEadd : PExpr -> PExpr -> PExpr + | PEsub : PExpr -> PExpr -> PExpr + | PEmul : PExpr -> PExpr -> PExpr + | PEopp : PExpr -> PExpr + | PEpow : PExpr -> N -> PExpr. + + +Polynomials in normal form are defined as: + + +.. coqtop:: in + + Inductive Pol : Type := + | Pc : C -> Pol + | Pinj : positive -> Pol -> Pol + | PX : Pol -> positive -> Pol -> Pol. + + +where ``Pinj n P`` denotes ``P`` in which :math:`V_i` is replaced by :math:`V_{i+n}` , +and ``PX P n Q`` denotes :math:`P \otimes V_1^n \oplus Q'`, `Q'` being `Q` where :math:`V_i` is replaced by :math:`V_{i+1}`. + +Variables maps are represented by list of ring elements, and two +interpretation functions, one that maps a variables map and a +polynomial to an element of the concrete ring, and the second one that +does the same for normal forms: + + +.. coqtop:: in + + + Definition PEeval : list R -> PExpr -> R := [...]. + Definition Pphi_dev : list R -> Pol -> R := [...]. + + +A function to normalize polynomials is defined, and the big theorem is +its correctness w.r.t interpretation, that is: + + +.. coqtop:: in + + Definition norm : PExpr -> Pol := [...]. + Lemma Pphi_dev_ok : + forall l pe npe, norm pe = npe -> PEeval l pe == Pphi_dev l npe. + + +So now, what is the scheme for a normalization proof? Let p be the +polynomial expression that the user wants to normalize. First a little +piece of |ML| code guesses the type of `p`, the ring theory `T` to use, an +abstract polynomial `ap` and a variables map `v` such that `p` is |bdi|- +equivalent to ``(PEeval`` `v` `ap`\ ``)``. Then we replace it by ``(Pphi_dev`` `v` +``(norm`` `ap`\ ``))``, using the main correctness theorem and we reduce it to a +concrete expression `p’`, which is the concrete normal form of `p`. This is summarized in this diagram: + +========= ====== ==== +`p` |ra| |re| +\ |eq| \ +`p’` |la| |le| +========= ====== ==== + +The user do not see the right part of the diagram. From outside, the +tactic behaves like a |bdi| simplification extended with AC rewriting +rules. Basically, the proof is only the application of the main +correctness theorem to well-chosen arguments. + +Dealing with fields +------------------------ + +.. tacn:: field + +The ``field`` tactic is an extension of the ``ring`` to deal with rational +expression. Given a rational expression :math:`F = 0`. It first reduces the +expression `F` to a common denominator :math:`N/D = 0` where `N` and `D` +are two ring expressions. For example, if we take :math:`F = (1 − 1/x) x − x + 1`, this +gives :math:`N = (x − 1) x − x^2 + x` and :math:`D = x`. It then calls ring to solve +:math:`N = 0`. +Note that ``field`` also generates non-zero conditions for all the +denominators it encounters in the reduction. In our example, it +generates the condition :math:`x \neq 0`. These conditions appear as one subgoal +which is a conjunction if there are several denominators. Non-zero +conditions are always polynomial expressions. For example when +reducing the expression :math:`1/(1 + 1/x)`, two side conditions are +generated: :math:`x \neq 0` and :math:`x + 1 \neq 0`. Factorized expressions are broken since +a field is an integral domain, and when the equality test on +coefficients is complete w.r.t. the equality of the target field, +constants can be proven different from zero automatically. + +The tactic must be loaded by ``Require Import Field``. New field +structures can be declared to the system with the ``Add Field`` command +(see below). The field of real numbers is defined in module ``RealField`` +(in ``plugins/setoid_ring``). It is exported by module ``Rbase``, so +that requiring ``Rbase`` or ``Reals`` is enough to use the field tactics on +real numbers. Rational numbers in canonical form are also declared as +a field in module ``Qcanon``. + + +.. example:: + + .. coqtop:: all + + Require Import Reals. + Open Scope R_scope. + Goal forall x, + x <> 0 -> (1 - 1 / x) * x - x + 1 = 0. + intros; field; auto. + Abort. + Goal forall x y, + y <> 0 -> y = x -> x / y = 1. + intros x y H H1; field [H1]; auto. + Abort. + +.. tacv:: field [{* @term}] + + decides the equality of two terms modulo + field operations and the equalities defined + by the :n:`@term`\ s. Each :n:`@term` has to be a proof of some equality + `m` ``=`` `p`, where `m` is a monomial (after “abstraction”), `p` a polynomial + and ``=`` the corresponding equality of the field structure. + +.. note:: + + rewriting works with the equality `m` ``=`` `p` only if `p` is a polynomial since + rewriting is handled by the underlying ring tactic. + +.. tacv:: field_simplify + + performs the simplification in the conclusion of the + goal, :math:`F_1 = F_2` becomes :math:`N_1 / D_1 = N_2 / D_2`. A normalization step + (the same as the one for rings) is then applied to :math:`N_1`, :math:`D_1`, + :math:`N_2` and :math:`D_2`. This way, polynomials remain in factorized form during the + fraction simplifications. This yields smaller expressions when + reducing to the same denominator since common factors can be canceled. + +.. tacv:: field_simplify [{* @term }] + + performs the simplification in the conclusion of the goal using the equalities + defined by the :n:`@term`\ s. + +.. tacv:: field_simplify [{* @term }] {* @term } + + performs the simplification in the terms :n:`@terms` of the conclusion of the goal + using the equalities defined by :n:`@term`\ s inside the brackets. + +.. tacv :: field_simplify in @ident + + performs the simplification in the assumption :n:`@ident`. + +.. tacv :: field_simplify [{* @term }] in @ident + + performs the simplification + in the assumption :n:`@ident` using the equalities defined by the :n:`@term`\ s. + +.. tacv:: field_simplify [{* @term }] {* @term } in @ident + + performs the simplification in the :n:`@term`\ s of the assumption :n:`@ident` using the + equalities defined by the :n:`@term`\ s inside the brackets. + +.. tacv:: field_simplify_eq + + performs the simplification in the conclusion of + the goal removing the denominator. :math:`F_1 = F_2` becomes :math:`N_1 D_2 = N_2 D_1`. + +.. tacv:: field_simplify_eq [ {* @term }] + + performs the simplification in + the conclusion of the goal using the equalities defined by + :n:`@term`\ s. + +.. tacv:: field_simplify_eq in @ident + + performs the simplification in the assumption :n:`@ident`. + +.. tacv:: field_simplify_eq [{* @term}] in @ident + + performs the simplification in the assumption :n:`@ident` using the equalities defined by + :n:`@terms`\ s and removing the denominator. + + +Adding a new field structure +--------------------------------- + +Declaring a new field consists in proving that a field signature (a +carrier set, an equality, and field operations: +``Field_theory.field_theory`` and ``Field_theory.semi_field_theory``) +satisfies the field axioms. Semi-fields (fields without + inverse) are +also supported. The equality can be either Leibniz equality, or any +relation declared as a setoid (see :ref:`tactics-enabled-on-user-provided-relations`). The definition of +fields and semi-fields is: + +.. coqtop:: in + + Record field_theory : Prop := mk_field { + F_R : ring_theory rO rI radd rmul rsub ropp req; + F_1_neq_0 : ~ 1 == 0; + Fdiv_def : forall p q, p / q == p * / q; + Finv_l : forall p, ~ p == 0 -> / p * p == 1 + }. + + Record semi_field_theory : Prop := mk_sfield { + SF_SR : semi_ring_theory rO rI radd rmul req; + SF_1_neq_0 : ~ 1 == 0; + SFdiv_def : forall p q, p / q == p * / q; + SFinv_l : forall p, ~ p == 0 -> / p * p == 1 + }. + + +The result of the normalization process is a fraction represented by +the following type: + +.. coqtop:: in + + Record linear : Type := mk_linear { + num : PExpr C; + denum : PExpr C; + condition : list (PExpr C) + }. + + +where ``num`` and ``denum`` are the numerator and denominator; ``condition`` is a +list of expressions that have appeared as a denominator during the +normalization process. These expressions must be proven different from +zero for the correctness of the algorithm. + +The syntax for adding a new field is + +.. cmd:: Add Field @ident : @term {? ( @field_mod {* , @field_mod } )}. + +The :n:`@ident` is not relevant. It is just used for error +messages. :n:`@term` is a proof that the field signature satisfies the +(semi-)field axioms. The optional list of modifiers is used to tailor +the behavior of the tactic. + +.. prodn:: + field_mod := @ring_mod %| completeness @term + +Since field tactics are built upon ``ring`` +tactics, all modifiers of the ``Add Ring`` apply. There is only one +specific modifier: + +completeness :n:`@term` + allows the field tactic to prove automatically + that the image of non-zero coefficients are mapped to non-zero + elements of the field. :n:`@term` is a proof of + + ``forall x y, [x] == [y] -> x ?=! y = true``, + + which is the completeness of equality on coefficients + w.r.t. the field equality. + + +History of ring +-------------------- + +First Samuel Boutin designed the tactic ``ACDSimpl``. This tactic did lot +of rewriting. But the proofs terms generated by rewriting were too big +for |Coq|’s type-checker. Let us see why: + +.. coqtop:: all + + Require Import ZArith. + Open Scope Z_scope. + Goal forall x y z : Z, + x + 3 + y + y * z = x + 3 + y + z * y. + intros; rewrite (Zmult_comm y z); reflexivity. + Save foo. + Print foo. + +At each step of rewriting, the whole context is duplicated in the +proof term. Then, a tactic that does hundreds of rewriting generates +huge proof terms. Since ``ACDSimpl`` was too slow, Samuel Boutin rewrote +it using reflection (see his article in TACS’97 [Bou97]_). Later, it +was rewritten by Patrick Loiseleur: the new tactic does not any +more require ``ACDSimpl`` to compile and it makes use of |bdi|-reduction not +only to replace the rewriting steps, but also to achieve the +interleaving of computation and reasoning (see :ref:`discussion_reflection`). He also wrote a +few |ML| code for the ``Add Ring`` command, that allow to register new rings +dynamically. + +Proofs terms generated by ring are quite small, they are linear in the +number of :math:`\oplus` and :math:`\otimes` operations in the normalized terms. Type-checking +those terms requires some time because it makes a large use of the +conversion rule, but memory requirements are much smaller. + + +.. _discussion_reflection: + + +Discussion +---------------- + + +Efficiency is not the only motivation to use reflection here. ``ring`` +also deals with constants, it rewrites for example the expression +``34 + 2 * x − x + 12`` to the expected result ``x + 46``. +For the tactic ``ACDSimpl``, the only constants were 0 and 1. +So the expression ``34 + 2 * (x − 1) + 12`` +is interpreted as :math:`V_0 \oplus V_1 \otimes (V_2 \ominus 1) \oplus V_3`\ , +with the variables mapping +:math:`\{V_0 \mapsto 34; V_1 \mapsto 2; V_2 \mapsto x; V_3 \mapsto 12\}`\ . +Then it is rewritten to ``34 − x + 2 * x + 12``, very far from the expected result. +Here rewriting is not sufficient: you have to do some kind of reduction +(some kind of computation) to achieve the normalization. + +The tactic ``ring`` is not only faster than a classical one: using +reflection, we get for free integration of computation and reasoning +that would be very complex to implement in the classic fashion. + +Is it the ultimate way to write tactics? The answer is: yes and no. +The ``ring`` tactic uses intensively the conversion rule of |Cic|, that is +replaces proof by computation the most as it is possible. It can be +useful in all situations where a classical tactic generates huge proof +terms. Symbolic Processing and Tautologies are in that case. But there +are also tactics like ``auto`` or ``linear`` that do many complex computations, +using side-effects and backtracking, and generate a small proof term. +Clearly, it would be significantly less efficient to replace them by +tactics using reflection. + +Another idea suggested by Benjamin Werner: reflection could be used to +couple an external tool (a rewriting program or a model checker) +with |Coq|. We define (in |Coq|) a type of terms, a type of *traces*, and +prove a correction theorem that states that *replaying traces* is safe +w.r.t some interpretation. Then we let the external tool do every +computation (using side-effects, backtracking, exception, or others +features that are not available in pure lambda calculus) to produce +the trace: now we can check in |Coq| that the trace has the expected +semantic by applying the correction lemma. + + + + + + +.. rubric:: Footnotes +.. [#f1] based on previous work from Patrick Loiseleur and Samuel Boutin + + + diff --git a/doc/sphinx/addendum/type-classes.rst b/doc/sphinx/addendum/type-classes.rst new file mode 100644 index 000000000..becebb421 --- /dev/null +++ b/doc/sphinx/addendum/type-classes.rst @@ -0,0 +1,587 @@ +.. include:: ../replaces.rst + +.. _typeclasses: + +Type Classes +============ + +:Source: https://coq.inria.fr/distrib/current/refman/type-classes.html +:Author: Matthieu Sozeau + +This chapter presents a quick reference of the commands related to type +classes. For an actual introduction to type classes, there is a +description of the system :cite:`sozeau08` and the literature on type +classes in Haskell which also applies. + + +Class and Instance declarations +------------------------------- + +The syntax for class and instance declarations is the same as the record +syntax of Coq: + +``Class Id (`` |p_1| ``:`` |t_1| ``) ⋯ (`` |p_n| ``:`` |t_n| ``) [: +sort] := {`` |f_1| ``:`` |u_1| ``; ⋮`` |f_m| ``:`` |u_m| ``}.`` + +``Instance ident : Id`` |p_1| ``⋯`` |p_n| ``:= {`` |f_1| ``:=`` |t_1| ``; ⋮`` |f_m| ``:=`` |t_m| ``}.`` + +The |p_i| ``:`` |t_i| variables are called the *parameters* of the class and +the |f_i| ``:`` |t_i| are called the *methods*. Each class definition gives +rise to a corresponding record declaration and each instance is a +regular definition whose name is given by ident and type is an +instantiation of the record type. + +We’ll use the following example class in the rest of the chapter: + +.. coqtop:: in + + Class EqDec (A : Type) := { + eqb : A -> A -> bool ; + eqb_leibniz : forall x y, eqb x y = true -> x = y }. + +This class implements a boolean equality test which is compatible with +Leibniz equality on some type. An example implementation is: + +.. coqtop:: in + + Instance unit_EqDec : EqDec unit := + { eqb x y := true ; + eqb_leibniz x y H := + match x, y return x = y with tt, tt => eq_refl tt end }. + +If one does not give all the members in the Instance declaration, Coq +enters the proof-mode and the user is asked to build inhabitants of +the remaining fields, e.g.: + +.. coqtop:: in + + Instance eq_bool : EqDec bool := + { eqb x y := if x then y else negb y }. + +.. coqtop:: all + + Proof. intros x y H. + +.. coqtop:: all + + destruct x ; destruct y ; (discriminate || reflexivity). + +.. coqtop:: all + + Defined. + +One has to take care that the transparency of every field is +determined by the transparency of the ``Instance`` proof. One can use +alternatively the ``Program Instance`` variant which has richer facilities +for dealing with obligations. + + +Binding classes +--------------- + +Once a type class is declared, one can use it in class binders: + +.. coqtop:: all + + Definition neqb {A} {eqa : EqDec A} (x y : A) := negb (eqb x y). + +When one calls a class method, a constraint is generated that is +satisfied only in contexts where the appropriate instances can be +found. In the example above, a constraint ``EqDec A`` is generated and +satisfied by ``eqa : EqDec A``. In case no satisfying constraint can be +found, an error is raised: + +.. coqtop:: all + + Fail Definition neqb' (A : Type) (x y : A) := negb (eqb x y). + +The algorithm used to solve constraints is a variant of the eauto +tactic that does proof search with a set of lemmas (the instances). It +will use local hypotheses as well as declared lemmas in +the ``typeclass_instances`` database. Hence the example can also be +written: + +.. coqtop:: all + + Definition neqb' A (eqa : EqDec A) (x y : A) := negb (eqb x y). + +However, the generalizing binders should be used instead as they have +particular support for type classes: + ++ They automatically set the maximally implicit status for type class + arguments, making derived functions as easy to use as class methods. + In the example above, ``A`` and ``eqa`` should be set maximally implicit. ++ They support implicit quantification on partially applied type + classes (:ref:`implicit-generalization`). Any argument not given as part of a type class + binder will be automatically generalized. ++ They also support implicit quantification on :ref:`superclasses`. + + +Following the previous example, one can write: + +.. coqtop:: all + + Generalizable Variables A B C. + + Definition neqb_impl `{eqa : EqDec A} (x y : A) := negb (eqb x y). + +Here ``A`` is implicitly generalized, and the resulting function is +equivalent to the one above. + +Parameterized Instances +----------------------- + +One can declare parameterized instances as in Haskell simply by giving +the constraints as a binding context before the instance, e.g.: + +.. coqtop:: in + + Instance prod_eqb `(EA : EqDec A, EB : EqDec B) : EqDec (A * B) := + { eqb x y := match x, y with + | (la, ra), (lb, rb) => andb (eqb la lb) (eqb ra rb) + end }. + +.. coqtop:: none + + Abort. + +These instances are used just as well as lemmas in the instance hint +database. + +Sections and contexts +--------------------- + +To ease the parametrization of developments by type classes, we +provide a new way to introduce variables into section contexts, +compatible with the implicit argument mechanism. The new command works +similarly to the ``Variables`` vernacular (:ref:`TODO-1.3.2-Definitions`), except it +accepts any binding context as argument. For example: + +.. coqtop:: all + + Section EqDec_defs. + + Context `{EA : EqDec A}. + + Global Instance option_eqb : EqDec (option A) := + { eqb x y := match x, y with + | Some x, Some y => eqb x y + | None, None => true + | _, _ => false + end }. + Admitted. + + End EqDec_defs. + + About option_eqb. + +Here the Global modifier redeclares the instance at the end of the +section, once it has been generalized by the context variables it +uses. + + +Building hierarchies +-------------------- + +.. _superclasses: + +Superclasses +~~~~~~~~~~~~ + +One can also parameterize classes by other classes, generating a +hierarchy of classes and superclasses. In the same way, we give the +superclasses as a binding context: + +.. coqtop:: all + + Class Ord `(E : EqDec A) := { le : A -> A -> bool }. + +Contrary to Haskell, we have no special syntax for superclasses, but +this declaration is morally equivalent to: + +:: + + Class `(E : EqDec A) => Ord A := + { le : A -> A -> bool }. + + +This declaration means that any instance of the ``Ord`` class must have +an instance of ``EqDec``. The parameters of the subclass contain at +least all the parameters of its superclasses in their order of +appearance (here A is the only one). As we have seen, ``Ord`` is encoded +as a record type with two parameters: a type ``A`` and an ``E`` of type +``EqDec A``. However, one can still use it as if it had a single +parameter inside generalizing binders: the generalization of +superclasses will be done automatically. + +.. coqtop:: all + + Definition le_eqb `{Ord A} (x y : A) := andb (le x y) (le y x). + +In some cases, to be able to specify sharing of structures, one may +want to give explicitly the superclasses. It is is possible to do it +directly in regular binders, and using the ``!`` modifier in class +binders. For example: + +.. coqtop:: all + + Definition lt `{eqa : EqDec A, ! Ord eqa} (x y : A) := andb (le x y) (neqb x y). + +The ``!`` modifier switches the way a binder is parsed back to the regular +interpretation of Coq. In particular, it uses the implicit arguments +mechanism if available, as shown in the example. + +Substructures +~~~~~~~~~~~~~ + +Substructures are components of a class which are instances of a class +themselves. They often arise when using classes for logical +properties, e.g.: + +.. coqtop:: none + + Require Import Relation_Definitions. + +.. coqtop:: in + + Class Reflexive (A : Type) (R : relation A) := + reflexivity : forall x, R x x. + + Class Transitive (A : Type) (R : relation A) := + transitivity : forall x y z, R x y -> R y z -> R x z. + +This declares singleton classes for reflexive and transitive relations, +(see the :ref:`singleton class <singleton-class>` variant for an +explanation). These may be used as part of other classes: + +.. coqtop:: all + + Class PreOrder (A : Type) (R : relation A) := + { PreOrder_Reflexive :> Reflexive A R ; + PreOrder_Transitive :> Transitive A R }. + +The syntax ``:>`` indicates that each ``PreOrder`` can be seen as a +``Reflexive`` relation. So each time a reflexive relation is needed, a +preorder can be used instead. This is very similar to the coercion +mechanism of ``Structure`` declarations. The implementation simply +declares each projection as an instance. + +One can also declare existing objects or structure projections using +the Existing Instance command to achieve the same effect. + + +Summary of the commands +----------------------- + + +.. _Class: + +.. cmd:: Class @ident {? @binders} : {? @sort} := {? @ident} { {+; @ident :{? >} @term } }. + + The ``Class`` command is used to declare a type class with parameters + ``binders`` and fields the declared record fields. + +Variants: + +.. _singleton-class: + +.. cmd:: Class @ident {? @binders} : {? @sort} := @ident : @term + + This variant declares a *singleton* class with a single method. This + singleton class is a so-called definitional class, represented simply + as a definition ``ident binders := term`` and whose instances are + themselves objects of this type. Definitional classes are not wrapped + inside records, and the trivial projection of an instance of such a + class is convertible to the instance itself. This can be useful to + make instances of existing objects easily and to reduce proof size by + not inserting useless projections. The class constant itself is + declared rigid during resolution so that the class abstraction is + maintained. + +.. cmd:: Existing Class @ident + + This variant declares a class a posteriori from a constant or + inductive definition. No methods or instances are defined. + +.. _Instance: + +.. cmd:: Instance @ident {? @binders} : Class t1 … tn [| priority] := { field1 := b1 ; …; fieldi := bi } + +The ``Instance`` command is used to declare a type class instance named +``ident`` of the class ``Class`` with parameters ``t1`` to ``tn`` and +fields ``b1`` to ``bi``, where each field must be a declared field of +the class. Missing fields must be filled in interactive proof mode. + +An arbitrary context of ``binders`` can be put after the name of the +instance and before the colon to declare a parameterized instance. An +optional priority can be declared, 0 being the highest priority as for +auto hints. If the priority is not specified, it defaults to the number +of non-dependent binders of the instance. + +Variants: + + +.. cmd:: Instance ident {? @binders} : forall {? @binders}, Class t1 … tn [| priority] := @term + + This syntax is used for declaration of singleton class instances or + for directly giving an explicit term of type ``forall binders, Class + t1 … tn``. One need not even mention the unique field name for + singleton classes. + +.. cmd:: Global Instance + + One can use the ``Global`` modifier on instances declared in a + section so that their generalization is automatically redeclared + after the section is closed. + +.. cmd:: Program Instance + + Switches the type-checking to Program (chapter :ref:`program`) and + uses the obligation mechanism to manage missing fields. + +.. cmd:: Declare Instance + + In a Module Type, this command states that a corresponding concrete + instance should exist in any implementation of thisModule Type. This + is similar to the distinction betweenParameter vs. Definition, or + between Declare Module and Module. + + +Besides the ``Class`` and ``Instance`` vernacular commands, there are a +few other commands related to type classes. + +.. _ExistingInstance: + +Existing Instance +~~~~~~~~~~~~~~~~~ + +.. cmd:: Existing Instance {+ @ident} [| priority] + +This commands adds an arbitrary list of constants whose type ends with +an applied type class to the instance database with an optional +priority. It can be used for redeclaring instances at the end of +sections, or declaring structure projections as instances. This is +equivalent to ``Hint Resolve ident : typeclass_instances``, except it +registers instances for ``Print Instances``. + +.. _Context: + +Context +~~~~~~~ + +.. cmd:: Context @binders + +Declares variables according to the given binding context, which might +use :ref:`implicit-generalization`. + + +.. _typeclasses-eauto: + +``typeclasses eauto`` +~~~~~~~~~~~~~~~~~~~~~ + +The ``typeclasses eauto`` tactic uses a different resolution engine than +eauto and auto. The main differences are the following: + ++ Contrary to ``eauto`` and ``auto``, the resolution is done entirely in + the new proof engine (as of Coq v8.6), meaning that backtracking is + available among dependent subgoals, and shelving goals is supported. + typeclasses eauto is a multi-goal tactic. It analyses the dependencies + between subgoals to avoid backtracking on subgoals that are entirely + independent. + ++ When called with no arguments, typeclasses eauto uses + thetypeclass_instances database by default (instead of core). + Dependent subgoals are automatically shelved, and shelved goals can + remain after resolution ends (following the behavior ofCoq 8.5). + *Note: * As of Coq 8.6, all:once (typeclasses eauto) faithfully + mimicks what happens during typeclass resolution when it is called + during refinement/type-inference, except that *only* declared class + subgoals are considered at the start of resolution during type + inference, while “all” can select non-class subgoals as well. It might + move to ``all:typeclasses eauto`` in future versions when the + refinement engine will be able to backtrack. + ++ When called with specific databases (e.g. with), typeclasses eauto + allows shelved goals to remain at any point during search and treat + typeclasses goals like any other. + ++ The transparency information of databases is used consistently for + all hints declared in them. It is always used when calling the + unifier. When considering the local hypotheses, we use the transparent + state of the first hint database given. Using an empty database + (created with Create HintDb for example) with unfoldable variables and + constants as the first argument of typeclasses eauto hence makes + resolution with the local hypotheses use full conversion during + unification. + + +Variants: + +#. ``typeclasses eauto [num]`` + + *Warning:* The semantics for the limit num + is different than for auto. By default, if no limit is given the + search is unbounded. Contrary to auto, introduction steps (intro) are + counted, which might result in larger limits being necessary when + searching with typeclasses eauto than auto. + +#. ``typeclasses eauto with {+ @ident}`` + + This variant runs resolution with the given hint databases. It treats + typeclass subgoals the same as other subgoals (no shelving of + non-typeclass goals in particular). + +.. _autoapply: + +``autoapply term with ident`` +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +The tactic autoapply applies a term using the transparency information +of the hint database ident, and does *no* typeclass resolution. This can +be used in ``Hint Extern``’s for typeclass instances (in the hint +database ``typeclass_instances``) to allow backtracking on the typeclass +subgoals created by the lemma application, rather than doing type class +resolution locally at the hint application time. + +.. _TypeclassesTransparent: + +Typeclasses Transparent, Typclasses Opaque +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +.. cmd:: Typeclasses { Transparent | Opaque } {+ @ident} + + This commands defines the transparency of the given identifiers + during type class resolution. It is useful when some constants + prevent some unifications and make resolution fail. It is also useful + to declare constants which should never be unfolded during + proof-search, like fixpoints or anything which does not look like an + abbreviation. This can additionally speed up proof search as the + typeclass map can be indexed by such rigid constants (see + :ref:`thehintsdatabasesforautoandeauto`). By default, all constants + and local variables are considered transparent. One should take care + not to make opaque any constant that is used to abbreviate a type, + like: + +:: + + relation A := A -> A -> Prop. + +This is equivalent to ``Hint Transparent, Opaque ident : typeclass_instances``. + + +Set Typeclasses Dependency Order +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +This option (on by default since 8.6) respects the dependency order +between subgoals, meaning that subgoals which are depended on by other +subgoals come first, while the non-dependent subgoals were put before +the dependent ones previously (Coq v8.5 and below). This can result in +quite different performance behaviors of proof search. + + +Set Typeclasses Filtered Unification +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +This option, available since Coq 8.6 and off by default, switches the +hint application procedure to a filter-then-unify strategy. To apply a +hint, we first check that the goal *matches* syntactically the +inferred or specified pattern of the hint, and only then try to +*unify* the goal with the conclusion of the hint. This can drastically +improve performance by calling unification less often, matching +syntactic patterns being very quick. This also provides more control +on the triggering of instances. For example, forcing a constant to +explicitely appear in the pattern will make it never apply on a goal +where there is a hole in that place. + + +Set Typeclasses Limit Intros +~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + + +This option (on by default) controls the ability to apply hints while +avoiding (functional) eta-expansions in the generated proof term. It +does so by allowing hints that conclude in a product to apply to a +goal with a matching product directly, avoiding an introduction. +*Warning:* this can be expensive as it requires rebuilding hint +clauses dynamically, and does not benefit from the invertibility +status of the product introduction rule, resulting in potentially more +expensive proof-search (i.e. more useless backtracking). + + +Set Typeclass Resolution For Conversion +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +This option (on by default) controls the use of typeclass resolution +when a unification problem cannot be solved during elaboration/type- +inference. With this option on, when a unification fails, typeclass +resolution is tried before launching unification once again. + + +Set Typeclasses Strict Resolution +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +Typeclass declarations introduced when this option is set have a +stricter resolution behavior (the option is off by default). When +looking for unifications of a goal with an instance of this class, we +“freeze” all the existentials appearing in the goals, meaning that +they are considered rigid during unification and cannot be +instantiated. + + +Set Typeclasses Unique Solutions +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +When a typeclass resolution is launched we ensure that it has a single +solution or fail. This ensures that the resolution is canonical, but +can make proof search much more expensive. + + +Set Typeclasses Unique Instances +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +Typeclass declarations introduced when this option is set have a more +efficient resolution behavior (the option is off by default). When a +solution to the typeclass goal of this class is found, we never +backtrack on it, assuming that it is canonical. + + +Typeclasses eauto `:=` +~~~~~~~~~~~~~~~~~~~~~~ + +.. cmd:: Typeclasses eauto := {? debug} {? {dfs | bfs}} depth + + This command allows more global customization of the type class + resolution tactic. The semantics of the options are: + + + ``debug`` In debug mode, the trace of successfully applied tactics is + printed. + + + ``dfs, bfs`` This sets the search strategy to depth-first search (the + default) or breadth-first search. + + + ``depth`` This sets the depth limit of the search. + + +Set Typeclasses Debug +~~~~~~~~~~~~~~~~~~~~~ + +.. cmd:: Set Typeclasses Debug {? Verbosity @num} + +These options allow to see the resolution steps of typeclasses that are +performed during search. The ``Debug`` option is synonymous to ``Debug +Verbosity 1``, and ``Debug Verbosity 2`` provides more information +(tried tactics, shelving of goals, etc…). + + +Set Refine Instance Mode +~~~~~~~~~~~~~~~~~~~~~~~~ + +The option Refine Instance Mode allows to switch the behavior of +instance declarations made through the Instance command. + ++ When it is on (the default), instances that have unsolved holes in + their proof-term silently open the proof mode with the remaining + obligations to prove. + ++ When it is off, they fail with an error instead. diff --git a/doc/sphinx/credits.rst b/doc/sphinx/credits.rst index a60f32645..fac0d0a4f 100644 --- a/doc/sphinx/credits.rst +++ b/doc/sphinx/credits.rst @@ -376,7 +376,7 @@ contributed by Jean Goubault was integrated in the basic theories. Pierre Courtieu developed a command and a tactic to reason on the inductive structure of recursively defined functions. -Jacek Chrzszcz designed and implemented the module system of |Coq| whose +Jacek Chrząszcz designed and implemented the module system of |Coq| whose foundations are in Judicaël Courant’s PhD thesis. The development was coordinated by C. Paulin. @@ -478,7 +478,7 @@ Marché and Bruno Barras. Claude Marché coordinated the edition of the Reference Manual for |Coq| V8.0. -Pierre Letouzey and Jacek Chrzszcz respectively maintained the +Pierre Letouzey and Jacek Chrząszcz respectively maintained the extraction tool and module system of |Coq|. Jean-Christophe Filliâtre, Pierre Letouzey, Hugo Herbelin and other diff --git a/doc/sphinx/index.rst b/doc/sphinx/index.rst index c5d4936b1..15e4ff3bc 100644 --- a/doc/sphinx/index.rst +++ b/doc/sphinx/index.rst @@ -24,6 +24,8 @@ Table of contents .. toctree:: :caption: The proof engine + proof-engine/vernacular-commands + proof-engine/proof-handling proof-engine/tactics proof-engine/detailed-tactic-examples proof-engine/ssreflect-proof-language @@ -38,15 +40,25 @@ Table of contents :caption: Practical tools practical-tools/coq-commands + practical-tools/utilities practical-tools/coqide .. toctree:: :caption: Addendum addendum/extended-pattern-matching + addendum/implicit-coercions addendum/canonical-structures + addendum/type-classes addendum/omega addendum/micromega + addendum/extraction + addendum/program + addendum/ring + addendum/nsatz + addendum/generalized-rewriting + addendum/parallel-proof-processing + addendum/miscellaneous-extensions .. toctree:: :caption: Reference diff --git a/doc/sphinx/language/gallina-extensions.rst b/doc/sphinx/language/gallina-extensions.rst index d618d90ad..1d6c11b38 100644 --- a/doc/sphinx/language/gallina-extensions.rst +++ b/doc/sphinx/language/gallina-extensions.rst @@ -2109,6 +2109,8 @@ case, this latter type is considered). Adds blocks of implicit types with different specifications. +.. _implicit-generalization: + Implicit generalization ~~~~~~~~~~~~~~~~~~~~~~~ @@ -2189,12 +2191,7 @@ an inductive type or any constant with a type of the form Then the user is able to apply an object that is not a function, but can be coerced to a function, and more generally to consider that a term of type ``A`` is of type ``B`` provided that there is a declared coercion -between ``A`` and ``B``. The main command is - -.. cmd:: Coercion @qualid : @class >-> @class. - -which declares the construction denoted by qualid as a coercion -between the two given classes. +between ``A`` and ``B``. More details and examples, and a description of the commands related to coercions are provided in :ref:`implicitcoercions`. diff --git a/doc/sphinx/practical-tools/utilities.rst b/doc/sphinx/practical-tools/utilities.rst new file mode 100644 index 000000000..620c002ff --- /dev/null +++ b/doc/sphinx/practical-tools/utilities.rst @@ -0,0 +1,999 @@ +.. include:: ../replaces.rst + +.. _utilities: + +--------------------- + Utilities +--------------------- + +The distribution provides utilities to simplify some tedious works +beside proof development, tactics writing or documentation. + + +Using Coq as a library +---------------------- + +In previous versions, ``coqmktop`` was used to build custom +toplevels - for example for better debugging or custom static +linking. Nowadays, the preferred method is to use ``ocamlfind``. + +The most basic custom toplevel is built using: + +:: + + % ocamlfind ocamlopt -thread -rectypes -linkall -linkpkg \ + -package coq.toplevel \ + toplevel/coqtop\_bin.ml -o my\_toplevel.native + + +For example, to statically link |L_tac|, you can just do: + +:: + + % ocamlfind ocamlopt -thread -rectypes -linkall -linkpkg \ + -package coq.toplevel -package coq.ltac \ + toplevel/coqtop\_bin.ml -o my\_toplevel.native +and similarly for other plugins. + + +Building a |Coq| project with coq_makefile +------------------------------------------ + +The majority of |Coq| projects are very similar: a collection of ``.v`` +files and eventually some ``.ml`` ones (a |Coq| plugin). The main piece of +metadata needed in order to build the project are the command line +options to ``coqc`` (e.g. ``-R``, ``-I``, see also: Section +:ref:`bycommandline`). Collecting the list of files and options is the job +of the ``_CoqProject`` file. + +A simple example of a ``_CoqProject`` file follows: + +:: + + -R theories/ MyCode + theories/foo.v + theories/bar.v + -I src/ + src/baz.ml4 + src/bazaux.ml + src/qux_plugin.mlpack + + +Currently, both |CoqIDE| and |ProofGeneral| (version ≥ ``4.3pre``) +understand ``_CoqProject`` files and invoke |Coq| with the desired options. + +The ``coq_makefile`` utility can be used to set up a build infrastructure +for the |Coq| project based on makefiles. The recommended way of +invoking ``coq_makefile`` is the following one: + +:: + + coq_makefile -f _CoqProject -o CoqMakefile + + +Such command generates the following files: + +CoqMakefile + is a generic makefile for ``GNU Make`` that provides + targets to build the project (both ``.v`` and ``.ml*`` files), to install it + system-wide in the ``coq-contrib`` directory (i.e. where |Coq| is installed) + as well as to invoke |coqdoc| to generate |HTML| documentation. + +CoqMakefile.conf + contains make variables assignments that reflect + the contents of the ``_CoqProject`` file as well as the path relevant to + |Coq|. + + +An optional file ``CoqMakefile.local`` can be provided by the user in order to +extend ``CoqMakefile``. In particular one can declare custom actions to be +performed before or after the build process. Similarly one can customize the +install target or even provide new targets. Extension points are documented in +paragraph :ref:`coqmakefile:local`. + +The extensions of the files listed in ``_CoqProject`` is used in order to +decide how to build them. In particular: + + ++ |Coq| files must use the ``.v`` extension ++ |OCaml| files must use the ``.ml`` or ``.mli`` extension ++ |OCaml| files that require pre processing for syntax + extensions (like ``VERNAC EXTEND``) must use the ``.ml4`` extension ++ In order to generate a plugin one has to list all |OCaml| + modules (i.e. ``Baz`` for ``baz.ml``) in a ``.mlpack`` file (or ``.mllib`` + file). + + +The use of ``.mlpack`` files has to be preferred over ``.mllib`` files, +since it results in a “packed” plugin: All auxiliary modules (as +``Baz`` and ``Bazaux``) are hidden inside the plugin’s “name space” +(``Qux_plugin``). This reduces the chances of begin unable to load two +distinct plugins because of a clash in their auxiliary module names. + +.. _coqmakefilelocal: + +CoqMakefile.local ++++++++++++++++++ + + + +The optional file ``CoqMakefile.local`` is included by the generated +file ``CoqMakefile``. It can contain two kinds of directives. + +Variable assignment + The variable must belong to the variables listed in the ``Parameters`` section of the generated makefile. + Here we describe only few of them. + :CAMLPKGS: + can be used to specify third party findlib packages, and is + passed to the OCaml compiler on building or linking of modules. Eg: + ``-package yojson``. + :CAMLFLAGS: + can be used to specify additional flags to the |OCaml| + compiler, like ``-bin-annot`` or ``-w``.... + :COQC, COQDEP, COQDOC: + can be set in order to use alternative binaries + (e.g. wrappers) + :COQ_SRC_SUBDIRS: can be extended by including other paths in which ``*.cm*`` files are searched. For example ``COQ\_SRC\_SUBDIRS+=user-contrib/Unicoq`` lets you build a plugin containing OCaml code that depends on the OCaml code of ``Unicoq``. + +Rule extension + The following makefile rules can be extended. + + .. example :: + + :: + + pre-all:: + echo "This line is print before making the all target" + install-extra:: + cp ThisExtraFile /there/it/goes + + ``pre-all::`` + run before the all target. One can use this to configure + the project, or initialize sub modules or check dependencies are met. + + ``post-all::`` + run after the all target. One can use this to run a test + suite, or compile extracted code. + + + ``install-extra::`` + run after install. One can use this to install extra files. + + ``install-doc::`` + One can use this to install extra doc. + + ``uninstall::`` + \ + + ``uninstall-doc::`` + \ + + ``clean::`` + \ + + ``cleanall::`` + \ + + ``archclean::`` + \ + + ``merlin-hook::`` + One can append lines to the generated .merlin file extending this + target. + +Timing targets and performance testing +++++++++++++++++++++++++++++++++++++++ + +The generated ``Makefile`` supports the generation of two kinds of timing +data: per-file build-times, and per-line times for an individual file. + +The following targets and Makefile variables allow collection of per- +file timing data: + + ++ ``TIMED=1`` + passing this variable will cause ``make`` to emit a line + describing the user-space build-time and peak memory usage for each + file built. + + .. note:: + On ``Mac OS``, this works best if you’ve installed ``gnu-time``. + + .. example:: + For example, the output of ``make TIMED=1`` may look like + this: + + :: + + COQDEP Fast.v + COQDEP Slow.v + COQC Slow.v + Slow (user: 0.34 mem: 395448 ko) + COQC Fast.v + Fast (user: 0.01 mem: 45184 ko) + ++ ``pretty-timed`` + this target stores the output of ``make TIMED=1`` into + ``time-of-build.log``, and displays a table of the times, sorted from + slowest to fastest, which is also stored in ``time-of-build-pretty.log``. + If you want to construct the ``log`` for targets other than the default + one, you can pass them via the variable ``TGTS``, e.g., ``make pretty-timed + TGTS="a.vo b.vo"``. + + .. :: + This target requires ``python`` to build the table. + + .. note:: + This target will *append* to the timing log; if you want a + fresh start, you must remove the ``filetime-of-build.log`` or + ``run make cleanall``. + + .. example:: + + For example, the output of ``make pretty-timed`` may look like this: + + :: + + COQDEP Fast.v + COQDEP Slow.v + COQC Slow.v + Slow (user: 0.36 mem: 393912 ko) + COQC Fast.v + Fast (user: 0.05 mem: 45992 ko) + Time | File Name + -------------------- + 0m00.41s | Total + -------------------- + 0m00.36s | Slow + 0m00.05s | Fast + + ++ ``print-pretty-timed-diff`` + this target builds a table of timing + changes between two compilations; run ``make make-pretty-timed-before`` to + build the log of the “before” times, and run ``make make-pretty-timed- + after`` to build the log of the “after” times. The table is printed on + the command line, and stored in ``time-of-build-both.log``. This target is + most useful for profiling the difference between two commits to a + repo. + + .. note:: + This target requires ``python`` to build the table. + + .. note:: + The ``make-pretty-timed-before`` and ``make-pretty-timed-after`` targets will + *append* to the timing log; if you want a fresh start, you must remove + the files ``time-of-build-before.log`` and ``time-of-build-after.log`` or run + ``make cleanall`` *before* building either the “before” or “after” + targets. + + .. note:: + The table will be sorted first by absolute time + differences rounded towards zero to a whole-number of seconds, then by + times in the “after” column, and finally lexicographically by file + name. This will put the biggest changes in either direction first, and + will prefer sorting by build-time over subsecond changes in build time + (which are frequently noise); lexicographic sorting forces an order on + files which take effectively no time to compile. + + .. example:: + For example, the output table from + ``make print-pretty-timed-diff`` may look like this: + + :: + + After | File Name | Before || Change | % Change + -------------------------------------------------------- + 0m00.39s | Total | 0m00.35s || +0m00.03s | +11.42% + -------------------------------------------------------- + 0m00.37s | Slow | 0m00.01s || +0m00.36s | +3600.00% + 0m00.02s | Fast | 0m00.34s || -0m00.32s | -94.11% + + +The following targets and ``Makefile`` variables allow collection of per- +line timing data: + + ++ ``TIMING=1`` + passing this variable will cause ``make`` to use ``coqc -time`` to + write to a ``.v.timing`` file for each ``.v`` file compiled, which contains + line-by-line timing information. + + .. example:: + For example, running ``make all TIMING=1`` may result in a file like this: + + :: + + Chars 0 - 26 [Require~Coq.ZArith.BinInt.] 0.157 secs (0.128u,0.028s) + Chars 27 - 68 [Declare~Reduction~comp~:=~vm_c...] 0. secs (0.u,0.s) + Chars 69 - 162 [Definition~foo0~:=~Eval~comp~i...] 0.153 secs (0.136u,0.019s) + Chars 163 - 208 [Definition~foo1~:=~Eval~comp~i...] 0.239 secs (0.236u,0.s) + ++ ``print-pretty-single-time-diff`` + :: + + print-pretty-single-time-diff BEFORE=path/to/file.v.before-timing AFTER=path/to/file.v.after-timing + this target will make a sorted table of the per-line timing differences + between the timing logs in the ``BEFORE`` and ``AFTER`` files, display it, and + save it to the file specified by the ``TIME_OF_PRETTY_BUILD_FILE`` variable, + which defaults to ``time-of-build-pretty.log``. + To generate the ``.v.before-timing`` or ``.v.after-timing`` files, you should + pass ``TIMING=before`` or ``TIMING=after`` rather than ``TIMING=1``. + + .. note:: + The sorting used here is the same as in the ``print-pretty-timed -diff`` target. + + .. note:: + This target requires python to build the table. + + .. example:: + For example, running ``print-pretty-single-time-diff`` might give a table like this: + + :: + + After | Code | Before || Change | % Change + --------------------------------------------------------------------------------------------------- + 0m00.50s | Total | 0m04.17s || -0m03.66s | -87.96% + --------------------------------------------------------------------------------------------------- + 0m00.145s | Chars 069 - 162 [Definition~foo0~:=~Eval~comp~i...] | 0m00.192s || -0m00.04s | -24.47% + 0m00.126s | Chars 000 - 026 [Require~Coq.ZArith.BinInt.] | 0m00.143s || -0m00.01s | -11.88% + N/A | Chars 027 - 068 [Declare~Reduction~comp~:=~nati...] | 0m00.s || +0m00.00s | N/A + 0m00.s | Chars 027 - 068 [Declare~Reduction~comp~:=~vm_c...] | N/A || +0m00.00s | N/A + 0m00.231s | Chars 163 - 208 [Definition~foo1~:=~Eval~comp~i...] | 0m03.836s || -0m03.60s | -93.97% + + ++ ``all.timing.diff``, ``path/to/file.v.timing.diff`` + The ``path/to/file.v.timing.diff`` target will make a ``.v.timing.diff`` file for + the corresponding ``.v`` file, with a table as would be generated by + the ``print-pretty-single-time-diff`` target; it depends on having already + made the corresponding ``.v.before-timing`` and ``.v.after-timing`` files, + which can be made by passing ``TIMING=before`` and ``TIMING=after``. + The ``all.timing.diff`` target will make such timing difference files for + all of the ``.v`` files that the ``Makefile`` knows about. It will fail if + some ``.v.before-timing`` or ``.v.after-timing`` files don’t exist. + + .. note:: + This target requires python to build the table. + + +Reusing/extending the generated Makefile +++++++++++++++++++++++++++++++++++++++++ + +Including the generated makefile with an include directive is +discouraged. The contents of this file, including variable names and +status of rules shall change in the future. Users are advised to +include ``Makefile.conf`` or call a target of the generated Makefile as in +``make -f Makefile target`` from another Makefile. + +One way to get access to all targets of the generated ``CoqMakefile`` is to +have a generic target for invoking unknown targets. + +.. example:: + + :: + + # KNOWNTARGETS will not be passed along to CoqMakefile + KNOWNTARGETS := CoqMakefile extra-stuff extra-stuff2 + # KNOWNFILES will not get implicit targets from the final rule, and so + # depending on them won't invoke the submake + # Warning: These files get declared as PHONY, so any targets depending + # on them always get rebuilt + KNOWNFILES := Makefile _CoqProject + + .DEFAULT_GOAL := invoke-coqmakefile + + CoqMakefile: Makefile _CoqProject + $(COQBIN)coq_makefile -f _CoqProject -o CoqMakefile + + invoke-coqmakefile: CoqMakefile + $(MAKE) --no-print-directory -f CoqMakefile $(filter-out $(KNOWNTARGETS),$(MAKECMDGOALS)) + + .PHONY: invoke-coqmakefile $(KNOWNFILES) + + #################################################################### + ## Your targets here ## + #################################################################### + + # This should be the last rule, to handle any targets not declared above + %: invoke-coqmakefile + @true + + + +Building a subset of the targets with -j +++++++++++++++++++++++++++++++++++++++++ + +To build, say, two targets foo.vo and bar.vo in parallel one can use +``make only TGTS="foo.vo bar.vo" -j``. + +.. note:: + + ``make foo.vo bar.vo -j`` has a different meaning for the make + utility, in particular it may build a shared prerequisite twice. + + +.. note:: + + For users of coq_makefile with version < 8.7 + + + Support for “sub-directory” is deprecated. To perform actions before + or after the build (like invoking ``make`` on a subdirectory) one can hook + in pre-all and post-all extension points. + + ``-extra-phony`` and ``-extra`` are deprecated. To provide additional target + (``.PHONY`` or not) please use ``CoqMakefile.local``. + + + +Modules dependencies +-------------------- + +In order to compute modules dependencies (so to use ``make``), |Coq| comes +with an appropriate tool, ``coqdep``. + +``coqdep`` computes inter-module dependencies for |Coq| and |OCaml| +programs, and prints the dependencies on the standard output in a +format readable by make. When a directory is given as argument, it is +recursively looked at. + +Dependencies of |Coq| modules are computed by looking at ``Require`` +commands (``Require``, ``Require Export``, ``Require Import``), but also at the +command ``Declare ML Module``. + +Dependencies of |OCaml| modules are computed by looking at +`open` commands and the dot notation *module.value*. However, this is +done approximately and you are advised to use ``ocamldep`` instead for the +|OCaml| modules dependencies. + +See the man page of ``coqdep`` for more details and options. + +The build infrastructure generated by ``coq_makefile`` uses ``coqdep`` to +automatically compute the dependencies among the files part of the +project. + + +Documenting |Coq| files with coqdoc +----------------------------------- + +|coqdoc| is a documentation tool for the proof assistant |Coq|, similar to +``javadoc`` or ``ocamldoc``. The task of |coqdoc| is + + +#. to produce a nice |Latex| and/or |HTML| document from the |Coq| + sources, readable for a human and not only for the proof assistant; +#. to help the user navigating in his own (or third-party) sources. + + + +Principles +~~~~~~~~~~ + +Documentation is inserted into |Coq| files as *special comments*. Thus +your files will compile as usual, whether you use |coqdoc| or not. |coqdoc| +presupposes that the given |Coq| files are well-formed (at least +lexically). Documentation starts with ``(**``, followed by a space, and +ends with the pending ``*)``. The documentation format is inspired by Todd +A. Coram’s *Almost Free Text (AFT)* tool: it is mainly ``ASCII`` text with +some syntax-light controls, described below. |coqdoc| is robust: it +shouldn’t fail, whatever the input is. But remember: “garbage in, +garbage out”. + + +|Coq| material inside documentation. +++++++++++++++++++++++++++++++++++ + +|Coq| material is quoted between the delimiters ``[`` and ``]``. Square brackets +may be nested, the inner ones being understood as being part of the +quoted code (thus you can quote a term like ``fun x => u`` by writing ``[fun +x => u]``). Inside quotations, the code is pretty-printed in the same +way as it is in code parts. + +Pre-formatted vernacular is enclosed by ``[[`` and ``]]``. The former must be +followed by a newline and the latter must follow a newline. + + +Pretty-printing. +++++++++++++++++ + +|coqdoc| uses different faces for identifiers and keywords. The pretty- +printing of |Coq| tokens (identifiers or symbols) can be controlled +using one of the following commands: + +:: + + + (** printing *token* %...LATEX...% #...html...# *) + + +or + +:: + + + (** printing *token* $...LATEX math...$ #...html...# *) + + +It gives the |Latex| and |HTML| texts to be produced for the given |Coq| +token. One of the |Latex| or |HTML| text may be omitted, causing the +default pretty-printing to be used for this token. + +The printing for one token can be removed with + +:: + + + (** remove printing *token* *) + + +Initially, the pretty-printing table contains the following mapping: + +==== === ==== ===== === ==== ==== === +`->` → `<-` ← `*` × +`<=` ≤ `>=` ≥ `=>` ⇒ +`<>` ≠ `<->` ↔ `|-` ⊢ +`\/` ∨ `/\` ∧ `~` ¬ +==== === ==== ===== === ==== ==== === + +Any of these can be overwritten or suppressed using the printing +commands. + +.. note :: + The recognition of tokens is done by a (``ocaml``) lex + automaton and thus applies the longest-match rule. For instance, `->~` + is recognized as a single token, where |Coq| sees two tokens. It is the + responsibility of the user to insert space between tokens *or* to give + pretty-printing rules for the possible combinations, e.g. + + :: + + (** printing ->~ %\ensuremath{\rightarrow\lnot}% *) + + + +Sections. ++++++++++ + +Sections are introduced by 1 to 4 leading stars (i.e. at the beginning +of the line) followed by a space. One star is a section, two stars a +sub-section, etc. The section title is given on the remaining of the +line. + +.. example:: + + :: + + (** * Well-founded relations + + In this section, we introduce... *) + + +Lists. +++++++ + +List items are introduced by a leading dash. coqdoc uses whitespace to +determine the depth of a new list item and which text belongs in which +list items. A list ends when a line of text starts at or before the +level of indenting of the list’s dash. A list item’s dash must always +be the first non-space character on its line (so, in particular, a +list can not begin on the first line of a comment - start it on the +second line instead). + +.. example:: + + :: + + We go by induction on [n]: + - If [n] is 0... + - If [n] is [S n'] we require... + + two paragraphs of reasoning, and two subcases: + + - In the first case... + - In the second case... + + So the theorem holds. + + + +Rules. +++++++ + +More than 4 leading dashes produce a horizontal rule. + + +Emphasis. ++++++++++ + +Text can be italicized by placing it in underscores. A non-identifier +character must precede the leading underscore and follow the trailing +underscore, so that uses of underscores in names aren’t mistaken for +emphasis. Usually, these are spaces or punctuation. + +:: + + This sentence contains some _emphasized text_. + + + +Escaping to |Latex| and |HTML|. ++++++++++++++++++++++++++++++++ + +Pure |Latex| or |HTML| material can be inserted using the following +escape sequences: + + ++ ``$...LATEX stuff...$`` inserts some |Latex| material in math mode. + Simply discarded in |HTML| output. ++ ``%...LATEX stuff...%`` inserts some |Latex| material. Simply + discarded in |HTML| output. ++ ``#...HTML stuff...#`` inserts some |HTML| material. Simply discarded in + |Latex| output. + +.. note:: + to simply output the characters ``$``, ``%`` and ``#`` and escaping + their escaping role, these characters must be doubled. + + +Verbatim +++++++++ + +Verbatim material is introduced by a leading ``<<`` and closed by ``>>`` +at the beginning of a line. + +.. example:: + + :: + + Here is the corresponding caml code: + << + let rec fact n = + if n <= 1 then 1 else n * fact (n-1) + >> + + + +Hyperlinks +++++++++++ + +Hyperlinks can be inserted into the |HTML| output, so that any +identifier is linked to the place of its definition. + +``coqc file.v`` automatically dumps localization information in +``file.glob`` or appends it to a file specified using option ``--dump-glob +file``. Take care of erasing this global file, if any, when starting +the whole compilation process. + +Then invoke |coqdoc| or ``coqdoc --glob-from file`` to tell |coqdoc| to look +for name resolutions into the file ``file`` (it will look in ``file.glob`` +by default). + +Identifiers from the |Coq| standard library are linked to the Coq web +site at `<http://coq.inria.fr/library/>`_. This behavior can be changed +using command line options ``--no-externals`` and ``--coqlib``; see below. + + +Hiding / Showing parts of the source. ++++++++++++++++++++++++++++++++++++++ + +Some parts of the source can be hidden using command line options ``-g`` +and ``-l`` (see below), or using such comments: + +:: + + + (* begin hide *) + *some Coq material* + (* end hide *) + + +Conversely, some parts of the source which would be hidden can be +shown using such comments: + +:: + + + (* begin show *) + *some Coq material* + (* end show *) + + +The latter cannot be used around some inner parts of a proof, but can +be used around a whole proof. + + +Usage +~~~~~ + +|coqdoc| is invoked on a shell command line as follows: +``coqdoc <options and files>``. +Any command line argument which is not an option is considered to be a +file (even if it starts with a ``-``). |Coq| files are identified by the +suffixes ``.v`` and ``.g`` and |Latex| files by the suffix ``.tex``. + + +:|HTML| output: This is the default output. One |HTML| file is created for + each |Coq| file given on the command line, together with a file + ``index.html`` (unless ``option-no-index is passed``). The |HTML| pages use a + style sheet named ``style.css``. Such a file is distributed with |coqdoc|. +:|Latex| output: A single |Latex| file is created, on standard + output. It can be redirected to a file with option ``-o``. The order of + files on the command line is kept in the final document. |Latex| + files given on the command line are copied ‘as is’ in the final + document . DVI and PostScript can be produced directly with the + options ``-dvi`` and ``-ps`` respectively. +:TEXmacs output: To translate the input files to TEXmacs format, + to be used by the TEXmacs |Coq| interface. + + + +Command line options +++++++++++++++++++++ + + +**Overall options** + + + :--|HTML|: Select a |HTML| output. + :--|Latex|: Select a |Latex| output. + :--dvi: Select a DVI output. + :--ps: Select a PostScript output. + :--texmacs: Select a TEXmacs output. + :--stdout: Write output to stdout. + :-o file, --output file: Redirect the output into the file ‘file’ + (meaningless with ``-html``). + :-d dir, --directory dir: Output files into directory ‘dir’ instead of + current directory (option ``-d`` does not change the filename specified + with option ``-o``, if any). + :--body-only: Suppress the header and trailer of the final document. + Thus, you can insert the resulting document into a larger one. + :-p string, --preamble string: Insert some material in the |Latex| + preamble, right before ``\begin{document}`` (meaningless with ``-html``). + :--vernac-file file,--tex-file file: Considers the file ‘file’ + respectively as a ``.v`` (or ``.g``) file or a ``.tex`` file. + :--files-from file: Read file names to process in file ‘file’ as if + they were given on the command line. Useful for program sources split + up into several directories. + :-q, --quiet: Be quiet. Do not print anything except errors. + :-h, --help: Give a short summary of the options and exit. + :-v, --version: Print the version and exit. + + + +**Index options** + + Default behavior is to build an index, for the |HTML| output only, + into ``index.html``. + + :--no-index: Do not output the index. + :--multi-index: Generate one page for each category and each letter in + the index, together with a top page ``index.html``. + :--index string: Make the filename of the index string instead of + “index”. Useful since “index.html” is special. + + + +**Table of contents option** + + :-toc, --table-of-contents: Insert a table of contents. For a |Latex| + output, it inserts a ``\tableofcontents`` at the beginning of the + document. For a |HTML| output, it builds a table of contents into + ``toc.html``. + :--toc-depth int: Only include headers up to depth ``int`` in the table of + contents. + + +**Hyperlinks options** + + :--glob-from file: Make references using |Coq| globalizations from file + file. (Such globalizations are obtained with Coq option ``-dump-glob``). + :--no-externals: Do not insert links to the |Coq| standard library. + :--external url coqdir: Use given URL for linking references whose + name starts with prefix ``coqdir``. + :--coqlib url: Set base URL for the Coq standard library (default is + `<http://coq.inria.fr/library/>`_). This is equivalent to ``--external url + Coq``. + :-R dir coqdir: Map physical directory dir to |Coq| logical + directory ``coqdir`` (similarly to |Coq| option ``-R``). + + .. note:: + option ``-R`` only has + effect on the files *following* it on the command line, so you will + probably need to put this option first. + + +**Title options** + + :-s , --short: Do not insert titles for the files. The default + behavior is to insert a title like “Library Foo” for each file. + :--lib-name string: Print “string Foo” instead of “Library Foo” in + titles. For example “Chapter” and “Module” are reasonable choices. + :--no-lib-name: Print just “Foo” instead of “Library Foo” in titles. + :--lib-subtitles: Look for library subtitles. When enabled, the + beginning of each file is checked for a comment of the form: + + :: + + + (** * ModuleName : text *) + + where ``ModuleName`` must be the name of the file. If it is present, the + text is used as a subtitle for the module in appropriate places. + :-t string, --title string: Set the document title. + + +**Contents options** + + :-g, --gallina: Do not print proofs. + :-l, --light: Light mode. Suppress proofs (as with ``-g``) and the following commands: + + + [Recursive] Tactic Definition + + Hint / Hints + + Require + + Transparent / Opaque + + Implicit Argument / Implicits + + Section / Variable / Hypothesis / End + + + + The behavior of options ``-g`` and ``-l`` can be locally overridden using the + ``(* begin show *) … (* end show *)`` environment (see above). + + There are a few options to drive the parsing of comments: + + :--parse-comments: Parses regular comments delimited by ``(*`` and ``*)`` as + well. They are typeset inline. + :--plain-comments: Do not interpret comments, simply copy them as + plain-text. + :--interpolate: Use the globalization information to typeset + identifiers appearing in |Coq| escapings inside comments. + +**Language options** + + + Default behavior is to assume ASCII 7 bits input files. + + :-latin1, --latin1: Select ISO-8859-1 input files. It is equivalent to + --inputenc latin1 --charset iso-8859-1. + :-utf8, --utf8: Set --inputenc utf8x for |Latex| output and--charset + utf-8 for |HTML| output. Also use Unicode replacements for a couple of + standard plain ASCII notations such as → for ``->`` and ∀ for ``forall``. |Latex| + UTF-8 support can be found + at `<http://www.ctan.org/pkg/unicode>`_. For the interpretation of Unicode + characters by |Latex|, extra packages which |coqdoc| does not provide + by default might be required, such as textgreek for some Greek letters + or ``stmaryrd`` for some mathematical symbols. If a Unicode character is + missing an interpretation in the utf8x input encoding, add + ``\DeclareUnicodeCharacter{code}{LATEX-interpretation}``. Packages + and declarations can be added with option ``-p``. + :--inputenc string: Give a |Latex| input encoding, as an option to |Latex| + package ``inputenc``. + :--charset string: Specify the |HTML| character set, to be inserted in + the |HTML| header. + + + +The coqdoc |Latex| style file +~~~~~~~~~~~~~~~~~~~~~~~~~~~ + +In case you choose to produce a document without the default |Latex| +preamble (by using option ``--no-preamble``), then you must insert into +your own preamble the command + +:: + + \usepackage{coqdoc} + +The package optionally takes the argument ``[color]`` to typeset +identifiers with colors (this requires the ``xcolor`` package). + +Then you may alter the rendering of the document by redefining some +macros: + +:coqdockw, coqdocid, …: The one-argument macros for typesetting + keywords and identifiers. Defaults are sans-serif for keywords and + italic for identifiers.For example, if you would like a slanted font + for keywords, you may insert + + :: + + \renewcommand{\coqdockw}[1]{\textsl{#1}} + + + anywhere between ``\usepackage{coqdoc}`` and ``\begin{document}``. + + +:coqdocmodule: + One-argument macro for typesetting the title of a ``.v`` + file. Default is + + :: + + \newcommand{\coqdocmodule}[1]{\section*{Module #1}} + + and you may redefine it using ``\renewcommand``. + +Embedded Coq phrases inside |Latex| documents +--------------------------------------------- + +When writing a documentation about a proof development, one may want +to insert |Coq| phrases inside a |Latex| document, possibly together +with the corresponding answers of the system. We provide a mechanical +way to process such |Coq| phrases embedded in |Latex| files: the ``coq-tex`` +filter. This filter extracts |Coq| phrases embedded in |Latex| files, +evaluates them, and insert the outcome of the evaluation after each +phrase. + +Starting with a file ``file.tex`` containing |Coq| phrases, the ``coq-tex`` +filter produces a file named ``file.v.tex`` with the Coq outcome. + +There are options to produce the |Coq| parts in smaller font, italic, +between horizontal rules, etc. See the man page of ``coq-tex`` for more +details. + +|Coq| and |GNU| |Emacs| +----------------------- + + +The |Coq| |Emacs| mode +~~~~~~~~~~~~~~~~~~~~~~~~~ + +|Coq| comes with a Major mode for |GNU| |Emacs|, ``gallina.el``. This mode +provides syntax highlighting and also a rudimentary indentation +facility in the style of the ``Caml`` |GNU| |Emacs| mode. + +Add the following lines to your ``.emacs`` file: + +:: + + (setq auto-mode-alist (cons '("\\.v$" . coq-mode) auto-mode-alist)) + (autoload 'coq-mode "gallina" "Major mode for editing Coq vernacular." t) + + +The |Coq| major mode is triggered by visiting a file with extension ``.v``, +or manually with the command ``M-x coq-mode``. It gives you the correct +syntax table for the |Coq| language, and also a rudimentary indentation +facility: + + ++ pressing ``Tab`` at the beginning of a line indents the line like the + line above; ++ extra ``Tab``s increase the indentation level (by 2 spaces by default); ++ ``M-Tab`` decreases the indentation level. + + +An inferior mode to run |Coq| under |Emacs|, by Marco Maggesi, is also +included in the distribution, in file ``inferior-coq.el``. Instructions to +use it are contained in this file. + + +Proof General +~~~~~~~~~~~~~ + +|ProofGeneral| is a generic interface for proof assistants based on +|Emacs|. The main idea is that the |Coq| commands you are editing are sent +to a |Coq| toplevel running behind |Emacs| and the answers of the system +automatically inserted into other |Emacs| buffers. Thus you don’t need +to copy-paste the |Coq| material from your files to the |Coq| toplevel or +conversely from the |Coq| toplevel to some files. + +|ProofGeneral| is developed and distributed independently of the system +|Coq|. It is freely available at `<https://proofgeneral.github.io/>`_. + + +Module specification +-------------------- + +Given a |Coq| vernacular file, the gallina filter extracts its +specification (inductive types declarations, definitions, type of +lemmas and theorems), removing the proofs parts of the file. The |Coq| +file ``file.v`` gives birth to the specification file ``file.g`` (where +the suffix ``.g`` stands for |Gallina|). + +See the man page of ``gallina`` for more details and options. + + +Man pages +--------- + +There are man pages for the commands ``coqdep``, ``gallina`` and ``coq-tex``. Man +pages are installed at installation time (see installation +instructions in file ``INSTALL``, step 6). diff --git a/doc/sphinx/proof-engine/proof-handling.rst b/doc/sphinx/proof-engine/proof-handling.rst new file mode 100644 index 000000000..52cde52c6 --- /dev/null +++ b/doc/sphinx/proof-engine/proof-handling.rst @@ -0,0 +1,592 @@ +.. include:: ../replaces.rst +.. _proofhandling: + +------------------- + Proof handling +------------------- + +In |Coq|’s proof editing mode all top-level commands documented in +Chapter :ref:`vernacularcommands` remain available and the user has access to specialized +commands dealing with proof development pragmas documented in this +section. He can also use some other specialized commands called +*tactics*. They are the very tools allowing the user to deal with +logical reasoning. They are documented in Chapter :ref:`tactics`. +When switching in editing proof mode, the prompt ``Coq <`` is changed into +``ident <`` where ``ident`` is the declared name of the theorem currently +edited. + +At each stage of a proof development, one has a list of goals to +prove. Initially, the list consists only in the theorem itself. After +having applied some tactics, the list of goals contains the subgoals +generated by the tactics. + +To each subgoal is associated a number of hypotheses called the *local +context* of the goal. Initially, the local context contains the local +variables and hypotheses of the current section (see Section :ref:`TODO_gallina_assumptions`) +and the local variables and hypotheses of the theorem statement. It is +enriched by the use of certain tactics (see e.g. ``intro`` in Section +:ref:`managingthelocalcontext`). + +When a proof is completed, the message ``Proof completed`` is displayed. +One can then register this proof as a defined constant in the +environment. Because there exists a correspondence between proofs and +terms of λ-calculus, known as the *Curry-Howard isomorphism* [[How80]_, +[Bar81]_, [Gir89]_, [Hue88]_ ], |Coq| +stores proofs as terms of |Cic|. Those terms +are called *proof terms*. + + +.. exn:: No focused proof + +Coq raises this error message when one attempts to use a proof editing command +out of the proof editing mode. + +Switching on/off the proof editing mode +------------------------------------------- + +The proof editing mode is entered by asserting a statement, which +typically is the assertion of a theorem: + +.. cmd:: Theorem @ident [@binders] : @form. + +The list of assertion commands is given in Section :ref:TODO-assertions_and_proof`. The +command ``Goal`` can also be used. + +.. cmd:: Goal @form. + +This is intended for quick assertion of statements, without knowing in +advance which name to give to the assertion, typically for quick +testing of the provability of a statement. If the proof of the +statement is eventually completed and validated, the statement is then +bound to the name ``Unnamed_thm`` (or a variant of this name not already +used for another statement). + +.. cmd:: Qed. + +This command is available in interactive editing proof mode when the +proof is completed. Then ``Qed`` extracts a proof term from the proof +script, switches back to Coq top-level and attaches the extracted +proof term to the declared name of the original goal. This name is +added to the environment as an ``Opaque`` constant. + + +.. exn:: Attempt to save an incomplete proof + +.. note:: + + Sometimes an error occurs when building the proof term, because + tactics do not enforce completely the term construction + constraints. + +The user should also be aware of the fact that since the +proof term is completely rechecked at this point, one may have to wait +a while when the proof is large. In some exceptional cases one may +even incur a memory overflow. + +.. cmdv:: Defined. + +Defines the proved term as a transparent constant. + +.. cmdv:: Save @ident. + +Forces the name of the original goal to be :n:`@ident`. This +command (and the following ones) can only be used if the original goal +has been opened using the ``Goal`` command. + + +.. cmd:: Admitted. + +This command is available in interactive editing proof mode to give up +the current proof and declare the initial goal as an axiom. + + +.. cmd:: Proof @term. + +This command applies in proof editing mode. It is equivalent to + +.. cmd:: exact @term. Qed. + +That is, you have to give the full proof in one gulp, as a +proof term (see Section :ref:`applyingtheorems`). + + +.. cmdv:: Proof. + +Is a noop which is useful to delimit the sequence of tactic commands +which start a proof, after a ``Theorem`` command. It is a good practice to +use ``Proof``. as an opening parenthesis, closed in the script with a +closing ``Qed``. + + +See also: ``Proof with tactic.`` in Section +:ref:`setimpautotactics`. + + +.. cmd:: Proof using @ident1 ... @identn. + +This command applies in proof editing mode. It declares the set of +section variables (see :ref:`TODO-gallina-assumptions`) used by the proof. At ``Qed`` time, the +system will assert that the set of section variables actually used in +the proof is a subset of the declared one. + +The set of declared variables is closed under type dependency. For +example if ``T`` is variable and a is a variable of type ``T``, the commands +``Proof using a`` and ``Proof using T a``` are actually equivalent. + + +.. cmdv:: Proof using @ident1 ... @identn with @tactic. + +in Section :ref:`setimpautotactics`. + +.. cmdv:: Proof using All. + +Use all section variables. + + +.. cmdv:: Proof using Type. + +.. cmdv:: Proof using. + +Use only section variables occurring in the statement. + + +.. cmdv:: Proof using Type*. + +The ``*`` operator computes the forward transitive closure. E.g. if the +variable ``H`` has type ``p < 5`` then ``H`` is in ``p*`` since ``p`` occurs in the type +of ``H``. ``Type*`` is the forward transitive closure of the entire set of +section variables occurring in the statement. + + +.. cmdv:: Proof using -(@ident1 ... @identn). + +Use all section variables except :n:`@ident1` ... :n:`@identn`. + + +.. cmdv:: Proof using @collection1 + @collection2 . + + +.. cmdv:: Proof using @collection1 - @collection2 . + + +.. cmdv:: Proof using @collection - ( @ident1 ... @identn ). + + +.. cmdv:: Proof using @collection * . + +Use section variables being, respectively, in the set union, set +difference, set complement, set forward transitive closure. See +Section :ref:`nameaset` to know how to form a named collection. The ``*`` operator +binds stronger than ``+`` and ``-``. + + +Proof using options +``````````````````` + +The following options modify the behavior of ``Proof using``. + + +.. cmdv:: Set Default Proof Using "@expression". + +Use :n:`@expression` as the default ``Proof``` using value. E.g. ``Set Default +Proof Using "a b"``. will complete all ``Proof`` commands not followed by a +using part with using ``a`` ``b``. + + +.. cmdv:: Set Suggest Proof Using. + +When ``Qed`` is performed, suggest a using annotation if the user did not +provide one. + +.. _`nameaset`: + +Name a set of section hypotheses for ``Proof using`` +```````````````````````````````````````````````````` + +The command ``Collection`` can be used to name a set of section +hypotheses, with the purpose of making ``Proof using`` annotations more +compact. + + +.. cmdv:: Collection Some := x y z. + +Define the collection named "Some" containing ``x``, ``y`` and ``z``. + + +.. cmdv:: Collection Fewer := Some - z. + +Define the collection named "Fewer" containing only ``x`` and ``y``. + + +.. cmdv:: Collection Many := Fewer + Some. +.. cmdv:: Collection Many := Fewer - Some. + +Define the collection named "Many" containing the set union or set +difference of "Fewer" and "Some". + + +.. cmdv:: Collection Many := Fewer - (x y). + +Define the collection named "Many" containing the set difference of +"Fewer" and the unnamed collection ``x`` ``y``. + + +.. cmd:: Abort. + +This command cancels the current proof development, switching back to +the previous proof development, or to the |Coq| toplevel if no other +proof was edited. + + +.. exn:: No focused proof (No proof-editing in progress) + + + +.. cmdv:: Abort @ident. + +Aborts the editing of the proof named :n:`@ident`. + +.. cmdv:: Abort All. + +Aborts all current goals, switching back to the |Coq| +toplevel. + + + +.. cmd:: Existential @num := @term. + +This command instantiates an existential variable. :n:`@num` is an index in +the list of uninstantiated existential variables displayed by ``Show +Existentials`` (described in Section :ref:`requestinginformation`). + +This command is intended to be used to instantiate existential +variables when the proof is completed but some uninstantiated +existential variables remain. To instantiate existential variables +during proof edition, you should use the tactic instantiate. + + +See also: ``instantiate (num:= term).`` in Section +:ref:`TODO-controllingtheproofflow`. +See also: ``Grab Existential Variables.`` below. + + +.. cmd:: Grab Existential Variables. + +This command can be run when a proof has no more goal to be solved but +has remaining uninstantiated existential variables. It takes every +uninstantiated existential variable and turns it into a goal. + + +Navigation in the proof tree +-------------------------------- + + +.. cmd:: Undo. + +This command cancels the effect of the last command. Thus, it +backtracks one step. + + +.. cmdv:: Undo @num. + +Repeats Undo :n:`@num` times. + +.. cmdv:: Restart. + +This command restores the proof editing process to the original goal. + + +.. exn:: No focused proof to restart + + +.. cmd:: Focus. + +This focuses the attention on the first subgoal to prove and the +printing of the other subgoals is suspended until the focused subgoal +is solved or unfocused. This is useful when there are many current +subgoals which clutter your screen. + + +.. cmdv:: Focus @num. + +This focuses the attention on the :n:`@num` th subgoal to +prove. + +*This command is deprecated since 8.8*: prefer the use of bullets or +focusing brackets instead, including :n:`@num : %{` + +.. cmd:: Unfocus. + +This command restores to focus the goal that were suspended by the +last ``Focus`` command. + +*This command is deprecated since 8.8.* + +.. cmd:: Unfocused. + +Succeeds if the proof is fully unfocused, fails is there are some +goals out of focus. + + +.. cmd:: %{ %| %} + +The command ``{`` (without a terminating period) focuses on the first +goal, much like ``Focus.`` does, however, the subproof can only be +unfocused when it has been fully solved ( *i.e.* when there is no +focused goal left). Unfocusing is then handled by ``}`` (again, without a +terminating period). See also example in next section. + +Note that when a focused goal is proved a message is displayed +together with a suggestion about the right bullet or ``}`` to unfocus it +or focus the next one. + +.. cmdv:: @num: %{ + +This focuses on the :n:`@num` th subgoal to prove. + +Error messages: + +.. exn:: This proof is focused, but cannot be unfocused this way + +You are trying to use ``}`` but the current subproof has not been fully solved. + +.. exn:: No such goal + +.. exn:: Brackets only support the single numbered goal selector + + +See also error messages about bullets below. + +Bullets +``````` + +Alternatively to ``{`` and ``}``, proofs can be structured with bullets. The +use of a bullet ``b`` for the first time focuses on the first goal ``g``, the +same bullet cannot be used again until the proof of ``g`` is completed, +then it is mandatory to focus the next goal with ``b``. The consequence is +that ``g`` and all goals present when ``g`` was focused are focused with the +same bullet ``b``. See the example below. + +Different bullets can be used to nest levels. The scope of bullet does +not go beyond enclosing ``{`` and ``}``, so bullets can be reused as further +nesting levels provided they are delimited by these. Available bullets +are ``-``, ``+``, ``*``, ``--``, ``++``, ``**``, ``---``, ``+++``, ``***``, ... (without a terminating period). + +Note again that when a focused goal is proved a message is displayed +together with a suggestion about the right bullet or ``}`` to unfocus it +or focus the next one. + +.. note:: + + In Proof General (``Emacs`` interface to |Coq|), you must use + bullets with the priority ordering shown above to have a correct + indentation. For example ``-`` must be the outer bullet and ``**`` the inner + one in the example below. + +The following example script illustrates all these features: + +.. example:: + .. coqtop:: all + + Goal (((True /\ True) /\ True) /\ True) /\ True. + Proof. + split. + - split. + + split. + ** { split. + - trivial. + - trivial. + } + ** trivial. + + trivial. + - assert True. + { trivial. } + assumption. + + +.. exn:: Wrong bullet @bullet1 : Current bullet @bullet2 is not finished. + +Before using bullet :n:`@bullet1` again, you should first finish proving the current focused goal. Note that :n:`@bullet1` and :n:`@bullet2` may be the same. + +.. exn:: Wrong bullet @bullet1 : Bullet @bullet2 is mandatory here. + +You must put :n:`@bullet2` to focus next goal. No other bullet is allowed here. + +.. exn:: No such goal. Focus next goal with bullet @bullet. + +You tried to applied a tactic but no goal where under focus. Using :n:`@bullet` is mandatory here. + +.. exn:: No such goal. Try unfocusing with %{. + +You just finished a goal focused by ``{``, you must unfocus it with ``}``. + +Set Bullet Behavior +``````````````````` + +The bullet behavior can be controlled by the following commands. + +.. opt:: Bullet Behavior "None". + +This makes bullets inactive. + +.. opt:: Bullet Behavior "Strict Subproofs". + +This makes bullets active (this is the default behavior). + + + +Requesting information +---------------------- + + +.. cmd:: Show. + +This command displays the current goals. + + +.. cmdv:: Show @num + +Displays only the :n:`@num`-th subgoal. + +.. exn:: No such goal +.. exn:: No focused proof + +.. cmdv:: Show @ident. + +Displays the named goal :n:`@ident`. This is useful in +particular to display a shelved goal but only works if the +corresponding existential variable has been named by the user +(see :ref:`exvariables`) as in the following example. + +.. example:: + + .. coqtop:: all + + Goal exists n, n = 0. + eexists ?[n]. + Show n. + +.. cmdv:: Show Script. + +Displays the whole list of tactics applied from the +beginning of the current proof. This tactics script may contain some +holes (subgoals not yet proved). They are printed under the form + +``<Your Tactic Text here>``. + +.. cmdv:: Show Proof. + +It displays the proof term generated by the tactics +that have been applied. If the proof is not completed, this term +contain holes, which correspond to the sub-terms which are still to be +constructed. These holes appear as a question mark indexed by an +integer, and applied to the list of variables in the context, since it +may depend on them. The types obtained by abstracting away the context +from the type of each hole-placer are also printed. + +.. cmdv:: Show Conjectures. + +It prints the list of the names of all the +theorems that are currently being proved. As it is possible to start +proving a previous lemma during the proof of a theorem, this list may +contain several names. + +.. cmdv:: Show Intro. + +If the current goal begins by at least one product, +this command prints the name of the first product, as it would be +generated by an anonymous ``intro``. The aim of this command is to ease +the writing of more robust scripts. For example, with an appropriate +Proof General macro, it is possible to transform any anonymous ``intro`` +into a qualified one such as ``intro y13``. In the case of a non-product +goal, it prints nothing. + +.. cmdv:: Show Intros. + +This command is similar to the previous one, it +simulates the naming process of an intros. + +.. cmdv:: Show Existentials. + +It displays the set of all uninstantiated +existential variables in the current proof tree, along with the type +and the context of each variable. + +.. cmdv:: Show Match @ident. + +This variant displays a template of the Gallina +``match`` construct with a branch for each constructor of the type +:n:`@ident` + +.. example:: + .. coqtop:: all + + Show Match nat. + +.. exn:: Unknown inductive type + +.. exn:: Show Universes. + +It displays the set of all universe constraints and +its normalized form at the current stage of the proof, useful for +debugging universe inconsistencies. + + +.. cmd:: Guarded. + +Some tactics (e.g. refine :ref:`applyingtheorems`) allow to build proofs using +fixpoint or co-fixpoint constructions. Due to the incremental nature +of interactive proof construction, the check of the termination (or +guardedness) of the recursive calls in the fixpoint or cofixpoint +constructions is postponed to the time of the completion of the proof. + +The command ``Guarded`` allows checking if the guard condition for +fixpoint and cofixpoint is violated at some time of the construction +of the proof without having to wait the completion of the proof. + + +Controlling the effect of proof editing commands +------------------------------------------------ + + +.. opt:: Hyps Limit @num. + +This option controls the maximum number of hypotheses displayed in goals +after the application of a tactic. All the hypotheses remain usable +in the proof development. +When unset, it goes back to the default mode which is to print all +available hypotheses. + + +.. opt:: Automatic Introduction. + +This option controls the way binders are handled +in assertion commands such as ``Theorem ident [binders] : form``. When the +option is set, which is the default, binders are automatically put in +the local context of the goal to prove. + +The option can be unset by issuing ``Unset Automatic Introduction``. When +the option is unset, binders are discharged on the statement to be +proved and a tactic such as intro (see Section :ref:`managingthelocalcontext`) has to be +used to move the assumptions to the local context. + + +Controlling memory usage +------------------------ + +When experiencing high memory usage the following commands can be used +to force |Coq| to optimize some of its internal data structures. + + +.. cmd:: Optimize Proof. + +This command forces |Coq| to shrink the data structure used to represent +the ongoing proof. + + +.. cmd:: Optimize Heap. + +This command forces the |OCaml| runtime to perform a heap compaction. +This is in general an expensive operation. +See: `OCaml Gc <http://caml.inria.fr/pub/docs/manual-ocaml/libref/Gc.html#VALcompact>`_ +There is also an analogous tactic ``optimize_heap`` (see~:ref:`tactic-optimizeheap`) diff --git a/doc/sphinx/proof-engine/ssreflect-proof-language.rst b/doc/sphinx/proof-engine/ssreflect-proof-language.rst index 61dffa024..bd71e5ed8 100644 --- a/doc/sphinx/proof-engine/ssreflect-proof-language.rst +++ b/doc/sphinx/proof-engine/ssreflect-proof-language.rst @@ -451,7 +451,7 @@ Anonymous arguments ~~~~~~~~~~~~~~~~~~~ When in a definition, the type of a certain argument is mandatory, but -not its name, one usually use “arrow” abstractions for prenex +not its name, one usually uses “arrow” abstractions for prenex arguments, or the ``(_ : term)`` syntax for inner arguments. In |SSR|, the latter can be replaced by the open syntax ``of term`` or (equivalently) ``& term``, which are both syntactically equivalent to a @@ -518,7 +518,7 @@ is a valid tactic expression. The pose tactic is also improved for the local definition of higher order terms. Local definitions of functions can use the same syntax as -global ones. For example the tactic ``pose`` supoprts parameters: +global ones. For example, the tactic ``pose`` supoprts parameters: .. example:: @@ -1295,7 +1295,7 @@ is a synonym for: intro top; first [refine top | refine (top _) | refine (top _ _) | …]; clear top. -where ``top`` is fresh name, and the sequence of refine tactics tries to +where ``top`` is a fresh name, and the sequence of refine tactics tries to catch the appropriate number of wildcards to be inserted. Note that this use of the refine tactic implies that the tactic tries to match the goal up to expansion of constants and evaluation of subterms. @@ -1573,7 +1573,7 @@ The :token:`i_pattern` s can be seen as a variant of *intro patterns* :ref:`tactics`: each performs an introduction operation, i.e., pops some variables or assumptions from the goal. -An :token:`s_item` can simplify the set of subgoals or the subgoal themselves: +An :token:`s_item` can simplify the set of subgoals or the subgoals themselves: + ``//`` removes all the “trivial” subgoals that can be resolved by the |SSR| tactic ``done`` described in :ref:`terminators_ssr`, i.e., @@ -1831,7 +1831,7 @@ compact syntax: case: {2}_ / eqP. -were ``_`` is interpreted as ``(_ == _)`` since +where ``_`` is interpreted as ``(_ == _)`` since ``eqP T a b : reflect (a = b) (a == b)`` and reflect is a type family with one index. @@ -2074,7 +2074,7 @@ is equivalent to: do [done | by move=> top; apply top]. -where top is a fresh name affected to the top assumption of the goal. +where ``top`` is a fresh name assigned to the top assumption of the goal. This applied form is supported by the : discharge tactical, and the tactic: @@ -2090,7 +2090,7 @@ is equivalent to: (see section :ref:`discharge_ssr` for the documentation of the apply: combination). -Warning The list of tactics, possibly chained by semi-columns, that +Warning The list of tactics, possibly chained by semicolons, that follows a by keyword is considered as a parenthesized block applied to the current goal. Hence for example if the tactic: @@ -2123,7 +2123,7 @@ generated by the previous tactic. This covers the frequent cases where a tactic generates two subgoals one of which can be easily disposed of. -This is an other powerful way of linearization of scripts, since it +This is another powerful way of linearization of scripts, since it happens very often that a trivial subgoal can be solved in a less than one line tactic. For instance, the tactic: @@ -2131,14 +2131,14 @@ one line tactic. For instance, the tactic: :name: last tries to solve the last subgoal generated by the first -tactic using the given second tactic , and fails if it does not succeeds. -Its analogous +tactic using the given second tactic, and fails if it does not succeed. +Its analogue .. tacn:: @tactic ; first by @tactic :name: first tries to solve the first subgoal generated by the first tactic using the -second given tactic, and fails if it does not succeeds. +second given tactic, and fails if it does not succeed. |SSR| also offers an extension of this facility, by supplying tactics to *permute* the subgoals generated by a tactic. The tactic: @@ -2259,14 +2259,14 @@ For instance, the tactic: tactic; do 1? rewrite mult_comm. -rewrites at most one time the lemma ``mult_com`` in all the subgoals +rewrites at most one time the lemma ``mult_comm`` in all the subgoals generated by tactic , whereas the tactic: .. coqtop:: in tactic; do 2! rewrite mult_comm. -rewrites exactly two times the lemma ``mult_com`` in all the subgoals +rewrites exactly two times the lemma ``mult_comm`` in all the subgoals generated by tactic, and fails if this rewrite is not possible in some subgoal. @@ -2335,10 +2335,10 @@ to the following one: .. tacv:: @tactic in {+ @clear_switch | {? @ } @ident | ( @ident ) | ( {? @ } @ident := @c_pattern ) } {? * } In its simplest form the last option lets one rename hypotheses that -can’t be cleared (like section variables). For example ``(y := x)`` +can’t be cleared (like section variables). For example, ``(y := x)`` generalizes over ``x`` and reintroduces the generalized variable under the name ``y`` (and does not clear ``x``). -For a more precise description this form of localization refer +For a more precise description of this form of localization refer to :ref:`advanced_generalization_ssr`. @@ -2351,7 +2351,7 @@ Forward reasoning structures the script by explicitly specifying some assumptions to be added to the proof context. It is closely associated with the declarative style of proof, since an extensive use of these highlighted statements make the script closer to a (very detailed) -text book proof. +textbook proof. Forward chaining tactics allow to state an intermediate lemma and start a piece of script dedicated to the proof of this statement. The use of closing @@ -2492,7 +2492,7 @@ also supported (assuming x occurs in the goal only): have {x} -> : x = y. -An other frequent use of the intro patterns combined with ``have`` is the +Another frequent use of the intro patterns combined with ``have`` is the destruction of existential assumptions like in the tactic: .. example:: @@ -2845,8 +2845,8 @@ term -> G. If the optional list of :token:`itent` is present on the left side of ``/``, these constants are generalized in the -premise (term -> G) of the first subgoal. By default the body of local -definitions is erased. This behavior can be inhibited prefixing the +premise (term -> G) of the first subgoal. By default bodies of local +definitions are erased. This behavior can be inhibited by prefixing the name of the local definition with the ``@`` character. In the second subgoal, the tactic: @@ -2936,7 +2936,7 @@ renaming does not require the original variable to be cleared. The syntax ``(@x := y)`` generates a let-in abstraction but with the following caveat: ``x`` will not bind ``y``, but its body, whenever ``y`` can be -unfolded. This cover the case of both local and global definitions, as +unfolded. This covers the case of both local and global definitions, as illustrated in the following example. .. example:: @@ -3035,7 +3035,7 @@ operation should be performed: specifies if and how the rewrite operation should be repeated. + A rewrite operation matches the occurrences of a *rewrite pattern*, - and replaces these occurrences by an other term, according to the + and replaces these occurrences by another term, according to the given :token:`r_item`. The optional *redex switch* ``[r_pattern]``, which should always be surrounded by brackets, gives explicitly this rewrite @@ -3329,7 +3329,7 @@ The rewrite tactic can be provided a *tuple* of rewrite rules, or more generally a tree of such rules, since this tuple can feature arbitrary inner parentheses. We call *multirule* such a generalized rewrite rule. This feature is of special interest when it is combined with -multiplier switches, which makes the rewrite tactic iterates the +multiplier switches, which makes the rewrite tactic iterate the rewrite operations prescribed by the rules on the current goal. @@ -3473,7 +3473,7 @@ efficient ones, e.g. for the purpose of a correctness proof. Wildcards vs abstractions ````````````````````````` -The rewrite tactic supports :token:`r_items` containing holes. For example in +The rewrite tactic supports :token:`r_items` containing holes. For example, in the tactic ``rewrite (_ : _ * 0 = 0).`` the term ``_ * 0 = 0`` is interpreted as ``forall n : nat, n * 0 = 0.`` Anyway this tactic is *not* equivalent to @@ -3736,8 +3736,8 @@ replaces the occurrence(s) of :token:`ident` coded by the We found that it was usually preferable to prevent the expansion of some functions by the partial evaluation switch ``/=``, unless this -allowed the evaluation of a condition. This is possible thanks to an -other mechanism of term tagging, resting on the following *Notation*: +allowed the evaluation of a condition. This is possible thanks to another +mechanism of term tagging, resting on the following *Notation*: .. coqtop:: in @@ -3781,7 +3781,7 @@ arithmetic operations. We define for instance: The operation ``addn`` behaves exactly like ``plus``, except that ``(addn (S n) m)`` will not simplify spontaneously to -``(S (addn n m))`` (the two terms, however, are inter-convertible). +``(S (addn n m))`` (the two terms, however, are convertible). In addition, the unfolding step: ``rewrite /addn`` will replace ``addn`` directly with ``plus``, so the ``nosimpl`` form is essentially invisible. @@ -3792,7 +3792,7 @@ essentially invisible. Congruence ~~~~~~~~~~ -Because of the way matching interferes with type families parameters, +Because of the way matching interferes with parameters of type families, the tactic: .. coqtop:: in @@ -3912,8 +3912,8 @@ The simple form of patterns used so far, terms possibly containing wild cards, often require an additional :token:`occ_switch` to be specified. While this may work pretty fine for small goals, the use of polymorphic functions and dependent types may lead to an invisible -duplication of functions arguments. These copies usually end up in -types hidden by the implicit arguments machinery or by user defined +duplication of function arguments. These copies usually end up in +types hidden by the implicit arguments machinery or by user-defined notations. In these situations computing the right occurrence numbers is very tedious because they must be counted on the goal as printed after setting the Printing All flag. Moreover the resulting script is @@ -3981,7 +3981,7 @@ pattern for the redex looking at the rule used for rewriting. The first :token:`c_pattern` is the simplest form matching any context but selecting a specific redex and has been described in the previous sections. We have seen so far that the possibility of selecting a -redex using a term with holes is already a powerful mean of redex +redex using a term with holes is already a powerful means of redex selection. Similarly, any terms provided by the user in the more complex forms of :token:`c_patterns` presented in the tables above can contain @@ -4064,7 +4064,7 @@ Contextual pattern in set and the : tactical As already mentioned in section :ref:`abbreviations_ssr` the ``set`` tactic takes as an argument a term in open syntax. This term is interpreted as the -simplest for of :token:`c_pattern`. To void confusion in the grammar, open +simplest form of :token:`c_pattern`. To avoid confusion in the grammar, open syntax is supported only for the simplest form of patterns, while parentheses are required around more complex patterns. @@ -4086,17 +4086,17 @@ parentheses are required around more complex patterns. set t := (a + _ in X in _ = X). -Since the user may define an infix notation for ``in`` the former tactic -may result ambiguous. The disambiguation rule implemented is to prefer +Since the user may define an infix notation for ``in`` the result of the former +tactic may be ambiguous. The disambiguation rule implemented is to prefer patterns over simple terms, but to interpret a pattern with double -parentheses as a simple term. For example the following tactic would +parentheses as a simple term. For example, the following tactic would capture any occurrence of the term ``a in A``. .. coqtop:: in set t := ((a in A)). -Contextual pattern can also be used as arguments of the ``:`` tactical. +Contextual patterns can also be used as arguments of the ``:`` tactical. For example: .. coqtop:: in @@ -4139,7 +4139,7 @@ Contextual patterns in rewrite Note that the right hand side of ``addn0`` is undetermined, but the rewrite pattern specifies the redex explicitly. The right hand side - of ``addn0`` is unified with the term identified by ``X``, ``0`` here. + of ``addn0`` is unified with the term identified by ``X``, here ``0``. The following pattern does not specify a redex, since it identifies an @@ -4269,7 +4269,7 @@ generation (see section :ref:`generation_of_equations_ssr`). .. example:: - The following script illustrate a toy example of this feature. Let us + The following script illustrates a toy example of this feature. Let us define a function adding an element at the end of a list: .. coqtop:: reset @@ -4283,7 +4283,7 @@ generation (see section :ref:`generation_of_equations_ssr`). .. coqtop:: all Variable d : Type. - Fixpoint add_last(s : list d) (z : d) {struct s} : list d := + Fixpoint add_last (s : list d) (z : d) {struct s} : list d := if s is cons x s' then cons x (add_last s' z) else z :: nil. One can define an alternative, reversed, induction principle on @@ -4296,7 +4296,7 @@ generation (see section :ref:`generation_of_equations_ssr`). forall s : list d, P s. Then the combination of elimination views with equation names result - in a concise syntax for reasoning inductively using the user defined + in a concise syntax for reasoning inductively using the user-defined elimination scheme. .. coqtop:: all @@ -4305,8 +4305,8 @@ generation (see section :ref:`generation_of_equations_ssr`). elim/last_ind_list E : l=> [| u v]; last first. -User provided eliminators (potentially generated with the ``Function`` -|Coq|’s command) can be combined with the type family switches described +User-provided eliminators (potentially generated with |Coq|’s ``Function`` +command) can be combined with the type family switches described in section :ref:`type_families_ssr`. Consider an eliminator ``foo_ind`` of type: @@ -4341,7 +4341,7 @@ The ``elim/`` tactic distinguishes two cases: As explained in section :ref:`type_families_ssr`, the initial prefix of ``ei`` can be omitted. -Here an example of a regular, but non trivial, eliminator. +Here is an example of a regular, but nontrivial, eliminator. .. example:: @@ -4423,7 +4423,7 @@ Here an example of a regular, but non trivial, eliminator. ``P`` should be the same as the second argument of ``plus``, in the second argument of ``P``, but ``y`` and ``z`` do no unify. -Here an example of a truncated eliminator: +Here is an example of a truncated eliminator: .. example:: @@ -4481,7 +4481,7 @@ Interpreting assumptions ~~~~~~~~~~~~~~~~~~~~~~~~ Interpreting an assumption in the context of a proof consists in -applying it a lemma before generalizing, and/or decomposing this +applying to it a lemma before generalizing, and/or decomposing this assumption. For instance, with the extensive use of boolean reflection (see section :ref:`views_and_reflection_ssr`.4), it is quite frequent to need to decompose the logical interpretation of (the boolean @@ -4689,7 +4689,7 @@ the bookkeeping tactical ``=>`` since this would be redundant with the Boolean reflection ~~~~~~~~~~~~~~~~~~ -In the Calculus of Inductive Construction, there is an obvious +In the Calculus of Inductive Constructions, there is an obvious distinction between logical propositions and boolean values. On the one hand, logical propositions are objects of *sort* ``Prop`` which is the carrier of intuitionistic reasoning. Logical connectives in @@ -5002,7 +5002,7 @@ but they also allow complex transformation, involving negations. Note that views, being part of :token:`i_pattern`, can be used to interpret assertions too. For example the following script asserts ``a && b`` but -actually used its propositional interpretation. +actually uses its propositional interpretation. .. example:: @@ -5038,7 +5038,7 @@ applied to a goal ``top`` is interpreted in the following way: Like assumption interpretation view hints, goal interpretation ones -are user defined lemmas stored (see section :ref:`views_and_reflection_ssr`) in the ``Hint View`` +are user-defined lemmas stored (see section :ref:`views_and_reflection_ssr`) in the ``Hint View`` database bridging the possible gap between the type of ``term`` and the type of the goal. @@ -5132,7 +5132,7 @@ See the files ``ssreflect.v`` and ``ssrbool.v`` for examples. Multiple views ~~~~~~~~~~~~~~ -The hypotheses and the goal can be interpreted applying multiple views +The hypotheses and the goal can be interpreted by applying multiple views in sequence. Both move and apply can be followed by an arbitrary number of ``/term``. The main difference between the following two tactics @@ -5189,7 +5189,7 @@ equivalences are indeed taken into account, otherwise only single .. cmd:: Search {? @pattern } {* {? - } %( @string %| @pattern %) {? % @ident} } {? in {+ {? - } @qualid } } -where :token:`qualid` is the name of an open module. This command search returns +where :token:`qualid` is the name of an open module. This command returns the list of lemmas: @@ -5214,7 +5214,7 @@ Note that: + As for regular terms, patterns can feature scope indications. For instance, the command: ``Search _ (_ + _)%N.`` lists all the lemmas whose - statement (conclusion or hypotheses) involve an application of the + statement (conclusion or hypotheses) involves an application of the binary operation denoted by the infix ``+`` symbol in the ``N`` scope (which is |SSR| scope for natural numbers). + Patterns with holes should be surrounded by parentheses. @@ -5491,7 +5491,7 @@ prenex implicits declaration see :ref:`parametric_polymorphism_ssr` used for such generated names. .. [#7] More precisely, it should have a quantified inductive type with a assumptions and m − a constructors. -.. [#8] This is an implementation feature: there is not such obstruction +.. [#8] This is an implementation feature: there is no such obstruction in the metatheory .. [#9] The current state of the proof shall be displayed by the Show Proof command of |Coq| proof mode. diff --git a/doc/sphinx/proof-engine/tactics.rst b/doc/sphinx/proof-engine/tactics.rst index da34e3b55..2af73c28e 100644 --- a/doc/sphinx/proof-engine/tactics.rst +++ b/doc/sphinx/proof-engine/tactics.rst @@ -1635,7 +1635,7 @@ analysis on inductive or co-inductive objects (see :ref:`TODO-4.5`). .. tacv:: elim @term using @term .. tacv:: elim @term using @term with @bindings_list - Allows the user to give explicitly an elimination predicate :n:`@term` that + Allows the user to give explicitly an induction principle :n:`@term` that is not the standard one for the underlying inductive type of :n:`@term`. The :n:`@bindings_list` clause allows instantiating premises of the type of :n:`@term`. diff --git a/doc/sphinx/proof-engine/vernacular-commands.rst b/doc/sphinx/proof-engine/vernacular-commands.rst new file mode 100644 index 000000000..0bb6eea23 --- /dev/null +++ b/doc/sphinx/proof-engine/vernacular-commands.rst @@ -0,0 +1,1414 @@ +.. include:: ../preamble.rst +.. include:: ../replaces.rst + +.. _vernacularcommands: + +Vernacular commands +============================= + +.. _displaying: + +Displaying +-------------- + + +.. _Print: + +.. cmd:: Print @qualid. + +This command displays on the screen information about the declared or +defined object referred by :n:`@qualid`. + + +Error messages: + + +.. exn:: @qualid not a defined object + +.. exn:: Universe instance should have length :n:`num`. + +.. exn:: This object does not support universe names. + + +Variants: + + +.. cmdv:: Print Term @qualid. + +This is a synonym to ``Print`` :n:`@qualid` when :n:`@qualid` +denotes a global constant. + +.. cmdv:: About @qualid. + +This displays various information about the object +denoted by :n:`@qualid`: its kind (module, constant, assumption, inductive, +constructor, abbreviation, …), long name, type, implicit arguments and +argument scopes. It does not print the body of definitions or proofs. + +.. cmdv:: Print @qualid\@@name + +This locally renames the polymorphic universes of :n:`@qualid`. +An underscore means the raw universe is printed. +This form can be used with ``Print Term`` and ``About``. + +.. cmd:: Print All. + +This command displays information about the current state of the +environment, including sections and modules. + + +Variants: + + +.. cmdv:: Inspect @num. + +This command displays the :n:`@num` last objects of the +current environment, including sections and modules. + +.. cmdv:: Print Section @ident. + +The name :n:`@ident` should correspond to a currently open section, +this command displays the objects defined since the beginning of this +section. + + +.. _flags-options-tables: + +Flags, Options and Tables +----------------------------- + +|Coq| configurability is based on flags (e.g. Set Printing All in +Section :ref:`TODO-2.9-printing-full`), options (e.g. ``Set Printing Widthinteger`` in Section +:ref:`TODO-6.9.6-set-printing-width`), or tables (e.g. ``Add Printing Record ident``, in Section +:ref:`TODO-2.2.4-add-printing-record`). The names of flags, options and tables are made of non-empty sequences of identifiers +(conventionally with capital initial +letter). The general commands handling flags, options and tables are +given below. + +.. TODO : flag is not a syntax entry + +.. cmd:: Set @flag. + +This command switches :n:`@flag` on. The original state of :n:`@flag` is restored +when the current module ends. + + +Variants: + + +.. cmdv:: Local Set @flag. + +This command switches :n:`@flag` on. The original state +of :n:`@flag` is restored when the current *section* ends. + +.. cmdv:: Global Set @flag. + +This command switches :n:`@flag` on. The original state +of :n:`@flag` is *not* restored at the end of the module. Additionally, if +set in a file, :n:`@flag` is switched on when the file is `Require`-d. + + + +.. cmd:: Unset @flag. + +This command switches :n:`@flag` off. The original state of :n:`@flag` is restored +when the current module ends. + + +Variants: + +.. cmdv:: Local Unset @flag. + +This command switches :n:`@flag` off. The original +state of :n:`@flag` is restored when the current *section* ends. + +.. cmdv:: Global Unset @flag. + +This command switches :n:`@flag` off. The original +state of :n:`@flag` is *not* restored at the end of the module. Additionally, +if set in a file, :n:`@flag` is switched off when the file is `Require`-d. + + + +.. cmd:: Test @flag. + +This command prints whether :n:`@flag` is on or off. + + +.. cmd:: Set @option @value. + +This command sets :n:`@option` to :n:`@value`. The original value of ` option` is +restored when the current module ends. + + +Variants: + +.. TODO : option and value are not syntax entries + +.. cmdv:: Local Set @option @value. + +This command sets :n:`@option` to :n:`@value`. The +original value of :n:`@option` is restored at the end of the module. + +.. cmdv:: Global Set @option @value. + +This command sets :n:`@option` to :n:`@value`. The +original value of :n:`@option` is *not* restored at the end of the module. +Additionally, if set in a file, :n:`@option` is set to value when the file +is `Require`-d. + + + +.. cmd:: Unset @option. + +This command resets option to its default value. + + +Variants: + + +.. cmdv:: Local Unset @option. + +This command resets :n:`@option` to its default +value. The original state of :n:`@option` is restored when the current +*section* ends. + +.. cmdv:: Global Unset @option. + +This command resets :n:`@option` to its default +value. The original state of :n:`@option` is *not* restored at the end of the +module. Additionally, if unset in a file, :n:`@option` is reset to its +default value when the file is `Require`-d. + + + +.. cmd:: Test @option. + +This command prints the current value of :n:`@option`. + + +.. TODO : table is not a syntax entry + +.. cmd:: Add @table @value. +.. cmd:: Remove @table @value. +.. cmd:: Test @table @value. +.. cmd:: Test @table for @value. +.. cmd:: Print Table @table. + +These are general commands for tables. + +.. cmd:: Print Options. + +This command lists all available flags, options and tables. + + +Variants: + + +.. cmdv:: Print Tables. + +This is a synonymous of ``Print Options``. + + +.. _requests-to-the-environment: + +Requests to the environment +------------------------------- + +.. cmd:: Check @term. + +This command displays the type of :n:`@term`. When called in proof mode, the +term is checked in the local context of the current subgoal. + + +Variants: + +.. TODO : selector is not a syntax entry + +.. cmdv:: @selector: Check @term. + +specifies on which subgoal to perform typing +(see Section :ref:`TODO-8.1-invocation-of-tactics`). + +.. TODO : convtactic is not a syntax entry + +.. cmd:: Eval @convtactic in @term. + +This command performs the specified reduction on :n:`@term`, and displays +the resulting term with its type. The term to be reduced may depend on +hypothesis introduced in the first subgoal (if a proof is in +progress). + + +See also: Section :ref:`TODO-8.7-performing-computations`. + + +.. cmd:: Compute @term. + +This command performs a call-by-value evaluation of term by using the +bytecode-based virtual machine. It is a shortcut for ``Eval vm_compute in`` +:n:`@term`. + + +See also: Section :ref:`TODO-8.7-performing-computations`. + + +.. cmd::Extraction @term. + +This command displays the extracted term from :n:`@term`. The extraction is +processed according to the distinction between ``Set`` and ``Prop``; that is +to say, between logical and computational content (see Section +:ref:`TODO-4.1.1-sorts`). The extracted term is displayed in OCaml +syntax, +where global identifiers are still displayed as in |Coq| terms. + + +Variants: + + +.. cmdv:: Recursive Extraction {+ @qualid }. + +Recursively extracts all +the material needed for the extraction of the qualified identifiers. + + +See also: Chapter ref:`TODO-23-chapter-extraction`. + + +.. cmd:: Print Assumptions @qualid. + +This commands display all the assumptions (axioms, parameters and +variables) a theorem or definition depends on. Especially, it informs +on the assumptions with respect to which the validity of a theorem +relies. + + +Variants: + + +.. cmdv:: Print Opaque Dependencies @qualid. + +Displays the set of opaque constants :n:`@qualid` relies on in addition to +the assumptions. + +.. cmdv:: Print Transparent Dependencies @qualid. + +Displays the set of +transparent constants :n:`@qualid` relies on in addition to the assumptions. + +.. cmdv:: Print All Dependencies @qualid. + +Displays all assumptions and constants :n:`@qualid` relies on. + + + +.. cmd:: Search @qualid. + +This command displays the name and type of all objects (hypothesis of +the current goal, theorems, axioms, etc) of the current context whose +statement contains :n:`@qualid`. This command is useful to remind the user +of the name of library lemmas. + + +Error messages: + + +.. exn:: The reference @qualid was not found in the current environment + +There is no constant in the environment named qualid. + +Variants: + +.. cmdv:: Search @string. + +If :n:`@string` is a valid identifier, this command +displays the name and type of all objects (theorems, axioms, etc) of +the current context whose name contains string. If string is a +notation’s string denoting some reference :n:`@qualid` (referred to by its +main symbol as in `"+"` or by its notation’s string as in `"_ + _"` or +`"_ 'U' _"`, see Section :ref:`TODO-12.1-notations`), the command works like ``Search`` :n:`@qualid`. + +.. cmdv:: Search @string%@key. + +The string string must be a notation or the main +symbol of a notation which is then interpreted in the scope bound to +the delimiting key :n:`@key` (see Section :ref:`TODO-12.2.2-local-interpretation-rules-for-notations`). + +.. cmdv:: Search @term_pattern. + +This searches for all statements or types of +definition that contains a subterm that matches the pattern +`term_pattern` (holes of the pattern are either denoted by `_` or by +`?ident` when non linear patterns are expected). + +.. cmdv:: Search { + [-]@term_pattern_string }. + +where +:n:`@term_pattern_string` is a term_pattern, a string, or a string followed +by a scope delimiting key `%key`. This generalization of ``Search`` searches +for all objects whose statement or type contains a subterm matching +:n:`@term_pattern` (or :n:`@qualid` if :n:`@string` is the notation for a reference +qualid) and whose name contains all string of the request that +correspond to valid identifiers. If a term_pattern or a string is +prefixed by `-`, the search excludes the objects that mention that +term_pattern or that string. + +.. cmdv:: Search @term_pattern_string … @term_pattern_string inside {+ @qualid } . + +This restricts the search to constructions defined in the modules named by the given :n:`qualid` sequence. + +.. cmdv:: Search @term_pattern_string … @term_pattern_string outside {+ @qualid }. + +This restricts the search to constructions not defined in the modules named by the given :n:`qualid` sequence. + +.. cmdv:: @selector: Search [-]@term_pattern_string … [-]@term_pattern_string. + +This specifies the goal on which to search hypothesis (see +Section :ref:`TODO-8.1-invocation-of-tactics`). +By default the 1st goal is searched. This variant can +be combined with other variants presented here. + + +.. coqtop:: in + + Require Import ZArith. + +.. coqtop:: all + + Search Z.mul Z.add "distr". + + Search "+"%Z "*"%Z "distr" -positive -Prop. + + Search (?x * _ + ?x * _)%Z outside OmegaLemmas. + +.. note:: Up to |Coq| version 8.4, ``Search`` had the behavior of current +``SearchHead`` and the behavior of current Search was obtained with +command ``SearchAbout``. For compatibility, the deprecated name +SearchAbout can still be used as a synonym of Search. For +compatibility, the list of objects to search when using ``SearchAbout`` +may also be enclosed by optional[ ] delimiters. + + +.. cmd:: SearchHead @term. + +This command displays the name and type of all hypothesis of the +current goal (if any) and theorems of the current context whose +statement’s conclusion has the form `(term t1 .. tn)`. This command is +useful to remind the user of the name of library lemmas. + + + +.. coqtop:: reset all + + SearchHead le. + + SearchHead (@eq bool). + + +Variants: + +.. cmdv:: SearchHead @term inside {+ @qualid }. + +This restricts the search to constructions defined in the modules named by the given :n:`qualid` sequence. + +.. cmdv:: SearchHead term outside {+ @qualid }. + +This restricts the search to constructions not defined in the modules named by the given :n:`qualid` sequence. + +Error messages: + +.. exn:: Module/section @qualid not found + +No module :n:`@qualid` has been required +(see Section :ref:`TODO-6.5.1-require`). + +.. cmdv:: @selector: SearchHead @term. + +This specifies the goal on which to +search hypothesis (see Section :ref:`TODO-8.1-invocation-of-tactics`). +By default the 1st goal is +searched. This variant can be combined with other variants presented +here. + +.. note:: Up to |Coq| version 8.4, ``SearchHead`` was named ``Search``. + + +.. cmd:: SearchPattern @term. + +This command displays the name and type of all hypothesis of the +current goal (if any) and theorems of the current context whose +statement’s conclusion or last hypothesis and conclusion matches the +expressionterm where holes in the latter are denoted by `_`. +It is a +variant of Search @term_pattern that does not look for subterms but +searches for statements whose conclusion has exactly the expected +form, or whose statement finishes by the given series of +hypothesis/conclusion. + +.. coqtop:: in + + Require Import Arith. + +.. coqtop:: all + + SearchPattern (_ + _ = _ + _). + + SearchPattern (nat -> bool). + + SearchPattern (forall l : list _, _ l l). + +Patterns need not be linear: you can express that the same expression +must occur in two places by using pattern variables `?ident`. + + +.. coqtop:: all + + SearchPattern (?X1 + _ = _ + ?X1). + +Variants: + + +.. cmdv:: SearchPattern @term inside {+ @qualid } . + +This restricts the search to constructions defined in the modules named by the given :n:`qualid` sequence. + +.. cmdv:: SearchPattern @term outside {+ @qualid }. + +This restricts the search to constructions not defined in the modules named by the given :n:`qualid` sequence. + +.. cmdv:: @selector: SearchPattern @term. + +This specifies the goal on which to +search hypothesis (see Section :ref:`TODO-8.1-invocation-of-tactics`). By default the 1st goal is +searched. This variant can be combined with other variants presented +here. + + + +.. cmdv:: SearchRewrite @term. + +This command displays the name and type of all hypothesis of the +current goal (if any) and theorems of the current context whose +statement’s conclusion is an equality of which one side matches the +expression term. Holes in term are denoted by “_”. + +.. coqtop:: in + + Require Import Arith. + +.. coqtop:: all + + SearchRewrite (_ + _ + _). + +Variants: + + +.. cmdv:: SearchRewrite term inside {+ @qualid }. + +This restricts the search to constructions defined in the modules named by the given :n:`qualid` sequence. + +.. cmdv:: SearchRewrite @term outside {+ @qualid }. + +This restricts the search to constructions not defined in the modules named by the given :n:`qualid` sequence. + +.. cmdv:: @selector: SearchRewrite @term. + +This specifies the goal on which to +search hypothesis (see Section :ref:`TODO-8.1-invocation-of-tactics`). By default the 1st goal is +searched. This variant can be combined with other variants presented +here. + +.. note:: + + For the ``Search``, ``SearchHead``, ``SearchPattern`` and ``SearchRewrite`` + queries, it + is possible to globally filter the search results via the command + ``Add Search Blacklist`` :n:`@substring`. A lemma whose fully-qualified name + contains any of the declared substrings will be removed from the + search results. The default blacklisted substrings are ``_subproof`` + ``Private_``. The command ``Remove Search Blacklist ...`` allows expunging + this blacklist. + + +.. cmd:: Locate @qualid. + +This command displays the full name of objects whose name is a prefix +of the qualified identifier :n:`@qualid`, and consequently the |Coq| module in +which they are defined. It searches for objects from the different +qualified name spaces of |Coq|: terms, modules, Ltac, etc. + +.. coqtop:: none + + Set Printing Depth 50. + +.. coqtop:: all + + Locate nat. + + Locate Datatypes.O. + + Locate Init.Datatypes.O. + + Locate Coq.Init.Datatypes.O. + + Locate I.Dont.Exist. + +Variants: + + +.. cmdv:: Locate Term @qualid. + +As Locate but restricted to terms. + +.. cmdv:: Locate Module @qualid. + +As Locate but restricted to modules. + +.. cmdv:: Locate Ltac @qualid. + +As Locate but restricted to tactics. + + +See also: Section :ref:`TODO-12.1.10-LocateSymbol` + + +.. _loading-files: + +Loading files +----------------- + +|Coq| offers the possibility of loading different parts of a whole +development stored in separate files. Their contents will be loaded as +if they were entered from the keyboard. This means that the loaded +files are ASCII files containing sequences of commands for |Coq|’s +toplevel. This kind of file is called a *script* for |Coq|. The standard +(and default) extension of |Coq|’s script files is .v. + + +.. cmd:: Load @ident. + +This command loads the file named :n:`ident`.v, searching successively in +each of the directories specified in the *loadpath*. (see Section +:ref:`TODO-2.6.3-libraries-and-filesystem`) + +Files loaded this way cannot leave proofs open, and the ``Load`` +command cannot be used inside a proof either. + +Variants: + + +.. cmdv:: Load @string. + +Loads the file denoted by the string :n:`@string`, where +string is any complete filename. Then the `~` and .. abbreviations are +allowed as well as shell variables. If no extension is specified, |Coq| +will use the default extension ``.v``. + +.. cmdv:: Load Verbose @ident. + +.. cmdv:: Load Verbose @string. + +Display, while loading, +the answers of |Coq| to each command (including tactics) contained in +the loaded file See also: Section :ref:`TODO-6.9.1-silent`. + +Error messages: + +.. exn:: Can’t find file @ident on loadpath + +.. exn:: Load is not supported inside proofs + +.. exn:: Files processed by Load cannot leave open proofs + +.. _compiled-files: + +Compiled files +------------------ + +This section describes the commands used to load compiled files (see +Chapter :ref:`TODO-14-coq-commands` for documentation on how to compile a file). A compiled +file is a particular case of module called *library file*. + + +.. cmd:: Require @qualid. + +This command looks in the loadpath for a file containing module :n:`@qualid` +and adds the corresponding module to the environment of |Coq|. As +library files have dependencies in other library files, the command +``Require`` :n:`@qualid` recursively requires all library files the module +qualid depends on and adds the corresponding modules to the +environment of |Coq| too. |Coq| assumes that the compiled files have been +produced by a valid |Coq| compiler and their contents are then not +replayed nor rechecked. + +To locate the file in the file system, :n:`@qualid` is decomposed under the +form `dirpath.ident` and the file `ident.vo` is searched in the physical +directory of the file system that is mapped in |Coq| loadpath to the +logical path dirpath (see Section :ref:`TODO-2.6.3-libraries-and-filesystem`). The mapping between +physical directories and logical names at the time of requiring the +file must be consistent with the mapping used to compile the file. If +several files match, one of them is picked in an unspecified fashion. + + +Variants: + +.. cmdv:: Require Import @qualid. + +This loads and declares the module :n:`@qualid` +and its dependencies then imports the contents of :n:`@qualid` as described +in Section :ref:`TODO-2.5.8-import`.It does not import the modules on which +qualid depends unless these modules were themselves required in module +:n:`@qualid` +using ``Require Export``, as described below, or recursively required +through a sequence of ``Require Export``. If the module required has +already been loaded, ``Require Import`` :n:`@qualid` simply imports it, as ``Import`` +:n:`@qualid` would. + +.. cmdv:: Require Export @qualid. + +This command acts as ``Require Import`` :n:`@qualid`, +but if a further module, say `A`, contains a command ``Require Export`` `B`, +then the command ``Require Import`` `A` also imports the module `B.` + +.. cmdv:: Require [Import | Export] {+ @qualid }. + +This loads the +modules named by the :n:`qualid` sequence and their recursive +dependencies. If +``Import`` or ``Export`` is given, it also imports these modules and +all the recursive dependencies that were marked or transitively marked +as ``Export``. + +.. cmdv:: From @dirpath Require @qualid. + +This command acts as ``Require``, but picks +any library whose absolute name is of the form dirpath.dirpath’.qualid +for some `dirpath’`. This is useful to ensure that the :n:`@qualid` library +comes from a given package by making explicit its absolute root. + + + +Error messages: + +.. exn:: Cannot load qualid: no physical path bound to dirpath + +.. exn:: Cannot find library foo in loadpath + +The command did not find the +file foo.vo. Either foo.v exists but is not compiled or foo.vo is in a +directory which is not in your LoadPath (see Section :ref:`TODO-2.6.3-libraries-and-filesystem`). + +.. exn:: Compiled library ident.vo makes inconsistent assumptions over library qualid + +The command tried to load library file `ident.vo` that +depends on some specific version of library :n:`@qualid` which is not the +one already loaded in the current |Coq| session. Probably `ident.v` was +not properly recompiled with the last version of the file containing +module :n:`@qualid`. + +.. exn:: Bad magic number + +The file `ident.vo` was found but either it is not a +|Coq| compiled module, or it was compiled with an incompatible +version of |Coq|. + +.. exn:: The file `ident.vo` contains library dirpath and not library dirpath’ + +The library file `dirpath’` is indirectly required by the +``Require`` command but it is bound in the current loadpath to the +file `ident.vo` which was bound to a different library name `dirpath` at +the time it was compiled. + + +.. exn:: Require is not allowed inside a module or a module type + +This command +is not allowed inside a module or a module type being defined. It is +meant to describe a dependency between compilation units. Note however +that the commands Import and Export alone can be used inside modules +(see Section :ref:`TODO-2.5.8-import`). + + + +See also: Chapter :ref:`TODO-14-coq-commands` + + +.. cmd:: Print Libraries. + +This command displays the list of library files loaded in the +current |Coq| session. For each of these libraries, it also tells if it +is imported. + + +.. cmd:: Declare ML Module {+ @string } . + +This commands loads the OCaml compiled files +with names given by the :n:`@string` sequence +(dynamic link). It is mainly used to load tactics dynamically. The +files are searched into the current OCaml loadpath (see the +command ``Add ML Path`` in Section :ref:`TODO-2.6.3-libraries-and-filesystem`). Loading of OCaml files is only possible under the bytecode version of ``coqtop`` (i.e. +``coqtop`` called with option ``-byte``, see chapter :ref:`TODO-14-coq-commands`), or when |Coq| has been compiled with a +version of OCaml that supports native Dynlink (≥ 3.11). + + +Variants: + + +.. cmdv:: Local Declare ML Module {+ @string }. + +This variant is not +exported to the modules that import the module where they occur, even +if outside a section. + + + +Error messages: + +.. exn:: File not found on loadpath : @string + +.. exn:: Loading of ML object file forbidden in a native |Coq| + + + +.. cmd:: Print ML Modules. + +This prints the name of all OCaml modules loaded with ``Declare +ML Module``. To know from where these module were loaded, the user +should use the command Locate File (see Section :ref:`TODO-6.6.10-locate-file`) + + +.. _loadpath: + +Loadpath +------------ + +Loadpaths are preferably managed using |Coq| command line options (see +Section `2.6.3-libraries-and-filesystem`) but there remain vernacular commands to manage them +for practical purposes. Such commands are only meant to be issued in +the toplevel, and using them in source files is discouraged. + + +.. cmd:: Pwd. + +This command displays the current working directory. + + +.. cmd:: Cd @string. + +This command changes the current directory according to :n:`@string` which +can be any valid path. + + +Variants: + + +.. cmdv:: Cd. + +Is equivalent to Pwd. + + + +.. cmd:: Add LoadPath @string as @dirpath. + +This command is equivalent to the command line option +``-Q`` :n:`@string` :n:`@dirpath`. It adds the physical directory string to the current +|Coq| loadpath and maps it to the logical directory dirpath. + +Variants: + + +.. cmdv:: Add LoadPath @string. + +Performs as Add LoadPath :n:`@string` as :n:`@dirpath` but +for the empty directory path. + + + +.. cmd:: Add Rec LoadPath @string as @dirpath. + +This command is equivalent to the command line option +``-R`` :n:`@string` :n:`@dirpath`. It adds the physical directory string and all its +subdirectories to the current |Coq| loadpath. + +Variants: + + +.. cmdv:: Add Rec LoadPath @string. + +Works as ``Add Rec LoadPath`` :n:`@string` as :n:`@dirpath` but for the empty +logical directory path. + + + +.. cmd:: Remove LoadPath @string. + +This command removes the path :n:`@string` from the current |Coq| loadpath. + + +.. cmd:: Print LoadPath. + +This command displays the current |Coq| loadpath. + + +Variants: + + +.. cmdv:: Print LoadPath @dirpath. + +Works as ``Print LoadPath`` but displays only +the paths that extend the :n:`@dirpath` prefix. + + +.. cmd:: Add ML Path @string. + +This command adds the path :n:`@string` to the current OCaml +loadpath (see the command `Declare ML Module`` in Section :ref:`TODO-6.5-compiled-files`). + + +.. cmd:: Add Rec ML Path @string. + +This command adds the directory :n:`@string` and all its subdirectories to +the current OCaml loadpath (see the command ``Declare ML Module`` +in Section :ref:`TODO-6.5-compiled-files`). + + +.. cmd:: Print ML Path @string. + +This command displays the current OCaml loadpath. This +command makes sense only under the bytecode version of ``coqtop``, i.e. +using option ``-byte`` +(see the command Declare ML Module in Section :ref:`TODO-6.5-compiled-files`). + + +.. cmd:: Locate File @string. + +This command displays the location of file string in the current +loadpath. Typically, string is a .cmo or .vo or .v file. + + +.. cmd:: Locate Library @dirpath. + +This command gives the status of the |Coq| module dirpath. It tells if +the module is loaded and if not searches in the load path for a module +of logical name :n:`@dirpath`. + + +.. _backtracking: + +Backtracking +---------------- + +The backtracking commands described in this section can only be used +interactively, they cannot be part of a vernacular file loaded via +``Load`` or compiled by ``coqc``. + + +.. cmd:: Reset @ident. + +This command removes all the objects in the environment since :n:`@ident` +was introduced, including :n:`@ident`. :n:`@ident` may be the name of a defined or +declared object as well as the name of a section. One cannot reset +over the name of a module or of an object inside a module. + + +Error messages: + +.. exn:: @ident: no such entry + +Variants: + +.. cmd:: Reset Initial. + +Goes back to the initial state, just after the start +of the interactive session. + + + +.. cmd:: Back. + +This commands undoes all the effects of the last vernacular command. +Commands read from a vernacular file via a ``Load`` are considered as a +single command. Proof management commands are also handled by this +command (see Chapter :ref:`TODO-7-proof-handling`). For that, Back may have to undo more than +one command in order to reach a state where the proof management +information is available. For instance, when the last command is a +``Qed``, the management information about the closed proof has been +discarded. In this case, ``Back`` will then undo all the proof steps up to +the statement of this proof. + + +Variants: + + +.. cmdv:: Back @num. + +Undoes :n:`@num` vernacular commands. As for Back, some extra +commands may be undone in order to reach an adequate state. For +instance Back :n:`@num` will not re-enter a closed proof, but rather go just +before that proof. + + + +Error messages: + + +.. exn:: Invalid backtrack + +The user wants to undo more commands than available in the history. + +.. cmd:: BackTo @num. + +This command brings back the system to the state labeled :n:`@num`, +forgetting the effect of all commands executed after this state. The +state label is an integer which grows after each successful command. +It is displayed in the prompt when in -emacs mode. Just as ``Back`` (see +above), the ``BackTo`` command now handles proof states. For that, it may +have to undo some extra commands and end on a state `num′ ≤ num` if +necessary. + + +Variants: + + +.. cmdv:: Backtrack @num @num @num. + +`Backtrack` is a *deprecated* form of +`BackTo` which allows explicitly manipulating the proof environment. The +three numbers represent the following: + + + *first number* : State label to reach, as for BackTo. + + *second number* : *Proof state number* to unbury once aborts have been done. + |Coq| will compute the number of Undo to perform (see Chapter :ref:`TODO-7-proof-handling`). + + *third number* : Number of Abort to perform, i.e. the number of currently + opened nested proofs that must be canceled (see Chapter :ref:`TODO-7-proof-handling`). + + + + +Error messages: + + +.. exn:: Invalid backtrack + + +The destination state label is unknown. + + +.. _quitting-and-debugging: + +Quitting and debugging +-------------------------- + + +.. cmd:: Quit. + +This command permits to quit |Coq|. + + +.. cmd:: Drop. + +This is used mostly as a debug facility by |Coq|’s implementors and does +not concern the casual user. This command permits to leave |Coq| +temporarily and enter the OCaml toplevel. The OCaml +command: + + +:: + + #use "include";; + + +adds the right loadpaths and loads some toplevel printers for all +abstract types of |Coq|- section_path, identifiers, terms, judgments, …. +You can also use the file base_include instead, that loads only the +pretty-printers for section_paths and identifiers. You can return back +to |Coq| with the command: + + +:: + + go();; + + + +Warnings: + + +#. It only works with the bytecode version of |Coq| (i.e. `coqtop.byte`, + see Section `TODO-14.1-interactive-use`). +#. You must have compiled |Coq| from the source package and set the + environment variable COQTOP to the root of your copy of the sources + (see Section `14.3.2-customization-by-envionment-variables`). + + + +.. TODO : command is not a syntax entry + +.. cmd:: Time @command. + +This command executes the vernacular command :n:`@command` and displays the +time needed to execute it. + + +.. cmd:: Redirect @string @command. + +This command executes the vernacular command :n:`@command`, redirecting its +output to ":n:`@string`.out". + + +.. cmd:: Timeout @num @command. + +This command executes the vernacular command :n:`@command`. If the command +has not terminated after the time specified by the :n:`@num` (time +expressed in seconds), then it is interrupted and an error message is +displayed. + + +.. cmd:: Set Default Timeout @num. + +After using this command, all subsequent commands behave as if they +were passed to a Timeout command. Commands already starting by a +`Timeout` are unaffected. + + +.. cmd:: Unset Default Timeout. + +This command turns off the use of a default timeout. + +.. cmd:: Test Default Timeout. + +This command displays whether some default timeout has been set or not. + +.. cmd:: Fail @command. + +For debugging scripts, sometimes it is desirable to know +whether a command or a tactic fails. If the given :n:`@command` +fails, the ``Fail`` statement succeeds, without changing the proof +state, and in interactive mode, the system +prints a message confirming the failure. +If the given :n:`@command` succeeds, the statement is an error, and +it prints a message indicating that the failure did not occur. + +Error messages: + +.. exn:: The command has not failed! + +.. _controlling-display: + +Controlling display +----------------------- + + +.. cmd:: Set Silent. + +This command turns off the normal displaying. + + +.. cmd:: Unset Silent. + +This command turns the normal display on. + +TODO : check that spaces are handled well + +.. cmd:: Set Warnings ‘‘(@ident {* , @ident } )’’. + +This command configures the display of warnings. It is experimental, +and expects, between quotes, a comma-separated list of warning names +or categories. Adding - in front of a warning or category disables it, +adding + makes it an error. It is possible to use the special +categories all and default, the latter containing the warnings enabled +by default. The flags are interpreted from left to right, so in case +of an overlap, the flags on the right have higher priority, meaning +that `A,-A` is equivalent to `-A`. + + +.. cmd:: Set Search Output Name Only. + +This command restricts the output of search commands to identifier +names; turning it on causes invocations of ``Search``, ``SearchHead``, +``SearchPattern``, ``SearchRewrite`` etc. to omit types from their output, +printing only identifiers. + + +.. cmd:: Unset Search Output Name Only. + +This command turns type display in search results back on. + + +.. cmd:: Set Printing Width @integer. + +This command sets which left-aligned part of the width of the screen +is used for display. + + +.. cmd:: Unset Printing Width. + +This command resets the width of the screen used for display to its +default value (which is 78 at the time of writing this documentation). + + +.. cmd:: Test Printing Width. + +This command displays the current screen width used for display. + + +.. cmd:: Set Printing Depth @integer. + +This command sets the nesting depth of the formatter used for pretty- +printing. Beyond this depth, display of subterms is replaced by dots. + + +.. cmd:: Unset Printing Depth. + +This command resets the nesting depth of the formatter used for +pretty-printing to its default value (at the time of writing this +documentation, the default value is 50). + + +.. cmd:: Test Printing Depth. + +This command displays the current nesting depth used for display. + + +.. cmd:: Unset Printing Compact Contexts. + +This command resets the displaying of goals contexts to non compact +mode (default at the time of writing this documentation). Non compact +means that consecutive variables of different types are printed on +different lines. + + +.. cmd:: Set Printing Compact Contexts. + +This command sets the displaying of goals contexts to compact mode. +The printer tries to reduce the vertical size of goals contexts by +putting several variables (even if of different types) on the same +line provided it does not exceed the printing width (See Set Printing +Width above). + + +.. cmd:: Test Printing Compact Contexts. + +This command displays the current state of compaction of goal. + + +.. cmd:: Unset Printing Unfocused. + +This command resets the displaying of goals to focused goals only +(default). Unfocused goals are created by focusing other goals with +bullets (see :ref:`TODO-7.2.7-bullets`) or curly braces (see `7.2.6-curly-braces`). + + +.. cmd:: Set Printing Unfocused. + +This command enables the displaying of unfocused goals. The goals are +displayed after the focused ones and are distinguished by a separator. + + +.. cmd:: Test Printing Unfocused. + +This command displays the current state of unfocused goals display. + + +.. cmd:: Set Printing Dependent Evars Line. + +This command enables the printing of the “(dependent evars: …)” line +when -emacs is passed. + + +.. cmd:: Unset Printing Dependent Evars Line. + +This command disables the printing of the “(dependent evars: …)” line +when -emacs is passed. + + +Controlling the reduction strategies and the conversion algorithm +---------------------------------------------------------------------- + + +|Coq| provides reduction strategies that the tactics can invoke and two +different algorithms to check the convertibility of types. The first +conversion algorithm lazily compares applicative terms while the other +is a brute-force but efficient algorithm that first normalizes the +terms before comparing them. The second algorithm is based on a +bytecode representation of terms similar to the bytecode +representation used in the ZINC virtual machine [`98`]. It is +especially useful for intensive computation of algebraic values, such +as numbers, and for reflection-based tactics. The commands to fine- +tune the reduction strategies and the lazy conversion algorithm are +described first. + +.. cmd:: Opaque {+ @qualid }. + +This command has an effect on unfoldable constants, i.e. on constants +defined by ``Definition`` or ``Let`` (with an explicit body), or by a command +assimilated to a definition such as ``Fixpoint``, ``Program Definition``, etc, +or by a proof ended by ``Defined``. The command tells not to unfold the +constants in the :n:`@qualid` sequence in tactics using δ-conversion (unfolding +a constant is replacing it by its definition). + +``Opaque`` has also an effect on the conversion algorithm of |Coq|, telling +it to delay the unfolding of a constant as much as possible when |Coq| +has to check the conversion (see Section :ref:`TODO-4.3-conversion-rules`) of two distinct +applied constants. + +The scope of ``Opaque`` is limited to the current section, or current +file, unless the variant ``Global Opaque`` is used. + + +See also: sections :ref:`TODO-8.7-performing-computations`, :ref:`TODO-8.16-automatizing`, :ref:`TODO-7.1-switching-on-off-proof-editing-mode` + + +Error messages: + + +.. exn:: The reference @qualid was not found in the current environment + +There is no constant referred by :n:`@qualid` in the environment. +Nevertheless, if you asked ``Opaque`` `foo` `bar` and if `bar` does not exist, `foo` is set opaque. + +.. cmd:: Transparent {+ @qualid }. + +This command is the converse of `Opaque`` and it applies on unfoldable +constants to restore their unfoldability after an Opaque command. + +Note in particular that constants defined by a proof ended by Qed are +not unfoldable and Transparent has no effect on them. This is to keep +with the usual mathematical practice of *proof irrelevance*: what +matters in a mathematical development is the sequence of lemma +statements, not their actual proofs. This distinguishes lemmas from +the usual defined constants, whose actual values are of course +relevant in general. + +The scope of Transparent is limited to the current section, or current +file, unless the variant ``Global Transparent`` is +used. + + +Error messages: + + +.. exn:: The reference @qualid was not found in the current environment + +There is no constant referred by :n:`@qualid` in the environment. + + + +See also: sections :ref:`TODO-8.7-performing-computations`, :ref:`TODO-8.16-automatizing`, :ref:`TODO-7.1-switching-on-off-proof-editing-mode` + + +.. cmd:: Strategy @level [ {+ @qualid } ]. + +This command generalizes the behavior of Opaque and Transparent +commands. It is used to fine-tune the strategy for unfolding +constants, both at the tactic level and at the kernel level. This +command associates a level to the qualified names in the :n:`@qualid` +sequence. Whenever two +expressions with two distinct head constants are compared (for +instance, this comparison can be triggered by a type cast), the one +with lower level is expanded first. In case of a tie, the second one +(appearing in the cast type) is expanded. + +Levels can be one of the following (higher to lower): + + + ``opaque`` : level of opaque constants. They cannot be expanded by + tactics (behaves like +∞, see next item). + + :n:`@num` : levels indexed by an integer. Level 0 corresponds to the + default behavior, which corresponds to transparent constants. This + level can also be referred to as transparent. Negative levels + correspond to constants to be expanded before normal transparent + constants, while positive levels correspond to constants to be + expanded after normal transparent constants. + + ``expand`` : level of constants that should be expanded first (behaves + like −∞) + + +These directives survive section and module closure, unless the +command is prefixed by Local. In the latter case, the behavior +regarding sections and modules is the same as for the ``Transparent`` and +``Opaque`` commands. + + +.. cmd:: Print Strategy @qualid. + +This command prints the strategy currently associated to :n:`@qualid`. It +fails if :n:`@qualid` is not an unfoldable reference, that is, neither a +variable nor a constant. + + +Error messages: + + +.. exn:: The reference is not unfoldable. + + + +Variants: + + +.. cmdv:: Print Strategies. + +Print all the currently non-transparent strategies. + + + +.. cmd:: Declare Reduction @ident := @convtactic. + +This command allows giving a short name to a reduction expression, for +instance lazy beta delta [foo bar]. This short name can then be used +in ``Eval`` :n:`@ident` ``in`` ... or ``eval`` directives. This command +accepts the +Local modifier, for discarding this reduction name at the end of the +file or module. For the moment the name cannot be qualified. In +particular declaring the same name in several modules or in several +functor applications will be refused if these declarations are not +local. The name :n:`@ident` cannot be used directly as an Ltac tactic, but +nothing prevents the user to also perform a +``Ltac`` `ident` ``:=`` `convtactic`. + + +See also: sections :ref:`TODO-8.7-performing-computations` + + +.. _controlling-locality-of-commands: + +Controlling the locality of commands +----------------------------------------- + + +.. cmd:: Local @command. +.. cmd:: Global @command. + +Some commands support a Local or Global prefix modifier to control the +scope of their effect. There are four kinds of commands: + + ++ Commands whose default is to extend their effect both outside the + section and the module or library file they occur in. For these + commands, the Local modifier limits the effect of the command to the + current section or module it occurs in. As an example, the ``Coercion`` + (see Section :ref:`TODO-2.8-coercions`) and ``Strategy`` (see Section :ref:`TODO-6.10.3-strategy`) commands belong + to this category. ++ Commands whose default behavior is to stop their effect at the end + of the section they occur in but to extent their effect outside the + module or library file they occur in. For these commands, the Local + modifier limits the effect of the command to the current module if the + command does not occur in a section and the Global modifier extends + the effect outside the current sections and current module if the + command occurs in a section. As an example, the ``Implicit Arguments`` (see + Section :ref:`TODO-2.7-implicit-arguments`), Ltac (see Chapter :ref:`TODO-9-tactic-language`) or ``Notation`` (see Section + :ref:`TODO-12.1-notations`) commands belong to this category. Notice that a subclass of + these commands do not support extension of their scope outside + sections at all and the Global is not applicable to them. ++ Commands whose default behavior is to stop their effect at the end + of the section or module they occur in. For these commands, the Global + modifier extends their effect outside the sections and modules they + occurs in. The ``Transparent`` and ``Opaque`` (see Section :ref:`TODO-6.10-opaque`) commands belong to this category. ++ Commands whose default behavior is to extend their effect outside + sections but not outside modules when they occur in a section and to + extend their effect outside the module or library file they occur in + when no section contains them.For these commands, the Local modifier + limits the effect to the current section or module while the Global + modifier extends the effect outside the module even when the command + occurs in a section. The ``Set`` and ``Unset`` commands belong to this + category. diff --git a/doc/sphinx/replaces.rst b/doc/sphinx/replaces.rst index d4f6835ef..1b2e17221 100644 --- a/doc/sphinx/replaces.rst +++ b/doc/sphinx/replaces.rst @@ -64,6 +64,14 @@ .. |t_i| replace:: `t`\ :math:`_{i}` .. |t_m| replace:: `t`\ :math:`_{m}` .. |t_n| replace:: `t`\ :math:`_{n}` +.. |f_1| replace:: `f`\ :math:`_{1}` +.. |f_i| replace:: `f`\ :math:`_{i}` +.. |f_m| replace:: `f`\ :math:`_{m}` +.. |f_n| replace:: `f`\ :math:`_{n}` +.. |u_1| replace:: `u`\ :math:`_{1}` +.. |u_i| replace:: `u`\ :math:`_{i}` +.. |u_m| replace:: `u`\ :math:`_{m}` +.. |u_n| replace:: `u`\ :math:`_{n}` .. |term_0| replace:: `term`\ :math:`_{0}` .. |term_1| replace:: `term`\ :math:`_{1}` .. |term_2| replace:: `term`\ :math:`_{2}` diff --git a/doc/tools/coqrst/notations/TacticNotations.g b/doc/tools/coqrst/notations/TacticNotations.g index 5176c51d2..68658fe49 100644 --- a/doc/tools/coqrst/notations/TacticNotations.g +++ b/doc/tools/coqrst/notations/TacticNotations.g @@ -26,7 +26,7 @@ hole: ID; LGROUP: '{' [+*?]; LBRACE: '{'; RBRACE: '}'; -METACHAR: '%' [|()]; +METACHAR: '%' [|(){}]; ATOM: '@' | ~[@{} ]+; ID: '@' [a-zA-Z0-9_]+; WHITESPACE: ' '+; diff --git a/doc/tools/coqrst/notations/TacticNotationsLexer.py b/doc/tools/coqrst/notations/TacticNotationsLexer.py index ffa774b9b..61d8d2f9e 100644 --- a/doc/tools/coqrst/notations/TacticNotationsLexer.py +++ b/doc/tools/coqrst/notations/TacticNotationsLexer.py @@ -12,19 +12,19 @@ def serializedATN(): buf.write("\4\b\t\b\3\2\3\2\3\2\3\3\3\3\3\4\3\4\3\5\3\5\3\5\3\6\3") buf.write("\6\6\6\36\n\6\r\6\16\6\37\5\6\"\n\6\3\7\3\7\6\7&\n\7\r") buf.write("\7\16\7\'\3\b\6\b+\n\b\r\b\16\b,\2\2\t\3\3\5\4\7\5\t\6") - buf.write("\13\7\r\b\17\t\3\2\6\4\2,-AA\4\2*+~~\6\2\"\"BB}}\177\177") - buf.write("\6\2\62;C\\aac|\2\61\2\3\3\2\2\2\2\5\3\2\2\2\2\7\3\2\2") - buf.write("\2\2\t\3\2\2\2\2\13\3\2\2\2\2\r\3\2\2\2\2\17\3\2\2\2\3") - buf.write("\21\3\2\2\2\5\24\3\2\2\2\7\26\3\2\2\2\t\30\3\2\2\2\13") - buf.write("!\3\2\2\2\r#\3\2\2\2\17*\3\2\2\2\21\22\7}\2\2\22\23\t") - buf.write("\2\2\2\23\4\3\2\2\2\24\25\7}\2\2\25\6\3\2\2\2\26\27\7") - buf.write("\177\2\2\27\b\3\2\2\2\30\31\7\'\2\2\31\32\t\3\2\2\32\n") - buf.write("\3\2\2\2\33\"\7B\2\2\34\36\n\4\2\2\35\34\3\2\2\2\36\37") - buf.write("\3\2\2\2\37\35\3\2\2\2\37 \3\2\2\2 \"\3\2\2\2!\33\3\2") - buf.write("\2\2!\35\3\2\2\2\"\f\3\2\2\2#%\7B\2\2$&\t\5\2\2%$\3\2") - buf.write("\2\2&\'\3\2\2\2\'%\3\2\2\2\'(\3\2\2\2(\16\3\2\2\2)+\7") - buf.write("\"\2\2*)\3\2\2\2+,\3\2\2\2,*\3\2\2\2,-\3\2\2\2-\20\3\2") - buf.write("\2\2\7\2\37!\',\2") + buf.write("\13\7\r\b\17\t\3\2\6\4\2,-AA\4\2*+}\177\6\2\"\"BB}}\177") + buf.write("\177\6\2\62;C\\aac|\2\61\2\3\3\2\2\2\2\5\3\2\2\2\2\7\3") + buf.write("\2\2\2\2\t\3\2\2\2\2\13\3\2\2\2\2\r\3\2\2\2\2\17\3\2\2") + buf.write("\2\3\21\3\2\2\2\5\24\3\2\2\2\7\26\3\2\2\2\t\30\3\2\2\2") + buf.write("\13!\3\2\2\2\r#\3\2\2\2\17*\3\2\2\2\21\22\7}\2\2\22\23") + buf.write("\t\2\2\2\23\4\3\2\2\2\24\25\7}\2\2\25\6\3\2\2\2\26\27") + buf.write("\7\177\2\2\27\b\3\2\2\2\30\31\7\'\2\2\31\32\t\3\2\2\32") + buf.write("\n\3\2\2\2\33\"\7B\2\2\34\36\n\4\2\2\35\34\3\2\2\2\36") + buf.write("\37\3\2\2\2\37\35\3\2\2\2\37 \3\2\2\2 \"\3\2\2\2!\33\3") + buf.write("\2\2\2!\35\3\2\2\2\"\f\3\2\2\2#%\7B\2\2$&\t\5\2\2%$\3") + buf.write("\2\2\2&\'\3\2\2\2\'%\3\2\2\2\'(\3\2\2\2(\16\3\2\2\2)+") + buf.write("\7\"\2\2*)\3\2\2\2+,\3\2\2\2,*\3\2\2\2,-\3\2\2\2-\20\3") + buf.write("\2\2\2\7\2\37!\',\2") return buf.getvalue() diff --git a/doc/tools/coqrst/notations/html.py b/doc/tools/coqrst/notations/html.py index 44212d788..9c94a4b2d 100644 --- a/doc/tools/coqrst/notations/html.py +++ b/doc/tools/coqrst/notations/html.py @@ -43,7 +43,11 @@ class TacticNotationsToHTMLVisitor(TacticNotationsVisitor): tags.span(ctx.ID().getText()[1:], _class="hole") def visitMeta(self, ctx:TacticNotationsParser.MetaContext): - tags.span(ctx.METACHAR().getText()[1:], _class="meta") + txt = ctx.METACHAR().getText()[1:] + if (txt == "{") or (txt == "}"): + tags.span(txt) + else: + tags.span(txt, _class="meta") def visitWhitespace(self, ctx:TacticNotationsParser.WhitespaceContext): tags.span(" ") # TODO: no need for a <span> here diff --git a/engine/proofview.ml b/engine/proofview.ml index 22271dd02..639f48e77 100644 --- a/engine/proofview.ml +++ b/engine/proofview.ml @@ -710,13 +710,19 @@ let partition_unifiable sigma l = (** Shelves the unifiable goals under focus, i.e. the goals which appear in other goals under focus (the unfocused goals are not considered). *) -let shelve_unifiable = +let shelve_unifiable_informative = let open Proof in Pv.get >>= fun initial -> let (u,n) = partition_unifiable initial.solution initial.comb in Comb.set n >> InfoL.leaf (Info.Tactic (fun () -> Pp.str"shelve_unifiable")) >> - Shelf.modify (fun gls -> gls @ CList.map drop_state u) + let u = CList.map drop_state u in + Shelf.modify (fun gls -> gls @ u) >> + tclUNIT u + +let shelve_unifiable = + let open Proof in + shelve_unifiable_informative >>= fun _ -> tclUNIT () (** [guard_no_unifiable] returns the list of unifiable goals if some goals are unifiable (see {!shelve_unifiable}) in the current focus. *) @@ -1035,6 +1041,8 @@ module Unsafe = struct let advance = Evarutil.advance + let undefined = undefined + let mark_as_unresolvable p gl = { p with solution = mark_in_evm ~goal:false p.solution gl } diff --git a/engine/proofview.mli b/engine/proofview.mli index e7be66552..1905686fe 100644 --- a/engine/proofview.mli +++ b/engine/proofview.mli @@ -326,6 +326,9 @@ val unifiable : Evd.evar_map -> Evar.t -> Evar.t list -> bool considered). *) val shelve_unifiable : unit tactic +(** Idem but also returns the list of shelved variables *) +val shelve_unifiable_informative : Evar.t list tactic + (** [guard_no_unifiable] returns the list of unifiable goals if some goals are unifiable (see {!shelve_unifiable}) in the current focus. *) val guard_no_unifiable : Names.Name.t list option tactic @@ -466,6 +469,12 @@ module Unsafe : sig solved. *) val advance : Evd.evar_map -> Evar.t -> Evar.t option + (** [undefined sigma l] applies [advance] to the goals of [l], then + returns the subset of resulting goals which have not yet been + defined *) + val undefined : Evd.evar_map -> Proofview_monad.goal_with_state list -> + Proofview_monad.goal_with_state list + val typeclass_resolvable : unit Evd.Store.field end diff --git a/ide/MacOS/relatify_with-respect-to_.sh b/ide/MacOS/relatify_with-respect-to_.sh deleted file mode 100755 index a24af9395..000000000 --- a/ide/MacOS/relatify_with-respect-to_.sh +++ /dev/null @@ -1,15 +0,0 @@ -#!/bin/sh - -set -e - -for i in "$3/"*.dylib -do install_name_tool -change "$2"/$(basename $i) @executable_path/../Resources/lib/$(basename $i) "$1" -done -case "$1" in - *.dylib) - install_name_tool -id @executable_path/../Resources/lib/$(basename $1) $1 - for i in "$3"/*.dylib - do install_name_tool -change "$2/"$(basename $1) @executable_path/../Resources/lib/$(basename $1) $i - done;; - *) -esac diff --git a/interp/constrextern.ml b/interp/constrextern.ml index 19444988b..7792eff66 100644 --- a/interp/constrextern.ml +++ b/interp/constrextern.ml @@ -14,7 +14,6 @@ open CErrors open Util open Names open Nameops -open Constr open Termops open Libnames open Globnames @@ -479,7 +478,8 @@ and extern_notation_pattern (tmp_scope,scopes as allscopes) vars t = function if is_inactive_rule keyrule then raise No_match; let loc = t.loc in match DAst.get t with - | PatCstr (cstr,_,na) -> + | PatCstr (cstr,args,na) -> + let t = if na = Anonymous then t else DAst.make ?loc (PatCstr (cstr,args,Anonymous)) in let p = apply_notation_to_pattern ?loc (ConstructRef cstr) (match_notation_constr_cases_pattern t pat) allscopes vars keyrule in insert_pat_alias ?loc p na @@ -590,11 +590,17 @@ let explicitize inctx impl (cf,f) args = let expl () = match ip with | Some i -> - if not (List.is_empty impl) && is_status_implicit (List.nth impl (i-1)) then - raise Expl + (* Careful: It is possible to have declared implicits ending + before the principal argument *) + let is_impl = + try is_status_implicit (List.nth impl (i-1)) + with Failure _ -> false + in + if is_impl + then raise Expl else let (args1,args2) = List.chop i args in - let (impl1,impl2) = if List.is_empty impl then [],[] else List.chop i impl in + let (impl1,impl2) = try List.chop i impl with Failure _ -> impl, [] in let args1 = exprec 1 (args1,impl1) in let args2 = exprec (i+1) (args2,impl2) in let ip = Some (List.length args1) in @@ -1223,8 +1229,36 @@ let rec glob_of_pat avoid env sigma pat = DAst.make @@ match pat with | _ -> anomaly (Pp.str "PCase with non-trivial predicate but unknown inductive.") in GCases (RegularStyle,rtn,[glob_of_pat avoid env sigma tm,indnames],mat) - | PFix f -> DAst.get (Detyping.detype_names false avoid env (Global.env()) sigma (EConstr.of_constr (mkFix f))) (** FIXME bad env *) - | PCoFix c -> DAst.get (Detyping.detype_names false avoid env (Global.env()) sigma (EConstr.of_constr (mkCoFix c))) + | PFix ((ln,i),(lna,tl,bl)) -> + let def_avoid, def_env, lfi = + Array.fold_left + (fun (avoid, env, l) na -> + let id = Namegen.next_name_away na avoid in + (Id.Set.add id avoid, Name id :: env, id::l)) + (avoid, env, []) lna in + let n = Array.length tl in + let v = Array.map3 + (fun c t i -> Detyping.share_pattern_names glob_of_pat (i+1) [] def_avoid def_env sigma c (Patternops.lift_pattern n t)) + bl tl ln in + GRec(GFix (Array.map (fun i -> Some i, GStructRec) ln,i),Array.of_list (List.rev lfi), + Array.map (fun (bl,_,_) -> bl) v, + Array.map (fun (_,_,ty) -> ty) v, + Array.map (fun (_,bd,_) -> bd) v) + | PCoFix (ln,(lna,tl,bl)) -> + let def_avoid, def_env, lfi = + Array.fold_left + (fun (avoid, env, l) na -> + let id = Namegen.next_name_away na avoid in + (Id.Set.add id avoid, Name id :: env, id::l)) + (avoid, env, []) lna in + let ntys = Array.length tl in + let v = Array.map2 + (fun c t -> share_pattern_names glob_of_pat 0 [] def_avoid def_env sigma c (Patternops.lift_pattern ntys t)) + bl tl in + GRec(GCoFix ln,Array.of_list (List.rev lfi), + Array.map (fun (bl,_,_) -> bl) v, + Array.map (fun (_,_,ty) -> ty) v, + Array.map (fun (_,bd,_) -> bd) v) | PSort s -> GSort s let extern_constr_pattern env sigma pat = diff --git a/interp/impargs.ml b/interp/impargs.ml index 9ad62c0de..b424f73de 100644 --- a/interp/impargs.ml +++ b/interp/impargs.ml @@ -139,7 +139,7 @@ let argument_less = function | Hyp _, Conclusion -> true | Conclusion, _ -> false -let update pos rig (na,st) = +let update pos rig st = let e = if rig then match st with @@ -163,7 +163,7 @@ let update pos rig (na,st) = | Some (DepFlex fpos as x) -> if argument_less (pos,fpos) then DepFlex pos else x | Some Manual -> assert false - in na, Some e + in Some e (* modified is_rigid_reference with a truncated env *) let is_flexible_reference env sigma bound depth f = @@ -214,6 +214,8 @@ let add_free_rels_until strict strongly_strict revpat bound env sigma m pos acc let () = if not (Vars.noccur_between sigma 1 bound m) then frec true (env,1) m in acc +(* compute the list of implicit arguments *) + let rec is_rigid_head sigma t = match kind sigma t with | Rel _ | Evar _ -> false | Ind _ | Const _ | Var _ | Sort _ -> true @@ -226,7 +228,14 @@ let rec is_rigid_head sigma t = match kind sigma t with | Lambda _ | LetIn _ | Construct _ | CoFix _ | Fix _ | Prod _ | Meta _ | Cast _ -> assert false -(* calcule la liste des arguments implicites *) +let is_rigid env sigma t = + let open Context.Rel.Declaration in + let t = whd_all env sigma t in + match kind sigma t with + | Prod (na,a,b) -> + let (_,t) = splay_prod (push_rel (LocalAssum (na,a)) env) sigma b in + is_rigid_head sigma t + | _ -> true let find_displayed_name_in all avoid na (env, b) = let envnames_b = (env, b) in @@ -234,43 +243,54 @@ let find_displayed_name_in all avoid na (env, b) = if all then compute_and_force_displayed_name_in Evd.empty flag avoid na b else compute_displayed_name_in Evd.empty flag avoid na b -let compute_implicits_gen strict strongly_strict revpat contextual all env sigma (t : EConstr.t) = - let rigid = ref true in +let compute_implicits_names_gen all env sigma t = + let open Context.Rel.Declaration in + let rec aux env avoid names t = + let t = whd_all env sigma t in + match kind sigma t with + | Prod (na,a,b) -> + let na',avoid' = find_displayed_name_in all avoid na (names,b) in + aux (push_rel (LocalAssum (na,a)) env) avoid' (na'::names) b + | _ -> List.rev names + in aux env Id.Set.empty [] t + +let compute_implicits_names = compute_implicits_names_gen true + +let compute_implicits_explanation_gen strict strongly_strict revpat contextual env sigma t = let open Context.Rel.Declaration in - let rec aux env avoid n names (t : EConstr.t) = + let rec aux env n t = let t = whd_all env sigma t in match kind sigma t with - | Prod (na,a,b) -> - let na',avoid' = find_displayed_name_in all avoid na (names,b) in - add_free_rels_until strict strongly_strict revpat n env sigma a (Hyp (n+1)) - (aux (push_rel (LocalAssum (na',a)) env) avoid' (n+1) (na'::names) b) - | _ -> - rigid := is_rigid_head sigma t; - let names = List.rev names in - let v = Array.map (fun na -> na,None) (Array.of_list names) in - if contextual then - add_free_rels_until strict strongly_strict revpat n env sigma t Conclusion v - else v + | Prod (na,a,b) -> + add_free_rels_until strict strongly_strict revpat n env sigma a (Hyp (n+1)) + (aux (push_rel (LocalAssum (na,a)) env) (n+1) b) + | _ -> + let v = Array.make n None in + if contextual then + add_free_rels_until strict strongly_strict revpat n env sigma t Conclusion v + else v in match kind sigma (whd_all env sigma t) with - | Prod (na,a,b) -> - let na',avoid = find_displayed_name_in all Id.Set.empty na ([],b) in - let v = aux (push_rel (LocalAssum (na',a)) env) avoid 1 [na'] b in - !rigid, Array.to_list v - | _ -> true, [] + | Prod (na,a,b) -> + let v = aux (push_rel (LocalAssum (na,a)) env) 1 b in + Array.to_list v + | _ -> [] -let compute_implicits_flags env sigma f all t = - compute_implicits_gen +let compute_implicits_explanation_flags env sigma f t = + compute_implicits_explanation_gen (f.strict || f.strongly_strict) f.strongly_strict - f.reversible_pattern f.contextual all env sigma t + f.reversible_pattern f.contextual env sigma t -let compute_auto_implicits env sigma flags enriching t = - if enriching then compute_implicits_flags env sigma flags true t - else compute_implicits_gen false false false true true env sigma t +let compute_implicits_flags env sigma f all t = + List.combine + (compute_implicits_names_gen all env sigma t) + (compute_implicits_explanation_flags env sigma f t) -let compute_implicits_names env sigma t = - let _, impls = compute_implicits_gen false false false false true env sigma t in - List.map fst impls +let compute_auto_implicits env sigma flags enriching t = + List.combine + (compute_implicits_names env sigma t) + (if enriching then compute_implicits_explanation_flags env sigma flags t + else compute_implicits_explanation_gen false false false true env sigma t) (* Extra information about implicit arguments *) @@ -329,13 +349,16 @@ let rec prepare_implicits f = function Some (id,imp,(set_maximality imps' f.maximal,true)) :: imps' | _::imps -> None :: prepare_implicits f imps -let set_implicit id imp insmax = - (id,(match imp with None -> Manual | Some imp -> imp),insmax) - -let rec assoc_by_pos k = function - (ExplByPos (k', x), b) :: tl when Int.equal k k' -> (x,b), tl - | hd :: tl -> let (x, tl) = assoc_by_pos k tl in x, hd :: tl - | [] -> raise Not_found +(* +If found, returns Some (x,(b,fi,fo)) and l with the entry removed, +otherwise returns None and l unchanged. + *) +let assoc_by_pos k l = + let rec aux = function + (ExplByPos (k', x), b) :: tl when Int.equal k k' -> Some (x,b), tl + | hd :: tl -> let (x, tl) = aux tl in x, hd :: tl + | [] -> raise Not_found + in try aux l with Not_found -> None, l let check_correct_manual_implicits autoimps l = List.iter (function @@ -352,70 +375,65 @@ let check_correct_manual_implicits autoimps l = (str "Cannot set implicit argument number " ++ int i ++ str ": it has no name.")) l -let set_manual_implicits env flags enriching autoimps l = - let try_forced k l = - try - let (id, (b, fi, fo)), l' = assoc_by_pos k l in - if fo then - let id = match id with Some id -> id | None -> Id.of_string ("arg_" ^ string_of_int k) in - l', Some (id,Manual,(b,fi)) - else l, None - with Not_found -> l, None - in +(* Take a list l of explicitations, and map them to positions. *) +let flatten_explicitations l autoimps = + let rec aux k l = function + | (Name id,_)::imps -> + let value, l' = + try + let eq = explicitation_eq in + let flags = List.assoc_f eq (ExplByName id) l in + Some (Some id, flags), List.remove_assoc_f eq (ExplByName id) l + with Not_found -> assoc_by_pos k l + in value :: aux (k+1) l' imps + | (Anonymous,_)::imps -> + let value, l' = assoc_by_pos k l + in value :: aux (k+1) l' imps + | [] when List.is_empty l -> [] + | [] -> + check_correct_manual_implicits autoimps l; + [] + in aux 1 l autoimps + +let set_manual_implicits flags enriching autoimps l = if not (List.distinct l) then user_err Pp.(str "Some parameters are referred more than once."); (* Compare with automatic implicits to recover printing data and names *) - let rec merge k l = function - | (Name id,imp)::imps -> - let l',imp,m = - try - let eq = explicitation_eq in - let (b, fi, fo) = List.assoc_f eq (ExplByName id) l in - List.remove_assoc_f eq (ExplByName id) l, (Some Manual), (Some (b, fi)) - with Not_found -> - try - let (id, (b, fi, fo)), l' = assoc_by_pos k l in - l', (Some Manual), (Some (b,fi)) - with Not_found -> - let m = match enriching, imp with - | true, Some _ -> Some (flags.maximal, true) - | _ -> None - in - l, imp, m - in - let imps' = merge (k+1) l' imps in - let m = Option.map (fun (b,f) -> - (* match imp with Some Manual -> (b,f) *) - (* | _ -> *)set_maximality imps' b, f) m in - Option.map (set_implicit id imp) m :: imps' - | (Anonymous,imp)::imps -> - let l', forced = try_forced k l in - forced :: merge (k+1) l' imps - | [] when begin match l with [] -> true | _ -> false end -> [] - | [] -> - check_correct_manual_implicits autoimps l; - [] - in - merge 1 l autoimps - -let compute_semi_auto_implicits env sigma f manual t = - match manual with - | [] -> - if not f.auto then [DefaultImpArgs, []] - else let _,l = compute_implicits_flags env sigma f false t in - [DefaultImpArgs, prepare_implicits f l] - | _ -> - let _,autoimpls = compute_auto_implicits env sigma f f.auto t in - [DefaultImpArgs, set_manual_implicits env f f.auto autoimpls manual] + let rec merge k autoimps explimps = match autoimps, explimps with + | autoimp::autoimps, explimp::explimps -> + let imps' = merge (k+1) autoimps explimps in + begin match autoimp, explimp with + | (Name id,_), Some (_, (b, fi, _)) -> + Some (id, Manual, (set_maximality imps' b, fi)) + | (Name id,Some exp), None when enriching -> + Some (id, exp, (set_maximality imps' flags.maximal, true)) + | (Name _,_), None -> None + | (Anonymous,_), Some (Some id, (b, fi, true)) -> + Some (id,Manual,(b,fi)) + | (Anonymous,_), Some (None, (b, fi, true)) -> + let id = Id.of_string ("arg_" ^ string_of_int k) in + Some (id,Manual,(b,fi)) + | (Anonymous,_), Some (_, (_, _, false)) -> None + | (Anonymous,_), None -> None + end :: imps' + | [], [] -> [] + (* flatten_explicitations returns a list of the same length as autoimps *) + | _ -> assert false + in merge 1 autoimps (flatten_explicitations l autoimps) + +let compute_semi_auto_implicits env sigma f t = + if not f.auto then [DefaultImpArgs, []] + else let l = compute_implicits_flags env sigma f false t in + [DefaultImpArgs, prepare_implicits f l] (*s Constants. *) -let compute_constant_implicits flags manual cst = +let compute_constant_implicits flags cst = let env = Global.env () in let sigma = Evd.from_env env in let cb = Environ.lookup_constant cst env in let ty = of_constr cb.const_type in - let impls = compute_semi_auto_implicits env sigma flags manual ty in + let impls = compute_semi_auto_implicits env sigma flags ty in impls (*s Inductives and constructors. Their implicit arguments are stored @@ -423,7 +441,7 @@ let compute_constant_implicits flags manual cst = $i$ are the implicit arguments of the inductive and $v$ the array of implicit arguments of the constructors. *) -let compute_mib_implicits flags manual kn = +let compute_mib_implicits flags kn = let env = Global.env () in let sigma = Evd.from_env env in let mib = Environ.lookup_mind kn env in @@ -439,34 +457,34 @@ let compute_mib_implicits flags manual kn = let imps_one_inductive i mip = let ind = (kn,i) in let ar, _ = Global.type_of_global_in_context env (IndRef ind) in - ((IndRef ind,compute_semi_auto_implicits env sigma flags manual (of_constr ar)), + ((IndRef ind,compute_semi_auto_implicits env sigma flags (of_constr ar)), Array.mapi (fun j c -> - (ConstructRef (ind,j+1),compute_semi_auto_implicits env_ar sigma flags manual c)) + (ConstructRef (ind,j+1),compute_semi_auto_implicits env_ar sigma flags c)) (Array.map of_constr mip.mind_nf_lc)) in Array.mapi imps_one_inductive mib.mind_packets -let compute_all_mib_implicits flags manual kn = - let imps = compute_mib_implicits flags manual kn in +let compute_all_mib_implicits flags kn = + let imps = compute_mib_implicits flags kn in List.flatten (Array.map_to_list (fun (ind,cstrs) -> ind::Array.to_list cstrs) imps) (*s Variables. *) -let compute_var_implicits flags manual id = +let compute_var_implicits flags id = let env = Global.env () in let sigma = Evd.from_env env in - compute_semi_auto_implicits env sigma flags manual (NamedDecl.get_type (lookup_named id env)) + compute_semi_auto_implicits env sigma flags (NamedDecl.get_type (lookup_named id env)) (* Implicits of a global reference. *) -let compute_global_implicits flags manual = function - | VarRef id -> compute_var_implicits flags manual id - | ConstRef kn -> compute_constant_implicits flags manual kn +let compute_global_implicits flags = function + | VarRef id -> compute_var_implicits flags id + | ConstRef kn -> compute_constant_implicits flags kn | IndRef (kn,i) -> - let ((_,imps),_) = (compute_mib_implicits flags manual kn).(i) in imps + let ((_,imps),_) = (compute_mib_implicits flags kn).(i) in imps | ConstructRef ((kn,i),j) -> - let (_,cimps) = (compute_mib_implicits flags manual kn).(i) in snd cimps.(j-1) + let (_,cimps) = (compute_mib_implicits flags kn).(i) in snd cimps.(j-1) (* Merge a manual explicitation with an implicit_status list *) @@ -573,34 +591,34 @@ let rebuild_implicits (req,l) = | ImplLocal -> assert false | ImplConstant (con,flags) -> let oldimpls = snd (List.hd l) in - let newimpls = compute_constant_implicits flags [] con in + let newimpls = compute_constant_implicits flags con in req, [ConstRef con, List.map2 merge_impls oldimpls newimpls] | ImplMutualInductive (kn,flags) -> - let newimpls = compute_all_mib_implicits flags [] kn in + let newimpls = compute_all_mib_implicits flags kn in let rec aux olds news = - match olds, news with - | (_, oldimpls) :: old, (gr, newimpls) :: tl -> - (gr, List.map2 merge_impls oldimpls newimpls) :: aux old tl - | [], [] -> [] - | _, _ -> assert false + match olds, news with + | (_, oldimpls) :: old, (gr, newimpls) :: tl -> + (gr, List.map2 merge_impls oldimpls newimpls) :: aux old tl + | [], [] -> [] + | _, _ -> assert false in req, aux l newimpls | ImplInteractive (ref,flags,o) -> (if isVarRef ref && is_in_section ref then ImplLocal else req), match o with | ImplAuto -> - let oldimpls = snd (List.hd l) in - let newimpls = compute_global_implicits flags [] ref in - [ref,List.map2 merge_impls oldimpls newimpls] + let oldimpls = snd (List.hd l) in + let newimpls = compute_global_implicits flags ref in + [ref,List.map2 merge_impls oldimpls newimpls] | ImplManual userimplsize -> - let oldimpls = snd (List.hd l) in - if flags.auto then - let newimpls = List.hd (compute_global_implicits flags [] ref) in - let p = List.length (snd newimpls) - userimplsize in - let newimpls = on_snd (List.firstn p) newimpls in - [ref,List.map (fun o -> merge_impls o newimpls) oldimpls] - else - [ref,oldimpls] + let oldimpls = snd (List.hd l) in + if flags.auto then + let newimpls = List.hd (compute_global_implicits flags ref) in + let p = List.length (snd newimpls) - userimplsize in + let newimpls = on_snd (List.firstn p) newimpls in + [ref,List.map (fun o -> merge_impls o newimpls) oldimpls] + else + [ref,oldimpls] let classify_implicits (req,_ as obj) = match req with | ImplLocal -> Dispose @@ -622,7 +640,7 @@ let inImplicits : implicits_obj -> obj = let is_local local ref = local || isVarRef ref && is_in_section ref let declare_implicits_gen req flags ref = - let imps = compute_global_implicits flags [] ref in + let imps = compute_global_implicits flags ref in add_anonymous_leaf (inImplicits (req,[ref,imps])) let declare_implicits local ref = @@ -643,7 +661,7 @@ let declare_mib_implicits kn = let flags = !implicit_args in let imps = Array.map_to_list (fun (ind,cstrs) -> ind::(Array.to_list cstrs)) - (compute_mib_implicits flags [] kn) in + (compute_mib_implicits flags kn) in add_anonymous_leaf (inImplicits (ImplMutualInductive (kn,flags),List.flatten imps)) @@ -653,8 +671,8 @@ type manual_explicitation = Constrexpr.explicitation * (bool * bool * bool) type manual_implicits = manual_explicitation list let compute_implicits_with_manual env sigma typ enriching l = - let _,autoimpls = compute_auto_implicits env sigma !implicit_args enriching typ in - set_manual_implicits env !implicit_args enriching autoimpls l + let autoimpls = compute_auto_implicits env sigma !implicit_args enriching typ in + set_manual_implicits !implicit_args enriching autoimpls l let check_inclusion l = (* Check strict inclusion *) @@ -679,26 +697,26 @@ let declare_manual_implicits local ref ?enriching l = let env = Global.env () in let sigma = Evd.from_env env in let t, _ = Global.type_of_global_in_context env ref in + let t = of_constr t in let enriching = Option.default flags.auto enriching in - let isrigid,autoimpls = compute_auto_implicits env sigma flags enriching (of_constr t) in + let autoimpls = compute_auto_implicits env sigma flags enriching t in let l' = match l with | [] -> assert false | [l] -> - [DefaultImpArgs, set_manual_implicits env flags enriching autoimpls l] + [DefaultImpArgs, set_manual_implicits flags enriching autoimpls l] | _ -> - check_rigidity isrigid; - let l = List.map (fun imps -> (imps,List.length imps)) l in - let l = List.sort (fun (_,n1) (_,n2) -> n2 - n1) l in - check_inclusion l; - let nargs = List.length autoimpls in - List.map (fun (imps,n) -> - (LessArgsThan (nargs-n), - set_manual_implicits env flags enriching autoimpls imps)) l in + check_rigidity (is_rigid env sigma t); + let l = List.map (fun imps -> (imps,List.length imps)) l in + let l = List.sort (fun (_,n1) (_,n2) -> n2 - n1) l in + check_inclusion l; + let nargs = List.length autoimpls in + List.map (fun (imps,n) -> + (LessArgsThan (nargs-n), + set_manual_implicits flags enriching autoimpls imps)) l in let req = if is_local local ref then ImplLocal else ImplInteractive(ref,flags,ImplManual (List.length autoimpls)) - in - add_anonymous_leaf (inImplicits (req,[ref,l'])) + in add_anonymous_leaf (inImplicits (req,[ref,l'])) let maybe_declare_manual_implicits local ref ?enriching l = match l with diff --git a/interp/implicit_quantifiers.ml b/interp/implicit_quantifiers.ml index a1a3be70f..58df9abc4 100644 --- a/interp/implicit_quantifiers.ml +++ b/interp/implicit_quantifiers.ml @@ -245,6 +245,12 @@ let implicit_application env ?(allow_partial=true) f ty = CAst.make ?loc @@ CAppExpl ((None, id, inst), args), avoid in c, avoid +let warn_ignoring_implicit_status = + CWarnings.create ~name:"ignoring_implicit_status" ~category:"implicits" + (fun na -> + strbrk "Ignoring implicit status of product binder " ++ + Name.print na ++ strbrk " and following binders") + let implicits_of_glob_constr ?(with_products=true) l = let add_impl i na bk l = match bk with | Implicit -> @@ -260,20 +266,18 @@ let implicits_of_glob_constr ?(with_products=true) l = let abs na bk b = add_impl i na bk (aux (succ i) b) in - match DAst.get c with - | GProd (na, bk, t, b) -> - if with_products then abs na bk b - else - let () = match bk with - | Implicit -> - Feedback.msg_warning (strbrk "Ignoring implicit status of product binder " ++ - Name.print na ++ strbrk " and following binders") - | _ -> () - in [] - | GLambda (na, bk, t, b) -> abs na bk b - | GLetIn (na, b, t, c) -> aux i b - | GRec (fix_kind, nas, args, tys, bds) -> - let nb = match fix_kind with |GFix (_, n) -> n | GCoFix n -> n in - List.fold_left_i (fun i l (na,bk,_,_) -> add_impl i na bk l) i (aux (List.length args.(nb) + i) bds.(nb)) args.(nb) - | _ -> [] + match DAst.get c with + | GProd (na, bk, t, b) -> + if with_products then abs na bk b + else + let () = match bk with + | Implicit -> warn_ignoring_implicit_status na ?loc:c.CAst.loc + | _ -> () + in [] + | GLambda (na, bk, t, b) -> abs na bk b + | GLetIn (na, b, t, c) -> aux i b + | GRec (fix_kind, nas, args, tys, bds) -> + let nb = match fix_kind with |GFix (_, n) -> n | GCoFix n -> n in + List.fold_left_i (fun i l (na,bk,_,_) -> add_impl i na bk l) i (aux (List.length args.(nb) + i) bds.(nb)) args.(nb) + | _ -> [] in aux 1 l diff --git a/interp/notation_ops.ml b/interp/notation_ops.ml index a0d69ce79..aa9a6ed0d 100644 --- a/interp/notation_ops.ml +++ b/interp/notation_ops.ml @@ -1335,10 +1335,10 @@ let rec match_cases_pattern metas (terms,termlists,(),() as sigma) a1 a2 = match DAst.get a1, a2 with | r1, NVar id2 when Id.List.mem_assoc id2 metas -> (bind_env_cases_pattern sigma id2 a1),(0,[]) | PatVar Anonymous, NHole _ -> sigma,(0,[]) - | PatCstr ((ind,_ as r1),largs,_), NRef (ConstructRef r2) when eq_constructor r1 r2 -> + | PatCstr ((ind,_ as r1),largs,Anonymous), NRef (ConstructRef r2) when eq_constructor r1 r2 -> let l = try add_patterns_for_params_remove_local_defs r1 largs with Not_found -> raise No_match in sigma,(0,l) - | PatCstr ((ind,_ as r1),args1,_), NApp (NRef (ConstructRef r2),l2) + | PatCstr ((ind,_ as r1),args1,Anonymous), NApp (NRef (ConstructRef r2),l2) when eq_constructor r1 r2 -> let l1 = try add_patterns_for_params_remove_local_defs r1 args1 with Not_found -> raise No_match in let le2 = List.length l2 in diff --git a/intf/misctypes.ml b/intf/misctypes.ml index 9eb6f62cc..72db3b31c 100644 --- a/intf/misctypes.ml +++ b/intf/misctypes.ml @@ -142,19 +142,6 @@ type multi = | RepeatStar | RepeatPlus -type 'a core_destruction_arg = - | ElimOnConstr of 'a - | ElimOnIdent of lident - | ElimOnAnonHyp of int - -type 'a destruction_arg = - clear_flag * 'a core_destruction_arg - -type inversion_kind = - | SimpleInversion - | FullInversion - | FullInversionClear - type ('a, 'b) gen_universe_decl = { univdecl_instance : 'a; (* Declared universes *) univdecl_extensible_instance : bool; (* Can new universes be added *) diff --git a/intf/pattern.ml b/intf/pattern.ml index af2347674..76367b612 100644 --- a/intf/pattern.ml +++ b/intf/pattern.ml @@ -10,7 +10,6 @@ open Names open Globnames -open Constr open Misctypes (** {5 Patterns} *) @@ -37,8 +36,8 @@ type constr_pattern = | PIf of constr_pattern * constr_pattern * constr_pattern | PCase of case_info_pattern * constr_pattern * constr_pattern * (int * bool list * constr_pattern) list (** index of constructor, nb of args *) - | PFix of fixpoint - | PCoFix of cofixpoint + | PFix of (int array * int) * (Name.t array * constr_pattern array * constr_pattern array) + | PCoFix of int * (Name.t array * constr_pattern array * constr_pattern array) (** Nota : in a [PCase], the array of branches might be shorter than expected, denoting the use of a final "_ => _" branch *) diff --git a/intf/vernacexpr.ml b/intf/vernacexpr.ml index dc1110ad8..06f969f19 100644 --- a/intf/vernacexpr.ml +++ b/intf/vernacexpr.ml @@ -297,13 +297,9 @@ type inline = type module_ast_inl = module_ast * inline type module_binder = bool option * lident list * module_ast_inl -(** Cumulativity can be set globally, locally or unset locally and it - can not enabled at all. *) -type cumulative_inductive_parsing_flag = - | GlobalCumulativity - | GlobalNonCumulativity - | LocalCumulativity - | LocalNonCumulativity +(** [Some b] if locally enabled/disabled according to [b], [None] if + we should use the global flag. *) +type vernac_cumulative = VernacCumulative | VernacNonCumulative (** {6 The type of vernacular expressions} *) @@ -338,7 +334,7 @@ type nonrec vernac_expr = | VernacExactProof of constr_expr | VernacAssumption of (Decl_kinds.discharge * Decl_kinds.assumption_object_kind) * inline * (ident_decl list * constr_expr) with_coercion list - | VernacInductive of cumulative_inductive_parsing_flag * Decl_kinds.private_flag * inductive_flag * (inductive_expr * decl_notation list) list + | VernacInductive of vernac_cumulative option * Decl_kinds.private_flag * inductive_flag * (inductive_expr * decl_notation list) list | VernacFixpoint of Decl_kinds.discharge * (fixpoint_expr * decl_notation list) list | VernacCoFixpoint of Decl_kinds.discharge * (cofixpoint_expr * decl_notation list) list | VernacScheme of (lident option * scheme) list @@ -409,8 +405,6 @@ type nonrec vernac_expr = | VernacHints of string list * hints_expr | VernacSyntacticDefinition of lident * (Id.t list * constr_expr) * onlyparsing_flag - | VernacDeclareImplicits of reference or_by_notation * - (explicitation * bool * bool) list list | VernacArguments of reference or_by_notation * vernac_argument_status list (* Main arguments status list *) * (Name.t * vernac_implicit_status) list list (* Extra implicit status lists *) * @@ -418,8 +412,6 @@ type nonrec vernac_expr = [ `ReductionDontExposeCase | `ReductionNeverUnfold | `Rename | `ExtraScopes | `Assert | `ClearImplicits | `ClearScopes | `DefaultImplicits ] list - | VernacArgumentsScope of reference or_by_notation * - scope_name option list | VernacReserve of simple_binder list | VernacGeneralizable of (lident list) option | VernacSetOpacity of (Conv_oracle.level * reference or_by_notation list) @@ -446,7 +438,6 @@ type nonrec vernac_expr = | VernacRestart | VernacUndo of int | VernacUndoTo of int - | VernacBacktrack of int*int*int | VernacFocus of int option | VernacUnfocus | VernacUnfocused @@ -506,14 +497,13 @@ type vernac_type = | VtProofMode of string (* Queries are commands assumed to be "pure", that is to say, they don't modify the interpretation state. *) - | VtQuery of vernac_part_of_script * Feedback.route_id + | VtQuery (* To be removed *) | VtMeta | VtUnknown and vernac_qed_type = VtKeep | VtKeepAsAxiom | VtDrop (* Qed/Admitted, Abort *) and vernac_start = string * opacity_guarantee * Id.t list and vernac_sideff_type = Id.t list -and vernac_part_of_script = bool and opacity_guarantee = | GuaranteesOpacity (** Only generates opaque terms at [Qed] *) | Doesn'tGuaranteeOpacity (** May generate transparent terms even with [Qed].*) diff --git a/kernel/cbytegen.ml b/kernel/cbytegen.ml index 0766f49b3..70dc6867a 100644 --- a/kernel/cbytegen.ml +++ b/kernel/cbytegen.ml @@ -500,22 +500,19 @@ let rec compile_lam env reloc lam sz cont = | Lsort (Sorts.Prop _ as s) -> compile_structured_constant reloc (Const_sort s) sz cont | Lsort (Sorts.Type u) -> - (* We separate global and local universes in [u]. The former will be part - of the structured constant, while the later (if any) will be applied as - arguments. *) - let open Univ in begin - let u,s = Universe.compact u in - (* We assume that [Universe.type0m] is a neutral element for [Universe.sup] *) - let compile_get_univ reloc idx sz cont = - set_max_stack_size sz; - compile_fv_elem reloc (FVuniv_var idx) sz cont - in - if List.is_empty s then - compile_structured_constant reloc (Const_sort (Sorts.Type u)) sz cont - else - comp_app compile_structured_constant compile_get_univ reloc + (* We represent universes as a global constant with local universes + "compacted", i.e. as [u arg0 ... argn] where we will substitute (after + evaluation) [Var 0,...,Var n] with values of [arg0,...,argn] *) + let u,s = Univ.compact_univ u in + let compile_get_univ reloc idx sz cont = + set_max_stack_size sz; + compile_fv_elem reloc (FVuniv_var idx) sz cont + in + if List.is_empty s then + compile_structured_constant reloc (Const_sort (Sorts.Type u)) sz cont + else + comp_app compile_structured_constant compile_get_univ reloc (Const_sort (Sorts.Type u)) (Array.of_list s) sz cont - end | Llet (id,def,body) -> compile_lam env reloc def sz diff --git a/kernel/esubst.ml b/kernel/esubst.ml index a11a0dc00..91cc64523 100644 --- a/kernel/esubst.ml +++ b/kernel/esubst.ml @@ -19,6 +19,8 @@ open Util (*********************) (* Explicit lifts and basic operations *) +(* Invariant to preserve in this module: no lift contains two consecutive + [ELSHFT] nor two consecutive [ELLFT]. *) type lift = | ELID | ELSHFT of lift * int (* ELSHFT(l,n) == lift of n, then apply lift l *) @@ -28,15 +30,15 @@ type lift = let el_id = ELID (* compose a relocation of magnitude n *) -let rec el_shft_rec n = function - | ELSHFT(el,k) -> el_shft_rec (k+n) el +let el_shft_rec n = function + | ELSHFT(el,k) -> ELSHFT(el,k+n) | el -> ELSHFT(el,n) let el_shft n el = if Int.equal n 0 then el else el_shft_rec n el (* cross n binders *) -let rec el_liftn_rec n = function +let el_liftn_rec n = function | ELID -> ELID - | ELLFT(k,el) -> el_liftn_rec (n+k) el + | ELLFT(k,el) -> ELLFT(n+k, el) | el -> ELLFT(n, el) let el_liftn n el = if Int.equal n 0 then el else el_liftn_rec n el diff --git a/kernel/esubst.mli b/kernel/esubst.mli index b82d6fdf0..a674c425a 100644 --- a/kernel/esubst.mli +++ b/kernel/esubst.mli @@ -56,7 +56,11 @@ val comp : ('a subs * 'a -> 'a) -> 'a subs -> 'a subs -> 'a subs (** {6 Compact representation } *) (** Compact representation of explicit relocations - [ELSHFT(l,n)] == lift of [n], then apply [lift l]. - - [ELLFT(n,l)] == apply [l] to de Bruijn > [n] i.e under n binders. *) + - [ELLFT(n,l)] == apply [l] to de Bruijn > [n] i.e under n binders. + + Invariant ensured by the private flag: no lift contains two consecutive + [ELSHFT] nor two consecutive [ELLFT]. +*) type lift = private | ELID | ELSHFT of lift * int diff --git a/kernel/univ.ml b/kernel/univ.ml index be21381b7..ea3a52295 100644 --- a/kernel/univ.ml +++ b/kernel/univ.ml @@ -490,39 +490,6 @@ struct in List.fold_right (fun a acc -> aux a acc) u [] - (** [max_var_pred p u] returns the maximum variable level in [u] satisfying - [p], -1 if not found *) - let rec max_var_pred p u = - let open Level in - match u with - | [] -> -1 - | (v, _) :: u -> - match var_index v with - | Some i when p i -> max i (max_var_pred p u) - | _ -> max_var_pred p u - - let rec remap_var u i j = - let open Level in - match u with - | [] -> [] - | (v, incr) :: u when var_index v = Some i -> - (Level.var j, incr) :: remap_var u i j - | _ :: u -> remap_var u i j - - let rec compact u max_var i = - if i >= max_var then (u,[]) else - let j = max_var_pred (fun j -> j < i) u in - if Int.equal i (j+1) then - let (u,s) = compact u max_var (i+1) in - (u, i :: s) - else - let (u,s) = compact (remap_var u i j) max_var (i+1) in - (u, j+1 :: s) - - let compact u = - let max_var = max_var_pred (fun _ -> true) u in - compact u max_var 0 - (* Returns the formal universe that is greater than the universes u and v. Used to type the products. *) let sup x y = merge_univs x y @@ -1208,6 +1175,20 @@ let abstract_cumulativity_info (univs, variance) = let subst, univs = abstract_universes univs in subst, (univs, variance) +let rec compact_univ s vars i u = + match u with + | [] -> (s, List.rev vars) + | (lvl, _) :: u -> + match Level.var_index lvl with + | Some k when not (LMap.mem lvl s) -> + let lvl' = Level.var i in + compact_univ (LMap.add lvl lvl' s) (k :: vars) (i+1) u + | _ -> compact_univ s vars i u + +let compact_univ u = + let (s, s') = compact_univ LMap.empty [] 0 u in + (subst_univs_level_universe s u, s') + (** Pretty-printing *) let pr_constraints prl = Constraint.pr prl diff --git a/kernel/univ.mli b/kernel/univ.mli index 629d83fb8..aaed899bf 100644 --- a/kernel/univ.mli +++ b/kernel/univ.mli @@ -128,12 +128,6 @@ sig val map : (Level.t * int -> 'a) -> t -> 'a list - (** [compact u] remaps local variables in [u] such that their indices become - consecutive. It returns the new universe and the mapping. - Example: compact [(Var 0, i); (Prop, 0); (Var 2; j))] = - [(Var 0,i); (Prop, 0); (Var 1; j)], [0; 2] - *) - val compact : t -> t * int list end type universe = Universe.t @@ -504,6 +498,13 @@ val abstract_cumulativity_info : CumulativityInfo.t -> Instance.t * ACumulativit val make_abstract_instance : AUContext.t -> Instance.t +(** [compact_univ u] remaps local variables in [u] such that their indices become + consecutive. It returns the new universe and the mapping. + Example: compact_univ [(Var 0, i); (Prop, 0); (Var 2; j))] = + [(Var 0,i); (Prop, 0); (Var 1; j)], [0; 2] +*) +val compact_univ : Universe.t -> Universe.t * int list + (** {6 Pretty-printing of universes. } *) val pr_constraint_type : constraint_type -> Pp.t diff --git a/lib/aux_file.ml b/lib/aux_file.ml index 7d9c528e7..0f9476605 100644 --- a/lib/aux_file.ml +++ b/lib/aux_file.ml @@ -55,7 +55,7 @@ let record_in_aux_at ?loc key v = match loc with | Some loc -> let i, j = Loc.unloc loc in Printf.fprintf oc "%d %d %s %S\n" i j key v - | None -> Printf.fprintf oc "--- %s %S\n" key v + | None -> Printf.fprintf oc "0 0 %s %S\n" key v ) !oc let current_loc : Loc.t option ref = ref None diff --git a/lib/loc.ml b/lib/loc.ml index 6f5283aab..1a09091bf 100644 --- a/lib/loc.ml +++ b/lib/loc.ml @@ -62,6 +62,11 @@ let merge_opt l1 l2 = match l1, l2 with | None, Some l -> Some l | Some l1, Some l2 -> Some (merge l1 l2) +let finer l1 l2 = match l1, l2 with + | None, _ -> false + | Some l , None -> true + | Some l1, Some l2 -> l1.fname = l2.fname && merge l1 l2 = l2 + let unloc loc = (loc.bp, loc.ep) let shift_loc kb kp loc = { loc with bp = loc.bp + kb ; ep = loc.ep + kp } diff --git a/lib/loc.mli b/lib/loc.mli index 813c45fbb..23df1ebd9 100644 --- a/lib/loc.mli +++ b/lib/loc.mli @@ -42,6 +42,10 @@ val merge : t -> t -> t val merge_opt : t option -> t option -> t option (** Merge locations, usually generating the largest possible span *) +val finer : t option -> t option -> bool +(** Answers [true] when the first location is more defined, or, when + both defined, included in the second one *) + val shift_loc : int -> int -> t -> t (** [shift_loc loc n p] shifts the beginning of location by [n] and the end by [p]; it is assumed that the shifts do not change the diff --git a/parsing/g_vernac.ml4 b/parsing/g_vernac.ml4 index 8543d2b84..593dcbf58 100644 --- a/parsing/g_vernac.ml4 +++ b/parsing/g_vernac.ml4 @@ -161,20 +161,10 @@ GEXTEND Gram | IDENT "Let"; id = identref; b = def_body -> VernacDefinition ((DoDischarge, Let), (lname_of_lident id, None), b) (* Gallina inductive declarations *) - | cum = cumulativity_token; priv = private_token; f = finite_token; + | cum = OPT cumulativity_token; priv = private_token; f = finite_token; indl = LIST1 inductive_definition SEP "with" -> let (k,f) = f in let indl=List.map (fun ((a,b,c,d),e) -> ((a,b,c,k,d),e)) indl in - let cum = - match cum with - Some true -> LocalCumulativity - | Some false -> LocalNonCumulativity - | None -> - if Flags.is_polymorphic_inductive_cumulativity () then - GlobalCumulativity - else - GlobalNonCumulativity - in VernacInductive (cum, priv,f,indl) | "Fixpoint"; recs = LIST1 rec_definition SEP "with" -> VernacFixpoint (NoDischarge, recs) @@ -257,7 +247,8 @@ GEXTEND Gram | IDENT "Class" -> (Class true,BiFinite) ] ] ; cumulativity_token: - [ [ IDENT "Cumulative" -> Some true | IDENT "NonCumulative" -> Some false | -> None ] ] + [ [ IDENT "Cumulative" -> VernacCumulative + | IDENT "NonCumulative" -> VernacNonCumulative ] ] ; private_token: [ [ IDENT "Private" -> true | -> false ] ] @@ -601,14 +592,6 @@ GEXTEND Gram ; END -let warn_deprecated_arguments_scope = - CWarnings.create ~name:"deprecated-arguments-scope" ~category:"deprecated" - (fun () -> strbrk "Arguments Scope is deprecated; use Arguments instead") - -let warn_deprecated_implicit_arguments = - CWarnings.create ~name:"deprecated-implicit-arguments" ~category:"deprecated" - (fun () -> strbrk "Implicit Arguments is deprecated; use Arguments instead") - (* Extensions: implicits, coercions, etc. *) GEXTEND Gram GLOBAL: gallina_ext instance_name hint_info; @@ -691,20 +674,6 @@ GEXTEND Gram let more_implicits = Option.default [] more_implicits in VernacArguments (qid, args, more_implicits, !slash_position, mods) - - (* moved there so that camlp5 factors it with the previous rule *) - | IDENT "Arguments"; IDENT "Scope"; qid = smart_global; - "["; scl = LIST0 [ "_" -> None | sc = IDENT -> Some sc ]; "]" -> - warn_deprecated_arguments_scope ~loc:!@loc (); - VernacArgumentsScope (qid,scl) - - (* Implicit *) - | IDENT "Implicit"; IDENT "Arguments"; qid = smart_global; - pos = LIST0 [ "["; l = LIST0 implicit_name; "]" -> - List.map (fun (id,b,f) -> (ExplByName id,b,f)) l ] -> - warn_deprecated_implicit_arguments ~loc:!@loc (); - VernacDeclareImplicits (qid,pos) - | IDENT "Implicit"; "Type"; bl = reserv_list -> VernacReserve bl @@ -734,12 +703,6 @@ GEXTEND Gram [`ClearImplicits; `ClearScopes] ] ] ; - implicit_name: - [ [ "!"; id = ident -> (id, false, true) - | id = ident -> (id,false,false) - | "["; "!"; id = ident; "]" -> (id,true,true) - | "["; id = ident; "]" -> (id,true, false) ] ] - ; scope: [ [ "%"; key = IDENT -> key ] ] ; @@ -1065,8 +1028,6 @@ GEXTEND Gram | IDENT "Back" -> VernacBack 1 | IDENT "Back"; n = natural -> VernacBack n | IDENT "BackTo"; n = natural -> VernacBackTo n - | IDENT "Backtrack"; n = natural ; m = natural ; p = natural -> - VernacBacktrack (n,m,p) (* Tactic Debugger *) | IDENT "Debug"; IDENT "On" -> diff --git a/plugins/funind/functional_principles_types.ml b/plugins/funind/functional_principles_types.ml index 7a9bbd92c..804548ce5 100644 --- a/plugins/funind/functional_principles_types.ml +++ b/plugins/funind/functional_principles_types.ml @@ -628,16 +628,19 @@ let build_scheme fas = user_err ~hdr:"FunInd.build_scheme" (str "Cannot find " ++ Libnames.pr_reference f) in - let evd',f = Evd.fresh_global (Global.env ()) !evd f_as_constant in + let evd',f = Evd.fresh_global (Global.env ()) !evd f_as_constant in let _ = evd := evd' in let _ = Typing.e_type_of ~refresh:true (Global.env ()) evd (EConstr.of_constr f) in - (destConst f,sort) + if isConst f + then (destConst f,sort) + else user_err Pp.(pr_constr_env (Global.env ()) !evd f ++spc () ++ str "should be the named of a globally defined function") ) fas ) in let bodies_types = make_scheme evd pconstants in + List.iter2 (fun (princ_id,_,_) def_entry -> ignore diff --git a/plugins/funind/glob_term_to_relation.ml b/plugins/funind/glob_term_to_relation.ml index 49f7aae43..319b410df 100644 --- a/plugins/funind/glob_term_to_relation.ml +++ b/plugins/funind/glob_term_to_relation.ml @@ -1512,7 +1512,7 @@ let do_build_inductive in let msg = str "while trying to define"++ spc () ++ - Ppvernac.pr_vernac Vernacexpr.(VernacExpr([], VernacInductive(GlobalNonCumulativity,false,Declarations.Finite,repacked_rel_inds))) + Ppvernac.pr_vernac Vernacexpr.(VernacExpr([], VernacInductive(None,false,Declarations.Finite,repacked_rel_inds))) ++ fnl () ++ msg in @@ -1527,7 +1527,7 @@ let do_build_inductive in let msg = str "while trying to define"++ spc () ++ - Ppvernac.pr_vernac Vernacexpr.(VernacExpr([], VernacInductive(GlobalNonCumulativity,false,Declarations.Finite,repacked_rel_inds))) + Ppvernac.pr_vernac Vernacexpr.(VernacExpr([], VernacInductive(None,false,Declarations.Finite,repacked_rel_inds))) ++ fnl () ++ CErrors.print reraise in diff --git a/plugins/funind/invfun.ml b/plugins/funind/invfun.ml index 2743a8a2f..ae84eaa93 100644 --- a/plugins/funind/invfun.ml +++ b/plugins/funind/invfun.ml @@ -969,7 +969,7 @@ let functional_inversion kn hid fconst f_correct : Tacmach.tactic = Proofview.V82.of_tactic (generalize [applist(f_correct,(Array.to_list f_args)@[res;mkVar hid])]); thin [hid]; Proofview.V82.of_tactic (Simple.intro hid); - Proofview.V82.of_tactic (Inv.inv FullInversion None (NamedHyp hid)); + Proofview.V82.of_tactic (Inv.inv Inv.FullInversion None (NamedHyp hid)); (fun g -> let new_ids = List.filter (fun id -> not (Id.Set.mem id old_ids)) (pf_ids_of_hyps g) in tclMAP (revert_graph kn pre_tac) (hid::new_ids) g diff --git a/plugins/ltac/pltac.mli b/plugins/ltac/pltac.mli index 6637de745..434feba95 100644 --- a/plugins/ltac/pltac.mli +++ b/plugins/ltac/pltac.mli @@ -25,7 +25,7 @@ val constr_may_eval : (constr_expr,reference or_by_notation,constr_expr) may_eva val constr_eval : (constr_expr,reference or_by_notation,constr_expr) may_eval Gram.entry val uconstr : constr_expr Gram.entry val quantified_hypothesis : quantified_hypothesis Gram.entry -val destruction_arg : constr_expr with_bindings destruction_arg Gram.entry +val destruction_arg : constr_expr with_bindings Tactics.destruction_arg Gram.entry val int_or_var : int or_var Gram.entry val simple_tactic : raw_tactic_expr Gram.entry val simple_intropattern : constr_expr intro_pattern_expr CAst.t Gram.entry diff --git a/plugins/ltac/pptactic.mli b/plugins/ltac/pptactic.mli index 5951f2b11..aea00c240 100644 --- a/plugins/ltac/pptactic.mli +++ b/plugins/ltac/pptactic.mli @@ -84,7 +84,7 @@ type pp_tactic = { pptac_prods : grammar_terminals; } -val pr_goal_selector : toplevel:bool -> goal_selector -> Pp.t +val pr_goal_selector : toplevel:bool -> Vernacexpr.goal_selector -> Pp.t val declare_notation_tactic_pprule : KerName.t -> pp_tactic -> unit diff --git a/plugins/ltac/tacarg.mli b/plugins/ltac/tacarg.mli index 5347eda7d..59473a5e5 100644 --- a/plugins/ltac/tacarg.mli +++ b/plugins/ltac/tacarg.mli @@ -23,7 +23,7 @@ val wit_tactic : (raw_tactic_expr, glob_tactic_expr, Geninterp.Val.t) genarg_typ val wit_ltac : (raw_tactic_expr, glob_tactic_expr, unit) genarg_type val wit_destruction_arg : - (constr_expr with_bindings Tacexpr.destruction_arg, - glob_constr_and_expr with_bindings Tacexpr.destruction_arg, - delayed_open_constr_with_bindings Tacexpr.destruction_arg) genarg_type + (constr_expr with_bindings Tactics.destruction_arg, + glob_constr_and_expr with_bindings Tactics.destruction_arg, + delayed_open_constr_with_bindings Tactics.destruction_arg) genarg_type diff --git a/plugins/ltac/tacexpr.ml b/plugins/ltac/tacexpr.ml index 8b0c44041..3baa475ab 100644 --- a/plugins/ltac/tacexpr.ml +++ b/plugins/ltac/tacexpr.ml @@ -40,25 +40,29 @@ type goal_selector = Vernacexpr.goal_selector = | SelectList of (int * int) list | SelectId of Id.t | SelectAll +[@@ocaml.deprecated "Use Vernacexpr.goal_selector"] -type 'a core_destruction_arg = 'a Misctypes.core_destruction_arg = +type 'a core_destruction_arg = 'a Tactics.core_destruction_arg = | ElimOnConstr of 'a | ElimOnIdent of lident | ElimOnAnonHyp of int +[@@ocaml.deprecated "Use Tactics.core_destruction_arg"] type 'a destruction_arg = - clear_flag * 'a core_destruction_arg + clear_flag * 'a Tactics.core_destruction_arg +[@@ocaml.deprecated "Use Tactics.destruction_arg"] -type inversion_kind = Misctypes.inversion_kind = +type inversion_kind = Inv.inversion_kind = | SimpleInversion | FullInversion | FullInversionClear +[@@ocaml.deprecated "Use Tactics.inversion_kind"] type ('c,'d,'id) inversion_strength = | NonDepInversion of - inversion_kind * 'id list * 'd or_and_intro_pattern_expr CAst.t or_var option + Inv.inversion_kind * 'id list * 'd or_and_intro_pattern_expr CAst.t or_var option | DepInversion of - inversion_kind * 'c option * 'd or_and_intro_pattern_expr CAst.t or_var option + Inv.inversion_kind * 'c option * 'd or_and_intro_pattern_expr CAst.t or_var option | InversionUsing of 'c * 'id list type ('a,'b) location = HypLocation of 'a | ConclLocation of 'b @@ -69,7 +73,7 @@ type 'id message_token = | MsgIdent of 'id type ('dconstr,'id) induction_clause = - 'dconstr with_bindings destruction_arg * + 'dconstr with_bindings Tactics.destruction_arg * (intro_pattern_naming_expr CAst.t option (* eqn:... *) * 'dconstr or_and_intro_pattern_expr CAst.t or_var option) (* as ... *) * 'id clause_expr option (* in ... *) @@ -265,7 +269,7 @@ and 'a gen_tactic_expr = ('p,'a gen_tactic_expr) match_rule list | TacFun of 'a gen_tactic_fun_ast | TacArg of 'a gen_tactic_arg located - | TacSelect of goal_selector * 'a gen_tactic_expr + | TacSelect of Vernacexpr.goal_selector * 'a gen_tactic_expr (* For ML extensions *) | TacML of (ml_tactic_entry * 'a gen_tactic_arg list) Loc.located (* For syntax extensions *) diff --git a/plugins/ltac/tacexpr.mli b/plugins/ltac/tacexpr.mli index 8b0c44041..3baa475ab 100644 --- a/plugins/ltac/tacexpr.mli +++ b/plugins/ltac/tacexpr.mli @@ -40,25 +40,29 @@ type goal_selector = Vernacexpr.goal_selector = | SelectList of (int * int) list | SelectId of Id.t | SelectAll +[@@ocaml.deprecated "Use Vernacexpr.goal_selector"] -type 'a core_destruction_arg = 'a Misctypes.core_destruction_arg = +type 'a core_destruction_arg = 'a Tactics.core_destruction_arg = | ElimOnConstr of 'a | ElimOnIdent of lident | ElimOnAnonHyp of int +[@@ocaml.deprecated "Use Tactics.core_destruction_arg"] type 'a destruction_arg = - clear_flag * 'a core_destruction_arg + clear_flag * 'a Tactics.core_destruction_arg +[@@ocaml.deprecated "Use Tactics.destruction_arg"] -type inversion_kind = Misctypes.inversion_kind = +type inversion_kind = Inv.inversion_kind = | SimpleInversion | FullInversion | FullInversionClear +[@@ocaml.deprecated "Use Tactics.inversion_kind"] type ('c,'d,'id) inversion_strength = | NonDepInversion of - inversion_kind * 'id list * 'd or_and_intro_pattern_expr CAst.t or_var option + Inv.inversion_kind * 'id list * 'd or_and_intro_pattern_expr CAst.t or_var option | DepInversion of - inversion_kind * 'c option * 'd or_and_intro_pattern_expr CAst.t or_var option + Inv.inversion_kind * 'c option * 'd or_and_intro_pattern_expr CAst.t or_var option | InversionUsing of 'c * 'id list type ('a,'b) location = HypLocation of 'a | ConclLocation of 'b @@ -69,7 +73,7 @@ type 'id message_token = | MsgIdent of 'id type ('dconstr,'id) induction_clause = - 'dconstr with_bindings destruction_arg * + 'dconstr with_bindings Tactics.destruction_arg * (intro_pattern_naming_expr CAst.t option (* eqn:... *) * 'dconstr or_and_intro_pattern_expr CAst.t or_var option) (* as ... *) * 'id clause_expr option (* in ... *) @@ -265,7 +269,7 @@ and 'a gen_tactic_expr = ('p,'a gen_tactic_expr) match_rule list | TacFun of 'a gen_tactic_fun_ast | TacArg of 'a gen_tactic_arg located - | TacSelect of goal_selector * 'a gen_tactic_expr + | TacSelect of Vernacexpr.goal_selector * 'a gen_tactic_expr (* For ML extensions *) | TacML of (ml_tactic_entry * 'a gen_tactic_arg list) Loc.located (* For syntax extensions *) diff --git a/plugins/ltac/tactic_debug.ml b/plugins/ltac/tactic_debug.ml index e55b49fb4..105b5c59a 100644 --- a/plugins/ltac/tactic_debug.ml +++ b/plugins/ltac/tactic_debug.ml @@ -391,19 +391,14 @@ let explain_ltac_call_trace last trace loc = let skip_extensions trace = let rec aux = function - | (_,Tacexpr.LtacNameCall f as tac) :: _ - when Tacenv.is_ltac_for_ml_tactic f -> [tac] - | (_,Tacexpr.LtacNotationCall _ as tac) :: (_,Tacexpr.LtacMLCall _) :: _ -> + | (_,Tacexpr.LtacNotationCall _ as tac) :: (_,Tacexpr.LtacMLCall _) :: tail -> (* Case of an ML defined tactic with entry of the form <<"foo" args>> *) (* see tacextend.mlp *) - [tac] - | (_,Tacexpr.LtacMLCall _ as tac) :: _ -> [tac] + tac :: aux tail | t :: tail -> t :: aux tail | [] -> [] in List.rev (aux (List.rev trace)) -let finer_loc loc1 loc2 = Loc.merge_opt loc1 loc2 = loc2 - let extract_ltac_trace ?loc trace = let trace = skip_extensions trace in let (tloc,c),tail = List.sep_last trace in @@ -411,7 +406,7 @@ let extract_ltac_trace ?loc trace = (* We entered a user-defined tactic, we display the trace with location of the call *) let msg = hov 0 (explain_ltac_call_trace c tail loc ++ fnl()) in - (if finer_loc loc tloc then loc else tloc), Some msg + (if Loc.finer loc tloc then loc else tloc), Some msg else (* We entered a primitive tactic, we don't display trace but report on the finest location *) @@ -420,7 +415,7 @@ let extract_ltac_trace ?loc trace = let rec aux best_loc = function | (loc,_)::tail -> if Option.is_empty best_loc || - not (Option.is_empty loc) && finer_loc loc best_loc + not (Option.is_empty loc) && Loc.finer loc best_loc then aux loc tail else diff --git a/plugins/ssr/ssripats.ml b/plugins/ssr/ssripats.ml index 42566575c..7897cb170 100644 --- a/plugins/ssr/ssripats.ml +++ b/plugins/ssr/ssripats.ml @@ -133,6 +133,12 @@ let intro_clear ids future_ipats = isCLR_PUSHL clear_ids end +let tacCHECK_HYPS_EXIST hyps = Goal.enter begin fun gl -> + let ctx = Goal.hyps gl in + List.iter (Ssrcommon.check_hyp_exists ctx) hyps; + tclUNIT () +end + (** [=> []] *****************************************************************) let tac_case t = Goal.enter begin fun _ -> @@ -229,7 +235,9 @@ let rec ipat_tac1 future_ipats ipat : unit tactic = | IPatNoop -> tclUNIT () | IPatSimpl Nop -> tclUNIT () - | IPatClear ids -> intro_clear (List.map Ssrcommon.hyp_id ids) future_ipats + | IPatClear ids -> + tacCHECK_HYPS_EXIST ids <*> + intro_clear (List.map Ssrcommon.hyp_id ids) future_ipats | IPatSimpl (Simpl n) -> V82.tactic ~nf_evars:false (Ssrequality.simpltac (Simpl n)) diff --git a/plugins/ssr/ssrparser.ml4 b/plugins/ssr/ssrparser.ml4 index 0d82a9f09..5f3967440 100644 --- a/plugins/ssr/ssrparser.ml4 +++ b/plugins/ssr/ssrparser.ml4 @@ -585,21 +585,10 @@ let pr_ssripat _ _ _ = pr_ipat let pr_ssripats _ _ _ = pr_ipats let pr_ssriorpat _ _ _ = pr_iorpat -(* -let intern_ipat ist ipat = - let rec check_pat = function - | IPatClear clr -> ignore (List.map (intern_hyp ist) clr) - | IPatCase iorpat -> List.iter (List.iter check_pat) iorpat - | IPatDispatch iorpat -> List.iter (List.iter check_pat) iorpat - | IPatInj iorpat -> List.iter (List.iter check_pat) iorpat - | _ -> () in - check_pat ipat; ipat -*) - let intern_ipat ist = map_ipat (fun id -> id) - (intern_hyp ist) (* TODO: check with ltac, old code was ignoring the result *) + (intern_hyp ist) (glob_ast_closure_term ist) let intern_ipats ist = List.map (intern_ipat ist) diff --git a/pretyping/constr_matching.ml b/pretyping/constr_matching.ml index 888c76e3d..89d490a41 100644 --- a/pretyping/constr_matching.ml +++ b/pretyping/constr_matching.ml @@ -183,9 +183,36 @@ let push_binder na1 na2 t ctx = Namegen.next_ident_away Namegen.default_non_dependent_ident avoid in (na1, id2, t) :: ctx -let to_fix (idx, (nas, cs, ts)) = - let inj = EConstr.of_constr in - (idx, (nas, Array.map inj cs, Array.map inj ts)) +(* This is an optimization of the main pattern-matching which shares + the longest common prefix of the body and type of a fixpoint. The + only practical effect at the time of writing is in binding variable + names: these variable names must be bound only once since the user + view at a fix displays only a (maximal) shared common prefix *) + +let rec match_under_common_fix_binders sorec sigma binding_vars ctx ctx' env env' subst t1 t2 b1 b2 = + match t1, EConstr.kind sigma t2, b1, EConstr.kind sigma b2 with + | PProd(na1,c1,t1'), Prod(na2,c2,t2'), PLambda (_,c1',b1'), Lambda (na2',c2',b2') -> + let ctx = push_binder na1 na2 c2 ctx in + let ctx' = push_binder na1 na2' c2' ctx' in + let env = EConstr.push_rel (LocalAssum (na2,c2)) env in + let subst = sorec ctx env subst c1 c2 in + let subst = sorec ctx env subst c1' c2' in + let subst = add_binders na1 na2 binding_vars subst in + match_under_common_fix_binders sorec sigma binding_vars + ctx ctx' env env' subst t1' t2' b1' b2' + | PLetIn(na1,c1,u1,t1), LetIn(na2,c2,u2,t2), PLetIn(_,c1',u1',b1), LetIn(na2',c2',u2',b2) -> + let ctx = push_binder na1 na2 u2 ctx in + let ctx' = push_binder na1 na2' u2' ctx' in + let env = EConstr.push_rel (LocalDef (na2,c2,t2)) env in + let subst = sorec ctx env subst c1 c2 in + let subst = sorec ctx env subst c1' c2' in + let subst = Option.fold_left (fun subst u1 -> sorec ctx env subst u1 u2) subst u1 in + let subst = Option.fold_left (fun subst u1' -> sorec ctx env subst u1' u2') subst u1' in + let subst = add_binders na1 na2 binding_vars subst in + match_under_common_fix_binders sorec sigma binding_vars + ctx ctx' env env' subst t1 t2 b1 b2 + | _ -> + sorec ctx' env' (sorec ctx env subst t1 t2) b1 b2 let merge_binding sigma allow_bound_rels ctx n cT subst = let c = match ctx with @@ -364,8 +391,20 @@ let matches_core env sigma allow_bound_rels let chk_head = sorec ctx env (sorec ctx env subst a1 a2) p1 p2 in List.fold_left chk_branch chk_head br1 - | PFix c1, Fix _ when eq_constr sigma (mkFix (to_fix c1)) cT -> subst - | PCoFix c1, CoFix _ when eq_constr sigma (mkCoFix (to_fix c1)) cT -> subst + | PFix ((ln1,i1),(lna1,tl1,bl1)), Fix ((ln2,i2),(lna2,tl2,bl2)) + when Array.equal Int.equal ln1 ln2 && i1 = i2 -> + let ctx' = Array.fold_left3 (fun ctx na1 na2 t2 -> push_binder na1 na2 t2 ctx) ctx lna1 lna2 tl2 in + let env' = Array.fold_left2 (fun env na2 c2 -> EConstr.push_rel (LocalAssum (na2,c2)) env) env lna2 tl2 in + let subst = Array.fold_left4 (match_under_common_fix_binders sorec sigma binding_vars ctx ctx' env env') subst tl1 tl2 bl1 bl2 in + Array.fold_left2 (fun subst na1 na2 -> add_binders na1 na2 binding_vars subst) subst lna1 lna2 + + | PCoFix (i1,(lna1,tl1,bl1)), CoFix (i2,(lna2,tl2,bl2)) + when i1 = i2 -> + let ctx' = Array.fold_left3 (fun ctx na1 na2 t2 -> push_binder na1 na2 t2 ctx) ctx lna1 lna2 tl2 in + let env' = Array.fold_left2 (fun env na2 c2 -> EConstr.push_rel (LocalAssum (na2,c2)) env) env lna2 tl2 in + let subst = Array.fold_left4 (match_under_common_fix_binders sorec sigma binding_vars ctx ctx' env env') subst tl1 tl2 bl1 bl2 in + Array.fold_left2 (fun subst na1 na2 -> add_binders na1 na2 binding_vars subst) subst lna1 lna2 + | PEvar (c1,args1), Evar (c2,args2) when Evar.equal c1 c2 -> Array.fold_left2 (sorec ctx env) subst args1 args2 | (PRef _ | PVar _ | PRel _ | PApp _ | PProj _ | PLambda _ diff --git a/pretyping/detyping.ml b/pretyping/detyping.ml index 587892141..bb563220b 100644 --- a/pretyping/detyping.ml +++ b/pretyping/detyping.ml @@ -501,6 +501,97 @@ let detype_case computable detype detype_eqns testdep avoid data p c bl = let eqnl = detype_eqns constructs constagsl bl in GCases (tag,pred,[tomatch,(alias,aliastyp)],eqnl) +let rec share_names detype n l avoid env sigma c t = + match EConstr.kind sigma c, EConstr.kind sigma t with + (* factorize even when not necessary to have better presentation *) + | Lambda (na,t,c), Prod (na',t',c') -> + let na = match (na,na') with + Name _, _ -> na + | _, Name _ -> na' + | _ -> na in + let t' = detype avoid env sigma t in + let id = next_name_away na avoid in + let avoid = Id.Set.add id avoid and env = add_name (Name id) None t env in + share_names detype (n-1) ((Name id,Explicit,None,t')::l) avoid env sigma c c' + (* May occur for fix built interactively *) + | LetIn (na,b,t',c), _ when n > 0 -> + let t'' = detype avoid env sigma t' in + let b' = detype avoid env sigma b in + let id = next_name_away na avoid in + let avoid = Id.Set. add id avoid and env = add_name (Name id) (Some b) t' env in + share_names detype n ((Name id,Explicit,Some b',t'')::l) avoid env sigma c (lift 1 t) + (* Only if built with the f/n notation or w/o let-expansion in types *) + | _, LetIn (_,b,_,t) when n > 0 -> + share_names detype n l avoid env sigma c (subst1 b t) + (* If it is an open proof: we cheat and eta-expand *) + | _, Prod (na',t',c') when n > 0 -> + let t'' = detype avoid env sigma t' in + let id = next_name_away na' avoid in + let avoid = Id.Set.add id avoid and env = add_name (Name id) None t' env in + let appc = mkApp (lift 1 c,[|mkRel 1|]) in + share_names detype (n-1) ((Name id,Explicit,None,t'')::l) avoid env sigma appc c' + (* If built with the f/n notation: we renounce to share names *) + | _ -> + if n>0 then Feedback.msg_debug (strbrk "Detyping.detype: cannot factorize fix enough"); + let c = detype avoid env sigma c in + let t = detype avoid env sigma t in + (List.rev l,c,t) + +let rec share_pattern_names detype n l avoid env sigma c t = + let open Pattern in + if n = 0 then + let c = detype avoid env sigma c in + let t = detype avoid env sigma t in + (List.rev l,c,t) + else match c, t with + | PLambda (na,t,c), PProd (na',t',c') -> + let na = match (na,na') with + Name _, _ -> na + | _, Name _ -> na' + | _ -> na in + let t' = detype avoid env sigma t in + let id = next_name_away na avoid in + let avoid = Id.Set.add id avoid in + let env = Name id :: env in + share_pattern_names detype (n-1) ((Name id,Explicit,None,t')::l) avoid env sigma c c' + | _ -> + if n>0 then Feedback.msg_debug (strbrk "Detyping.detype: cannot factorize fix enough"); + let c = detype avoid env sigma c in + let t = detype avoid env sigma t in + (List.rev l,c,t) + +let detype_fix detype avoid env sigma (vn,_ as nvn) (names,tys,bodies) = + let def_avoid, def_env, lfi = + Array.fold_left2 + (fun (avoid, env, l) na ty -> + let id = next_name_away na avoid in + (Id.Set.add id avoid, add_name (Name id) None ty env, id::l)) + (avoid, env, []) names tys in + let n = Array.length tys in + let v = Array.map3 + (fun c t i -> share_names detype (i+1) [] def_avoid def_env sigma c (lift n t)) + bodies tys vn in + GRec(GFix (Array.map (fun i -> Some i, GStructRec) (fst nvn), snd nvn),Array.of_list (List.rev lfi), + Array.map (fun (bl,_,_) -> bl) v, + Array.map (fun (_,_,ty) -> ty) v, + Array.map (fun (_,bd,_) -> bd) v) + +let detype_cofix detype avoid env sigma n (names,tys,bodies) = + let def_avoid, def_env, lfi = + Array.fold_left2 + (fun (avoid, env, l) na ty -> + let id = next_name_away na avoid in + (Id.Set.add id avoid, add_name (Name id) None ty env, id::l)) + (avoid, env, []) names tys in + let ntys = Array.length tys in + let v = Array.map2 + (fun c t -> share_names detype 0 [] def_avoid def_env sigma c (lift ntys t)) + bodies tys in + GRec(GCoFix n,Array.of_list (List.rev lfi), + Array.map (fun (bl,_,_) -> bl) v, + Array.map (fun (_,_,ty) -> ty) v, + Array.map (fun (_,bd,_) -> bd) v) + let detype_universe sigma u = let fn (l, n) = Some (Termops.reference_of_level sigma l, n) in Univ.Universe.map fn u @@ -655,76 +746,8 @@ and detype_r d flags avoid env sigma t = (ci.ci_ind,ci.ci_pp_info.style, ci.ci_pp_info.cstr_tags,ci.ci_pp_info.ind_tags) p c bl - | Fix (nvn,recdef) -> detype_fix d flags avoid env sigma nvn recdef - | CoFix (n,recdef) -> detype_cofix d flags avoid env sigma n recdef - -and detype_fix d flags avoid env sigma (vn,_ as nvn) (names,tys,bodies) = - let def_avoid, def_env, lfi = - Array.fold_left2 - (fun (avoid, env, l) na ty -> - let id = next_name_away na avoid in - (Id.Set.add id avoid, add_name (Name id) None ty env, id::l)) - (avoid, env, []) names tys in - let n = Array.length tys in - let v = Array.map3 - (fun c t i -> share_names d flags (i+1) [] def_avoid def_env sigma c (lift n t)) - bodies tys vn in - GRec(GFix (Array.map (fun i -> Some i, GStructRec) (fst nvn), snd nvn),Array.of_list (List.rev lfi), - Array.map (fun (bl,_,_) -> bl) v, - Array.map (fun (_,_,ty) -> ty) v, - Array.map (fun (_,bd,_) -> bd) v) - -and detype_cofix d flags avoid env sigma n (names,tys,bodies) = - let def_avoid, def_env, lfi = - Array.fold_left2 - (fun (avoid, env, l) na ty -> - let id = next_name_away na avoid in - (Id.Set.add id avoid, add_name (Name id) None ty env, id::l)) - (avoid, env, []) names tys in - let ntys = Array.length tys in - let v = Array.map2 - (fun c t -> share_names d flags 0 [] def_avoid def_env sigma c (lift ntys t)) - bodies tys in - GRec(GCoFix n,Array.of_list (List.rev lfi), - Array.map (fun (bl,_,_) -> bl) v, - Array.map (fun (_,_,ty) -> ty) v, - Array.map (fun (_,bd,_) -> bd) v) - -and share_names d flags n l avoid env sigma c t = - match EConstr.kind sigma c, EConstr.kind sigma t with - (* factorize even when not necessary to have better presentation *) - | Lambda (na,t,c), Prod (na',t',c') -> - let na = match (na,na') with - Name _, _ -> na - | _, Name _ -> na' - | _ -> na in - let t' = detype d flags avoid env sigma t in - let id = next_name_away na avoid in - let avoid = Id.Set.add id avoid and env = add_name (Name id) None t env in - share_names d flags (n-1) ((Name id,Explicit,None,t')::l) avoid env sigma c c' - (* May occur for fix built interactively *) - | LetIn (na,b,t',c), _ when n > 0 -> - let t'' = detype d flags avoid env sigma t' in - let b' = detype d flags avoid env sigma b in - let id = next_name_away na avoid in - let avoid = Id.Set. add id avoid and env = add_name (Name id) (Some b) t' env in - share_names d flags n ((Name id,Explicit,Some b',t'')::l) avoid env sigma c (lift 1 t) - (* Only if built with the f/n notation or w/o let-expansion in types *) - | _, LetIn (_,b,_,t) when n > 0 -> - share_names d flags n l avoid env sigma c (subst1 b t) - (* If it is an open proof: we cheat and eta-expand *) - | _, Prod (na',t',c') when n > 0 -> - let t'' = detype d flags avoid env sigma t' in - let id = next_name_away na' avoid in - let avoid = Id.Set.add id avoid and env = add_name (Name id) None t' env in - let appc = mkApp (lift 1 c,[|mkRel 1|]) in - share_names d flags (n-1) ((Name id,Explicit,None,t'')::l) avoid env sigma appc c' - (* If built with the f/n notation: we renounce to share names *) - | _ -> - if n>0 then Feedback.msg_debug (strbrk "Detyping.detype: cannot factorize fix enough"); - let c = detype d flags avoid env sigma c in - let t = detype d flags avoid env sigma t in - (List.rev l,c,t) + | Fix (nvn,recdef) -> detype_fix (detype d flags) avoid env sigma nvn recdef + | CoFix (n,recdef) -> detype_cofix (detype d flags) avoid env sigma n recdef and detype_eqns d flags avoid env sigma ci computable constructs consnargsl bl = try diff --git a/pretyping/detyping.mli b/pretyping/detyping.mli index 32b94e1b0..817b8ba6e 100644 --- a/pretyping/detyping.mli +++ b/pretyping/detyping.mli @@ -56,6 +56,13 @@ val detype_sort : evar_map -> Sorts.t -> glob_sort val detype_rel_context : 'a delay -> ?lax:bool -> constr option -> Id.Set.t -> (names_context * env) -> evar_map -> rel_context -> 'a glob_decl_g list +val share_pattern_names : + (Id.Set.t -> names_context -> 'c -> Pattern.constr_pattern -> 'a) -> int -> + (Name.t * Decl_kinds.binding_kind * 'b option * 'a) list -> + Id.Set.t -> names_context -> 'c -> Pattern.constr_pattern -> + Pattern.constr_pattern -> + (Name.t * Decl_kinds.binding_kind * 'b option * 'a) list * 'a * 'a + val detype_closed_glob : ?lax:bool -> bool -> Id.Set.t -> env -> evar_map -> closed_glob_constr -> glob_constr (** look for the index of a named var or a nondep var as it is renamed *) diff --git a/pretyping/glob_ops.ml b/pretyping/glob_ops.ml index 74f2cefab..e89bbf7c3 100644 --- a/pretyping/glob_ops.ml +++ b/pretyping/glob_ops.ml @@ -136,7 +136,7 @@ let mk_glob_constr_eq f c1 c2 = match DAst.get c1, DAst.get c2 with | GIf (m1, (pat1, p1), c1, t1), GIf (m2, (pat2, p2), c2, t2) -> f m1 m2 && Name.equal pat1 pat2 && Option.equal f p1 p2 && f c1 c2 && f t1 t2 - | GRec (kn1, id1, decl1, c1, t1), GRec (kn2, id2, decl2, c2, t2) -> + | GRec (kn1, id1, decl1, t1, c1), GRec (kn2, id2, decl2, t2, c2) -> fix_kind_eq f kn1 kn2 && Array.equal Id.equal id1 id2 && Array.equal (fun l1 l2 -> List.equal (glob_decl_eq f) l1 l2) decl1 decl2 && Array.equal f c1 c2 && Array.equal f t1 t2 diff --git a/pretyping/patternops.ml b/pretyping/patternops.ml index dcb93bfb6..e52112fda 100644 --- a/pretyping/patternops.ml +++ b/pretyping/patternops.ml @@ -15,7 +15,6 @@ open Globnames open Nameops open Term open Constr -open Vars open Glob_term open Pp open Mod_subst @@ -57,10 +56,10 @@ let rec constr_pattern_eq p1 p2 = match p1, p2 with constr_pattern_eq p1 p2 && constr_pattern_eq r1 r2 && List.equal pattern_eq l1 l2 -| PFix f1, PFix f2 -> - fixpoint_eq f1 f2 -| PCoFix f1, PCoFix f2 -> - cofixpoint_eq f1 f2 +| PFix ((ln1,i1),f1), PFix ((ln2,i2),f2) -> + Array.equal Int.equal ln1 ln2 && Int.equal i1 i2 && rec_declaration_eq f1 f2 +| PCoFix (i1,f1), PCoFix (i2,f2) -> + Int.equal i1 i2 && rec_declaration_eq f1 f2 | PProj (p1, t1), PProj (p2, t2) -> Projection.equal p1 p2 && constr_pattern_eq t1 t2 | (PRef _ | PVar _ | PEvar _ | PRel _ | PApp _ | PSoApp _ @@ -71,19 +70,10 @@ let rec constr_pattern_eq p1 p2 = match p1, p2 with and pattern_eq (i1, j1, p1) (i2, j2, p2) = Int.equal i1 i2 && List.equal (==) j1 j2 && constr_pattern_eq p1 p2 -and fixpoint_eq ((arg1, i1), r1) ((arg2, i2), r2) = - Int.equal i1 i2 && - Array.equal Int.equal arg1 arg2 && - rec_declaration_eq r1 r2 - -and cofixpoint_eq (i1, r1) (i2, r2) = - Int.equal i1 i2 && - rec_declaration_eq r1 r2 - and rec_declaration_eq (n1, c1, r1) (n2, c2, r2) = Array.equal Name.equal n1 n2 && - Array.equal Constr.equal c1 c2 && - Array.equal Constr.equal r1 r2 + Array.equal constr_pattern_eq c1 c2 && + Array.equal constr_pattern_eq r1 r2 let rec occur_meta_pattern = function | PApp (f,args) -> @@ -123,8 +113,10 @@ let rec occurn_pattern n = function | PMeta _ | PSoApp _ -> true | PEvar (_,args) -> Array.exists (occurn_pattern n) args | PVar _ | PRef _ | PSort _ -> false - | PFix fix -> not (noccurn n (mkFix fix)) - | PCoFix cofix -> not (noccurn n (mkCoFix cofix)) + | PFix (_,(_,tl,bl)) -> + Array.exists (occurn_pattern n) tl || Array.exists (occurn_pattern (n+Array.length tl)) bl + | PCoFix (_,(_,tl,bl)) -> + Array.exists (occurn_pattern n) tl || Array.exists (occurn_pattern (n+Array.length tl)) bl let noccurn_pattern n c = not (occurn_pattern n c) @@ -209,8 +201,16 @@ let pattern_of_constr env sigma t = in PCase (cip, pattern_of_constr env p, pattern_of_constr env a, Array.to_list (Array.mapi branch_of_constr br)) - | Fix f -> PFix f - | CoFix f -> PCoFix f in + | Fix (lni,(lna,tl,bl)) -> + let push env na2 c2 = push_rel (LocalAssum (na2,c2)) env in + let env' = Array.fold_left2 push env lna tl in + PFix (lni,(lna,Array.map (pattern_of_constr env) tl, + Array.map (pattern_of_constr env') bl)) + | CoFix (ln,(lna,tl,bl)) -> + let push env na2 c2 = push_rel (LocalAssum (na2,c2)) env in + let env' = Array.fold_left2 push env lna tl in + PCoFix (ln,(lna,Array.map (pattern_of_constr env) tl, + Array.map (pattern_of_constr env') bl)) in pattern_of_constr env t (* To process patterns, we need a translation without typing at all. *) @@ -225,10 +225,14 @@ let map_pattern_with_binders g f l = function | PCase (ci,po,p,pl) -> PCase (ci,f l po,f l p, List.map (fun (i,n,c) -> (i,n,f l c)) pl) | PProj (p,pc) -> PProj (p, f l pc) + | PFix (lni,(lna,tl,bl)) -> + let l' = Array.fold_left (fun l na -> g na l) l lna in + PFix (lni,(lna,Array.map (f l) tl,Array.map (f l') bl)) + | PCoFix (ln,(lna,tl,bl)) -> + let l' = Array.fold_left (fun l na -> g na l) l lna in + PCoFix (ln,(lna,Array.map (f l) tl,Array.map (f l') bl)) (* Non recursive *) - | (PVar _ | PEvar _ | PRel _ | PRef _ | PSort _ | PMeta _ - (* Bound to terms *) - | PFix _ | PCoFix _ as x) -> x + | (PVar _ | PEvar _ | PRel _ | PRef _ | PSort _ | PMeta _ as x) -> x let error_instantiate_pattern id l = let is = match l with @@ -262,15 +266,12 @@ let instantiate_pattern env sigma lvar c = error_instantiate_pattern id (List.subtract Id.equal ctx vars) with Not_found (* Map.find failed *) -> x) - | (PFix _ | PCoFix _) -> user_err Pp.(str "Non instantiable pattern.") | c -> map_pattern_with_binders (fun id vars -> id::vars) aux vars c in aux [] c let rec liftn_pattern k n = function | PRel i as x -> if i >= n then PRel (i+k) else x - | PFix x -> PFix (destFix (liftn k n (mkFix x))) - | PCoFix x -> PCoFix (destCoFix (liftn k n (mkCoFix x))) | c -> map_pattern_with_binders (fun _ -> succ) (liftn_pattern k) n c let lift_pattern k = liftn_pattern k 1 @@ -337,19 +338,35 @@ let rec subst_pattern subst pat = if cip' == cip && typ' == typ && c' == c && branches' == branches then pat else PCase(cip', typ', c', branches') - | PFix fixpoint -> - let cstr = mkFix fixpoint in - let fixpoint' = destFix (subst_mps subst cstr) in - if fixpoint' == fixpoint then pat else - PFix fixpoint' - | PCoFix cofixpoint -> - let cstr = mkCoFix cofixpoint in - let cofixpoint' = destCoFix (subst_mps subst cstr) in - if cofixpoint' == cofixpoint then pat else - PCoFix cofixpoint' - -let mkPLambda na b = PLambda(na,PMeta None,b) -let rev_it_mkPLambda = List.fold_right mkPLambda + | PFix (lni,(lna,tl,bl)) -> + let tl' = Array.smartmap (subst_pattern subst) tl in + let bl' = Array.smartmap (subst_pattern subst) bl in + if bl' == bl && tl' == tl then pat + else PFix (lni,(lna,tl',bl')) + | PCoFix (ln,(lna,tl,bl)) -> + let tl' = Array.smartmap (subst_pattern subst) tl in + let bl' = Array.smartmap (subst_pattern subst) bl in + if bl' == bl && tl' == tl then pat + else PCoFix (ln,(lna,tl',bl')) + +let mkPLetIn na b t c = PLetIn(na,b,t,c) +let mkPProd na t u = PProd(na,t,u) +let mkPLambda na t b = PLambda(na,t,b) +let mkPLambdaUntyped na b = PLambda(na,PMeta None,b) +let rev_it_mkPLambdaUntyped = List.fold_right mkPLambdaUntyped + +let mkPProd_or_LetIn (na,_,bo,t) c = + match bo with + | None -> mkPProd na t c + | Some b -> mkPLetIn na b (Some t) c + +let mkPLambda_or_LetIn (na,_,bo,t) c = + match bo with + | None -> mkPLambda na t c + | Some b -> mkPLetIn na b (Some t) c + +let it_mkPProd_or_LetIn = List.fold_left (fun c d -> mkPProd_or_LetIn d c) +let it_mkPLambda_or_LetIn = List.fold_left (fun c d -> mkPLambda_or_LetIn d c) let err ?loc pp = user_err ?loc ~hdr:"pattern_of_glob_constr" pp @@ -428,7 +445,7 @@ let rec pat_of_raw metas vars = DAst.with_loc_val (fun ?loc -> function let pred = match p,indnames with | Some p, Some {CAst.v=(_,nal)} -> let nvars = na :: List.rev nal @ vars in - rev_it_mkPLambda nal (mkPLambda na (pat_of_raw metas nvars p)) + rev_it_mkPLambdaUntyped nal (mkPLambdaUntyped na (pat_of_raw metas nvars p)) | None, _ -> PMeta None | Some p, None -> match DAst.get p with @@ -450,9 +467,40 @@ let rec pat_of_raw metas vars = DAst.with_loc_val (fun ?loc -> function | GProj(p,c) -> PProj(p, pat_of_raw metas vars c) - | GPatVar _ | GIf _ | GLetTuple _ | GCases _ | GEvar _ | GRec _ -> + | GRec (GFix (ln,n), ids, decls, tl, cl) -> + if Array.exists (function (Some n, GStructRec) -> false | _ -> true) ln then + err ?loc (Pp.str "\"struct\" annotation is expected.") + else + let ln = Array.map (fst %> Option.get) ln in + let ctxtl = Array.map2 (pat_of_glob_in_context metas vars) decls tl in + let tl = Array.map (fun (ctx,tl) -> it_mkPProd_or_LetIn tl ctx) ctxtl in + let vars = Array.fold_left (fun vars na -> Name na::vars) vars ids in + let ctxtl = Array.map2 (pat_of_glob_in_context metas vars) decls cl in + let cl = Array.map (fun (ctx,cl) -> it_mkPLambda_or_LetIn cl ctx) ctxtl in + let names = Array.map (fun id -> Name id) ids in + PFix ((ln,n), (names, tl, cl)) + + | GRec (GCoFix n, ids, decls, tl, cl) -> + let ctxtl = Array.map2 (pat_of_glob_in_context metas vars) decls tl in + let tl = Array.map (fun (ctx,tl) -> it_mkPProd_or_LetIn tl ctx) ctxtl in + let vars = Array.fold_left (fun vars na -> Name na::vars) vars ids in + let ctxtl = Array.map2 (pat_of_glob_in_context metas vars) decls cl in + let cl = Array.map (fun (ctx,cl) -> it_mkPLambda_or_LetIn cl ctx) ctxtl in + let names = Array.map (fun id -> Name id) ids in + PCoFix (n, (names, tl, cl)) + + | GPatVar _ | GIf _ | GLetTuple _ | GCases _ | GEvar _ -> err ?loc (Pp.str "Non supported pattern.")) +and pat_of_glob_in_context metas vars decls c = + let rec aux acc vars = function + | (na,bk,b,t) :: decls -> + let decl = (na,bk,Option.map (pat_of_raw metas vars) b,pat_of_raw metas vars t) in + aux (decl::acc) (na::vars) decls + | [] -> + acc, pat_of_raw metas vars c + in aux [] vars decls + and pats_of_glob_branches loc metas vars ind brs = let get_arg p = match DAst.get p with | PatVar na -> @@ -477,7 +525,7 @@ and pats_of_glob_branches loc metas vars ind brs = (str "No unique branch for " ++ int j ++ str"-th constructor."); let lna = List.map get_arg lv in let vars' = List.rev lna @ vars in - let pat = rev_it_mkPLambda lna (pat_of_raw metas vars' br) in + let pat = rev_it_mkPLambdaUntyped lna (pat_of_raw metas vars' br) in let ext,pats = get_pat (Int.Set.add (j-1) indexes) brs in let tags = List.map (fun _ -> false) lv (* approximation, w/o let-in *) in ext, ((j-1, tags, pat) :: pats) diff --git a/printing/ppvernac.ml b/printing/ppvernac.ml index 7df0a0c94..7eb8396ac 100644 --- a/printing/ppvernac.ml +++ b/printing/ppvernac.ml @@ -155,13 +155,6 @@ open Decl_kinds let pr_locality local = if local then keyword "Local" else keyword "Global" - let pr_explanation (e,b,f) = - let a = match e with - | ExplByPos (n,_) -> anomaly (Pp.str "No more supported.") - | ExplByName id -> pr_id id in - let a = if f then str"!" ++ a else a in - if b then str "[" ++ a ++ str "]" else a - let pr_option_ref_value = function | QualidRefValue id -> pr_reference id | StringRefValue s -> qs s @@ -591,8 +584,6 @@ open Decl_kinds ) | VernacUndoTo i -> return (keyword "Undo" ++ spc() ++ keyword "To" ++ pr_intarg i) - | VernacBacktrack (i,j,k) -> - return (keyword "Backtrack" ++ spc() ++ prlist_with_sep sep int [i;j;k]) | VernacFocus i -> return (keyword "Focus" ++ pr_opt int i) | VernacShow s -> @@ -653,16 +644,6 @@ open Decl_kinds keyword "Bind Scope" ++ spc () ++ str sc ++ spc() ++ keyword "with" ++ spc () ++ prlist_with_sep spc pr_class_rawexpr cll ) - | VernacArgumentsScope (q,scl) -> - let pr_opt_scope = function - | None -> str"_" - | Some sc -> str sc - in - return ( - keyword "Arguments Scope" - ++ spc() ++ pr_smart_global q - ++ spc() ++ str"[" ++ prlist_with_sep sep pr_opt_scope scl ++ str"]" - ) | VernacInfix (({v=s},mv),q,sn) -> (* A Verifier *) return ( hov 0 (hov 0 (keyword "Infix " @@ -786,8 +767,9 @@ open Decl_kinds if p then let cm = match cum with - | GlobalCumulativity | LocalCumulativity -> "Cumulative" - | GlobalNonCumulativity | LocalNonCumulativity -> "NonCumulative" + | Some VernacCumulative -> "Cumulative" + | Some VernacNonCumulative -> "NonCumulative" + | None -> "" in cm ^ " " ^ kind else kind @@ -1016,18 +998,6 @@ open Decl_kinds | Some Flags.Current -> [SetOnlyParsing] | Some v -> [SetCompatVersion v])) ) - | VernacDeclareImplicits (q,[]) -> - return ( - hov 2 (keyword "Implicit Arguments" ++ spc() ++ pr_smart_global q) - ) - | VernacDeclareImplicits (q,impls) -> - return ( - hov 1 (keyword "Implicit Arguments" ++ spc () ++ - spc() ++ pr_smart_global q ++ spc() ++ - prlist_with_sep spc (fun imps -> - str"[" ++ prlist_with_sep sep pr_explanation imps ++ str"]") - impls) - ) | VernacArguments (q, args, more_implicits, nargs, mods) -> return ( hov 2 ( diff --git a/stm/stm.ml b/stm/stm.ml index 4b49d1998..ba0a2017a 100644 --- a/stm/stm.ml +++ b/stm/stm.ml @@ -1072,7 +1072,7 @@ let stm_vernac_interp ?proof ?route id st { verbose; loc; expr } : Vernacstate.t let is_filtered_command = function | VernacResetName _ | VernacResetInitial | VernacBack _ | VernacBackTo _ | VernacRestart | VernacUndo _ | VernacUndoTo _ - | VernacBacktrack _ | VernacAbortAll | VernacAbort _ -> true + | VernacAbortAll | VernacAbort _ -> true | _ -> false in let aux_interp st expr = @@ -1097,7 +1097,6 @@ let stm_vernac_interp ?proof ?route id st { verbose; loc; expr } : Vernacstate.t module Backtrack : sig val record : unit -> unit - val backto : Stateid.t -> unit (* we could navigate the dag, but this ways easy *) val branches_of : Stateid.t -> backup @@ -1122,14 +1121,6 @@ end = struct (* {{{ *) info.vcs_backup <- backup, branches) [VCS.current_branch (); VCS.Branch.master] - let backto oid = - let info = VCS.get_info oid in - match info.vcs_backup with - | None, _ -> - anomaly Pp.(str"Backtrack.backto "++str(Stateid.to_string oid)++ - str": a state with no vcs_backup.") - | Some vcs, _ -> VCS.restore vcs - let branches_of id = let info = VCS.get_info id in match info.vcs_backup with @@ -1220,7 +1211,6 @@ end = struct (* {{{ *) match Vcs_.branches vcs with [_] -> `Stop id | _ -> `Cont ()) () id in oid, VtLater - | VernacBacktrack (id,_,_) | VernacBackTo id -> Stateid.of_int id, VtNow | _ -> anomaly Pp.(str "incorrect VtMeta classification") @@ -2757,9 +2747,7 @@ let snapshot_vio ~doc ldir long_f_dot_vo = let reset_task_queue = Slaves.reset_task_queue (* Document building *) -let process_back_meta_command ~part_of_script ~newtip ~head oid aast w = - match part_of_script, w with - | true, w -> +let process_back_meta_command ~newtip ~head oid aast w = let id = VCS.new_node ~id:newtip () in let { mine; others } = Backtrack.branches_of oid in let valid = VCS.get_branch_pos head in @@ -2779,16 +2767,7 @@ let process_back_meta_command ~part_of_script ~newtip ~head oid aast w = VCS.commit id (Alias (oid,aast)); Backtrack.record (); if w == VtNow then ignore(finish ~doc:dummy_doc); `Ok - | false, VtNow -> - stm_prerr_endline (fun () -> "undo to state " ^ Stateid.to_string oid); - Backtrack.backto oid; - VCS.checkout_shallowest_proof_branch (); - Reach.known_state ~cache:(VCS.is_interactive ()) oid; `Ok - - | false, VtLater -> - anomaly(str"undo classifier: VtMeta + VtLater must imply part_of_script.") - -let process_transaction ?(newtip=Stateid.fresh ()) ?(part_of_script=true) +let process_transaction ?(newtip=Stateid.fresh ()) ({ verbose; loc; expr } as x) c = stm_pperr_endline (fun () -> str "{{{ processing: " ++ pr_ast x); let vcs = VCS.backup () in @@ -2802,22 +2781,10 @@ let process_transaction ?(newtip=Stateid.fresh ()) ?(part_of_script=true) (* Meta *) | VtMeta, _ -> let id, w = Backtrack.undo_vernac_classifier expr in - (* Special case Backtrack, as it is never part of a script. See #6240 *) - let part_of_script = begin match Vernacprop.under_control expr with - | VernacBacktrack _ -> false - | _ -> part_of_script - end in - process_back_meta_command ~part_of_script ~newtip ~head id x w + process_back_meta_command ~newtip ~head id x w + (* Query *) - | VtQuery (false,route), VtNow -> - let query_sid = VCS.cur_tip () in - (try - let st = Vernacstate.freeze_interp_state `No in - ignore(stm_vernac_interp ~route query_sid st x) - with e -> - let e = CErrors.push e in - Exninfo.iraise (State.exn_on ~valid:Stateid.dummy query_sid e)); `Ok - | VtQuery (true, route), w -> + | VtQuery, w -> let id = VCS.new_node ~id:newtip () in let queue = if !cur_opt.async_proofs_full then `QueryQueue (ref false) @@ -2829,9 +2796,6 @@ let process_transaction ?(newtip=Stateid.fresh ()) ?(part_of_script=true) VCS.commit id (mkTransCmd x [] false queue); Backtrack.record (); if w == VtNow then ignore(finish ~doc:dummy_doc); `Ok - | VtQuery (false,_), VtLater -> - anomaly(str"classifier: VtQuery + VtLater must imply part_of_script.") - (* Proof *) | VtStartProof (mode, guarantee, names), w -> let id = VCS.new_node ~id:newtip () in @@ -2884,18 +2848,22 @@ let process_transaction ?(newtip=Stateid.fresh ()) ?(part_of_script=true) Backtrack.record (); if w == VtNow then ignore(finish ~doc:dummy_doc); rc - (* Side effect on all branches *) + (* Side effect in a (still open) proof is replayed on all branches*) | VtSideff l, w -> - let in_proof = not (VCS.Branch.equal head VCS.Branch.master) in let id = VCS.new_node ~id:newtip () in - VCS.checkout VCS.Branch.master; - VCS.commit id (mkTransCmd x l in_proof `MainQueue); - (* We can't replay a Definition since universes may be differently - * inferred. This holds in Coq >= 8.5 *) - let action = match Vernacprop.under_control x.expr with - | VernacDefinition(_, _, DefineBody _) -> CherryPickEnv - | _ -> ReplayCommand x in - VCS.propagate_sideff ~action; + begin match (VCS.get_branch head).VCS.kind with + | `Edit _ -> VCS.commit id (mkTransCmd x l true `MainQueue); + | `Master -> VCS.commit id (mkTransCmd x l false `MainQueue); + | `Proof _ -> + VCS.checkout VCS.Branch.master; + VCS.commit id (mkTransCmd x l true `MainQueue); + (* We can't replay a Definition since universes may be differently + * inferred. This holds in Coq >= 8.5 *) + let action = match Vernacprop.under_control x.expr with + | VernacDefinition(_, _, DefineBody _) -> CherryPickEnv + | _ -> ReplayCommand x in + VCS.propagate_sideff ~action; + end; VCS.checkout_shallowest_proof_branch (); Backtrack.record (); if w == VtNow then ignore(finish ~doc:dummy_doc); `Ok @@ -2924,9 +2892,14 @@ let process_transaction ?(newtip=Stateid.fresh ()) ?(part_of_script=true) VCS.branch bname (`Proof (proof_mode, VCS.proof_nesting () + 1)); Proof_global.activate_proof_mode proof_mode [@ocaml.warning "-3"]; end else begin - VCS.commit id (mkTransCmd x [] in_proof `MainQueue); - (* We hope it can be replayed, but we can't really know *) - VCS.propagate_sideff ~action:(ReplayCommand x); + begin match (VCS.get_branch head).VCS.kind with + | `Edit _ -> VCS.commit id (mkTransCmd x [] in_proof `MainQueue); + | `Master -> VCS.commit id (mkTransCmd x [] in_proof `MainQueue); + | `Proof _ -> + VCS.commit id (mkTransCmd x [] in_proof `MainQueue); + (* We hope it can be replayed, but we can't really know *) + VCS.propagate_sideff ~action:(ReplayCommand x); + end; VCS.checkout_shallowest_proof_branch (); end in State.define ~safe_id:head_id ~cache:`Yes step id; @@ -3065,13 +3038,9 @@ let query ~doc ~at ~route s = let { CAst.loc; v=ast } = parse_sentence ~doc at s in let indentation, strlen = compute_indentation ?loc at in CWarnings.set_current_loc loc; - let clas = Vernac_classifier.classify_vernac ast in + let st = State.get_cached at in let aast = { verbose = true; indentation; strlen; loc; expr = ast } in - match clas with - | VtMeta , _ -> (* TODO: can this still happen ? *) - ignore(process_transaction ~part_of_script:false aast (VtMeta,VtNow)) - | _ -> - ignore(process_transaction aast (VtQuery (false,route), VtNow)) + ignore(stm_vernac_interp ~route at st aast) done; with | End_of_input -> () diff --git a/stm/stm.mli b/stm/stm.mli index a8eb10fb3..7a720aa72 100644 --- a/stm/stm.mli +++ b/stm/stm.mli @@ -39,14 +39,25 @@ module AsyncOpts : sig end -(** The STM doc type determines some properties such as what - uncompleted proofs are allowed and recording of aux files. *) +(** The STM document type [stm_doc_type] determines some properties + such as what uncompleted proofs are allowed and what gets recorded + to aux files. *) type stm_doc_type = - | VoDoc of string - | VioDoc of string - | Interactive of DirPath.t + | VoDoc of string (* file path *) + | VioDoc of string (* file path *) + | Interactive of DirPath.t (* module path *) -(* Main initalization routine *) +(** Coq initalization options: + + - [doc_type]: Type of document being created. + + - [require_libs]: list of libraries/modules to be pre-loaded at + startup. A tuple [(modname,modfrom,import)] is equivalent to [From + modfrom Require modname]; [import] works similarly to + [Library.require_library_from_dirpath], [Some false] will import + the module, [Some true] will additionally export it. + +*) type stm_init_options = { (* The STM will set some internal flags differently depending on the specified [doc_type]. This distinction should dissappear at some @@ -72,12 +83,14 @@ type stm_init_options = { (** The type of a STM document *) type doc +(** [init_core] performs some low-level initalization; should go away + in future releases. *) val init_core : unit -> unit -(* Starts a new document *) +(** [new_doc opt] Creates a new document with options [opt] *) val new_doc : stm_init_options -> doc * Stateid.t -(* [parse_sentence sid pa] Reads a sentence from [pa] with parsing +(** [parse_sentence sid pa] Reads a sentence from [pa] with parsing state [sid] Returns [End_of_input] if the stream ends *) val parse_sentence : doc:doc -> Stateid.t -> Pcoq.Gram.coq_parsable -> Vernacexpr.vernac_control CAst.t @@ -115,14 +128,15 @@ val query : doc:doc -> type focus = { start : Stateid.t; stop : Stateid.t; tip : Stateid.t } val edit_at : doc:doc -> Stateid.t -> doc * [ `NewTip | `Focus of focus ] -(* Evaluates the tip of the current branch *) +(* [observe doc sid]] Check / execute span [sid] *) +val observe : doc:doc -> Stateid.t -> doc + +(* [finish doc] Fully checks a document up to the "current" tip. *) val finish : doc:doc -> doc (* Internal use (fake_ide) only, do not use *) val wait : doc:doc -> doc -val observe : doc:doc -> Stateid.t -> doc - val stop_worker : string -> unit (* Joins the entire document. Implies finish, but also checks proofs *) diff --git a/stm/vernac_classifier.ml b/stm/vernac_classifier.ml index 9a8af3a58..c08cc6e36 100644 --- a/stm/vernac_classifier.ml +++ b/stm/vernac_classifier.ml @@ -16,8 +16,6 @@ open Vernacexpr let default_proof_mode () = Proof_global.get_default_proof_mode_name () [@ocaml.warning "-3"] -let string_of_in_script b = if b then " (inside script)" else "" - let string_of_parallel = function | `Yes (solve,abs) -> "par" ^ if solve then "solve" else "" ^ if abs then "abs" else "" @@ -34,7 +32,7 @@ let string_of_vernac_type = function "ProofStep " ^ string_of_parallel parallel ^ Option.default "" proof_block_detection | VtProofMode s -> "ProofMode " ^ s - | VtQuery (b, route) -> "Query " ^ string_of_in_script b ^ " route " ^ string_of_int route + | VtQuery -> "Query" | VtMeta -> "Meta " let string_of_vernac_when = function @@ -70,7 +68,7 @@ let classify_vernac e = | VernacEndProof _ | VernacExactProof _ -> VtQed VtKeep, VtLater (* Query *) | VernacShow _ | VernacPrint _ | VernacSearch _ | VernacLocate _ - | VernacCheckMayEval _ -> VtQuery (true,Feedback.default_route), VtLater + | VernacCheckMayEval _ -> VtQuery, VtLater (* ProofStep *) | VernacProof _ | VernacFocus _ | VernacUnfocus @@ -145,7 +143,7 @@ let classify_vernac e = | VernacAddLoadPath _ | VernacRemoveLoadPath _ | VernacAddMLPath _ | VernacChdir _ | VernacCreateHintDb _ | VernacRemoveHints _ | VernacHints _ - | VernacDeclareImplicits _ | VernacArguments _ | VernacArgumentsScope _ + | VernacArguments _ | VernacReserve _ | VernacGeneralizable _ | VernacSetOpacity _ | VernacSetStrategy _ @@ -183,7 +181,7 @@ let classify_vernac e = | VernacBack _ | VernacAbortAll | VernacUndoTo _ | VernacUndo _ | VernacResetName _ | VernacResetInitial - | VernacBacktrack _ | VernacBackTo _ | VernacRestart -> VtMeta, VtNow + | VernacBackTo _ | VernacRestart -> VtMeta, VtNow (* What are these? *) | VernacRestoreState _ | VernacWriteState _ -> VtSideff [], VtNow @@ -205,7 +203,7 @@ let classify_vernac e = static_control_classifier ~poly e | VernacFail e -> (* Fail Qed or Fail Lemma must not join/fork the DAG *) (match static_control_classifier ~poly e with - | ( VtQuery _ | VtProofStep _ | VtSideff _ + | ( VtQuery | VtProofStep _ | VtSideff _ | VtProofMode _ | VtMeta), _ as x -> x | VtQed _, _ -> VtProofStep { parallel = `No; proof_block_detection = None }, @@ -214,6 +212,6 @@ let classify_vernac e = in static_control_classifier ~poly:(Flags.is_universe_polymorphism ()) e -let classify_as_query = VtQuery (true,Feedback.default_route), VtLater +let classify_as_query = VtQuery, VtLater let classify_as_sideeff = VtSideff [], VtLater let classify_as_proofstep = VtProofStep { parallel = `No; proof_block_detection = None}, VtLater diff --git a/tactics/equality.mli b/tactics/equality.mli index c0be917a0..ccf454c3e 100644 --- a/tactics/equality.mli +++ b/tactics/equality.mli @@ -80,20 +80,20 @@ val discrConcl : unit Proofview.tactic val discrHyp : Id.t -> unit Proofview.tactic val discrEverywhere : evars_flag -> unit Proofview.tactic val discr_tac : evars_flag -> - constr with_bindings destruction_arg option -> unit Proofview.tactic + constr with_bindings Tactics.destruction_arg option -> unit Proofview.tactic (* Below, if flag is [None], it takes the value from the dynamic value of the option *) val inj : inj_flags option -> intro_patterns option -> evars_flag -> clear_flag -> constr with_bindings -> unit Proofview.tactic val injClause : inj_flags option -> intro_patterns option -> evars_flag -> - constr with_bindings destruction_arg option -> unit Proofview.tactic + constr with_bindings Tactics.destruction_arg option -> unit Proofview.tactic val injHyp : inj_flags option -> clear_flag -> Id.t -> unit Proofview.tactic val injConcl : inj_flags option -> unit Proofview.tactic val simpleInjClause : inj_flags option -> evars_flag -> - constr with_bindings destruction_arg option -> unit Proofview.tactic + constr with_bindings Tactics.destruction_arg option -> unit Proofview.tactic -val dEq : keep_proofs:(bool option) -> evars_flag -> constr with_bindings destruction_arg option -> unit Proofview.tactic -val dEqThen : keep_proofs:(bool option) -> evars_flag -> (clear_flag -> constr -> int -> unit Proofview.tactic) -> constr with_bindings destruction_arg option -> unit Proofview.tactic +val dEq : keep_proofs:(bool option) -> evars_flag -> constr with_bindings Tactics.destruction_arg option -> unit Proofview.tactic +val dEqThen : keep_proofs:(bool option) -> evars_flag -> (clear_flag -> constr -> int -> unit Proofview.tactic) -> constr with_bindings Tactics.destruction_arg option -> unit Proofview.tactic val make_iterated_tuple : env -> evar_map -> constr -> (constr * types) -> evar_map * (constr * constr * constr) diff --git a/tactics/inv.ml b/tactics/inv.ml index 067fc8941..d76c9a697 100644 --- a/tactics/inv.ml +++ b/tactics/inv.ml @@ -64,6 +64,11 @@ let var_occurs_in_pf gl id = type inversion_status = Dep of constr option | NoDep +type inversion_kind = + | SimpleInversion + | FullInversion + | FullInversionClear + let compute_eqn env sigma n i ai = (mkRel (n-i),get_type_of env sigma (mkRel (n-i))) diff --git a/tactics/inv.mli b/tactics/inv.mli index c63d57af5..9d4ffdd7b 100644 --- a/tactics/inv.mli +++ b/tactics/inv.mli @@ -15,6 +15,11 @@ open Tactypes type inversion_status = Dep of constr option | NoDep +type inversion_kind = + | SimpleInversion + | FullInversion + | FullInversionClear + val inv_clause : inversion_kind -> or_and_intro_pattern option -> Id.t list -> quantified_hypothesis -> unit Proofview.tactic diff --git a/tactics/tacticals.ml b/tactics/tacticals.ml index 958a205a1..a97ae8f65 100644 --- a/tactics/tacticals.ml +++ b/tactics/tacticals.ml @@ -369,9 +369,36 @@ module New = struct tclTHENSFIRSTn t1 l (tclUNIT()) let tclTHENFIRST t1 t2 = tclTHENFIRSTn t1 [|t2|] + + let tclBINDFIRST t1 t2 = + t1 >>= fun ans -> + Proofview.Unsafe.tclGETGOALS >>= fun gls -> + match gls with + | [] -> tclFAIL 0 (str "Expect at least one goal.") + | hd::tl -> + Proofview.Unsafe.tclSETGOALS [hd] <*> t2 ans >>= fun ans -> + Proofview.Unsafe.tclNEWGOALS tl <*> + Proofview.tclUNIT ans + let tclTHENLASTn t1 l = tclTHENS3PARTS t1 [||] (tclUNIT()) l let tclTHENLAST t1 t2 = tclTHENLASTn t1 [|t2|] + + let option_of_failure f x = try Some (f x) with Failure _ -> None + + let tclBINDLAST t1 t2 = + t1 >>= fun ans -> + Proofview.Unsafe.tclGETGOALS >>= fun gls -> + match option_of_failure List.sep_last gls with + | None -> tclFAIL 0 (str "Expect at least one goal.") + | Some (last,firstn) -> + Proofview.Unsafe.tclSETGOALS [last] <*> t2 ans >>= fun ans -> + Proofview.Unsafe.tclGETGOALS >>= fun newgls -> + tclEVARMAP >>= fun sigma -> + let firstn = Proofview.Unsafe.undefined sigma firstn in + Proofview.Unsafe.tclSETGOALS (firstn@newgls) <*> + Proofview.tclUNIT ans + let tclTHENS t l = tclINDEPENDENT begin t <*>Proofview.tclORELSE (* converts the [SizeMismatch] error into an ltac error *) diff --git a/tactics/tacticals.mli b/tactics/tacticals.mli index f0ebac780..340d8fbf3 100644 --- a/tactics/tacticals.mli +++ b/tactics/tacticals.mli @@ -196,8 +196,10 @@ module New : sig (** [tclTHENFIRST tac1 tac2 gls] applies the tactic [tac1] to [gls] and [tac2] to the first resulting subgoal *) val tclTHENFIRST : unit tactic -> unit tactic -> unit tactic + val tclBINDFIRST : 'a tactic -> ('a -> 'b tactic) -> 'b tactic val tclTHENLASTn : unit tactic -> unit tactic array -> unit tactic val tclTHENLAST : unit tactic -> unit tactic -> unit tactic + val tclBINDLAST : 'a tactic -> ('a -> 'b tactic) -> 'b tactic (* [tclTHENS t l = t <*> tclDISPATCH l] *) val tclTHENS : unit tactic -> unit tactic list -> unit tactic (* [tclTHENLIST [t1;…;tn]] is [t1<*>…<*>tn] *) diff --git a/tactics/tactics.ml b/tactics/tactics.ml index 834d73bdd..d0ec3358a 100644 --- a/tactics/tactics.ml +++ b/tactics/tactics.ml @@ -1159,6 +1159,13 @@ let tactic_infer_flags with_evar = { Pretyping.fail_evar = not with_evar; Pretyping.expand_evars = true } +type 'a core_destruction_arg = + | ElimOnConstr of 'a + | ElimOnIdent of lident + | ElimOnAnonHyp of int + +type 'a destruction_arg = + clear_flag * 'a core_destruction_arg let onOpenInductionArg env sigma tac = function | clear_flag,ElimOnConstr f -> @@ -4987,15 +4994,15 @@ let anon_id = Id.of_string "anonymous" let name_op_to_name name_op object_kind suffix = let open Proof_global in let default_gk = (Global, false, object_kind) in + let name, gk = match Proof_global.V82.get_current_initial_conclusions () with + | (id, (_, gk)) -> Some id, gk + | exception NoCurrentProof -> None, default_gk + in match name_op with - | Some s -> - (try let _, gk, _ = Pfedit.current_proof_statement () in s, gk - with NoCurrentProof -> s, default_gk) - | None -> - let name, gk = - try let name, gk, _ = Pfedit.current_proof_statement () in name, gk - with NoCurrentProof -> anon_id, default_gk in - add_suffix name suffix, gk + | Some s -> s, gk + | None -> + let name = Option.default anon_id name in + add_suffix name suffix, gk let tclABSTRACT ?(opaque=true) name_op tac = let s, gk = if opaque diff --git a/tactics/tactics.mli b/tactics/tactics.mli index 079baa3ef..7809dbf48 100644 --- a/tactics/tactics.mli +++ b/tactics/tactics.mli @@ -95,6 +95,14 @@ val try_intros_until : (** Apply a tactic on a quantified hypothesis, an hypothesis in context or a term with bindings *) +type 'a core_destruction_arg = + | ElimOnConstr of 'a + | ElimOnIdent of lident + | ElimOnAnonHyp of int + +type 'a destruction_arg = + clear_flag * 'a core_destruction_arg + val onInductionArg : (clear_flag -> constr with_bindings -> unit Proofview.tactic) -> constr with_bindings destruction_arg -> unit Proofview.tactic diff --git a/test-suite/bugs/closed/1341.v b/test-suite/bugs/closed/1341.v index 8c5a38859..79a0a14d7 100644 --- a/test-suite/bugs/closed/1341.v +++ b/test-suite/bugs/closed/1341.v @@ -8,7 +8,7 @@ Hypothesis Xst : forall A, Equivalence (Xeq A). Variable map : forall A B, (A -> B) -> X A -> X B. -Implicit Arguments map [A B]. +Arguments map [A B]. Goal forall A B (a b:X (B -> A)) (c:X A) (f:A -> B -> A), Xeq _ a b -> Xeq _ b (map f c) -> Xeq _ a (map f c). intros A B a b c f Hab Hbc. diff --git a/test-suite/bugs/closed/1844.v b/test-suite/bugs/closed/1844.v index 17eeb3529..c41e45900 100644 --- a/test-suite/bugs/closed/1844.v +++ b/test-suite/bugs/closed/1844.v @@ -5,7 +5,7 @@ Definition zeq := Z.eq_dec. Definition update (A: Set) (x: Z) (v: A) (s: Z -> A) : Z -> A := fun y => if zeq x y then v else s y. -Implicit Arguments update [A]. +Arguments update [A]. Definition ident := Z. Parameter operator: Set. diff --git a/test-suite/bugs/closed/1891.v b/test-suite/bugs/closed/1891.v index 685811176..5024a5bc9 100644 --- a/test-suite/bugs/closed/1891.v +++ b/test-suite/bugs/closed/1891.v @@ -3,7 +3,7 @@ Definition f (A: Set) (l: T A): unit := tt. - Implicit Arguments f [A]. + Arguments f [A]. Lemma L (x: T unit): (unit -> T unit) -> unit. Proof. diff --git a/test-suite/bugs/closed/1951.v b/test-suite/bugs/closed/1951.v index 7558b0b86..e950554c4 100644 --- a/test-suite/bugs/closed/1951.v +++ b/test-suite/bugs/closed/1951.v @@ -42,7 +42,7 @@ match s as a return (S a) with pair (ind2 a0) IHl) l) end. (* some induction principle *) -Implicit Arguments ind [S]. +Arguments ind [S]. Lemma k : a -> Type. (* some ininteresting lemma *) intro;pattern H;apply ind;intros. diff --git a/test-suite/bugs/closed/1981.v b/test-suite/bugs/closed/1981.v index 99952682d..a3d942930 100644 --- a/test-suite/bugs/closed/1981.v +++ b/test-suite/bugs/closed/1981.v @@ -1,4 +1,4 @@ -Implicit Arguments ex_intro [A]. +Arguments ex_intro [A]. Goal exists n : nat, True. eapply ex_intro. exact 0. exact I. diff --git a/test-suite/bugs/closed/2362.v b/test-suite/bugs/closed/2362.v index febb9c7bb..10e86cd12 100644 --- a/test-suite/bugs/closed/2362.v +++ b/test-suite/bugs/closed/2362.v @@ -8,7 +8,7 @@ Class Pointed (M:Type -> Type) := Unset Implicit Arguments. Inductive FPair (A B:Type) (neutral: B) : Type:= fpair : forall (a:A) (b:B), FPair A B neutral. -Implicit Arguments fpair [[A] [B] [neutral]]. +Arguments fpair {A B neutral}. Set Implicit Arguments. diff --git a/test-suite/bugs/closed/2378.v b/test-suite/bugs/closed/2378.v index 23a58501f..6d73d58d4 100644 --- a/test-suite/bugs/closed/2378.v +++ b/test-suite/bugs/closed/2378.v @@ -63,7 +63,7 @@ Fixpoint lpSat st f: Prop := end. End PropLogic. -Implicit Arguments lpSat. +Arguments lpSat : default implicits. Fixpoint LPTransfo Pred1 Pred2 p2lp (f: LP Pred1): LP Pred2 := match f with @@ -71,7 +71,7 @@ Fixpoint LPTransfo Pred1 Pred2 p2lp (f: LP Pred1): LP Pred2 := | LPAnd _ f1 f2 => LPAnd _ (LPTransfo Pred1 Pred2 p2lp f1) (LPTransfo Pred1 Pred2 p2lp f2) | LPNot _ f1 => LPNot _ (LPTransfo Pred1 Pred2 p2lp f1) end. -Implicit Arguments LPTransfo. +Arguments LPTransfo : default implicits. Definition addIndex (Ind:Type) (Pred: Ind -> Type) (i: Ind) f := LPTransfo (fun p => LPPred _ (existT (fun i => Pred i) i p)) f. @@ -139,7 +139,7 @@ Definition trProd (State: Type) Ind (Pred: Ind -> Type) (tts: Ind -> TTS State) {i:Ind & Pred i} -> LP (Predicate _ (TTSIndexedProduct _ Ind tts)) := fun p => addIndex Ind _ (projS1 p) (tr (projS1 p) (projS2 p)). -Implicit Arguments trProd. +Arguments trProd : default implicits. Require Import Setoid. Theorem satTrProd: diff --git a/test-suite/bugs/closed/2404.v b/test-suite/bugs/closed/2404.v index 8ac696e91..f6ec67601 100644 --- a/test-suite/bugs/closed/2404.v +++ b/test-suite/bugs/closed/2404.v @@ -22,13 +22,13 @@ Section Derived. Definition bexportw := exportw base. Definition bwweak := wweak base. - Implicit Arguments bexportw [a b]. + Arguments bexportw [a b]. Inductive RstarSetProof {I : Type} (T : I -> I -> Type) : I -> I -> Type := starReflS : forall a, RstarSetProof T a a | starTransS : forall i j k, T i j -> (RstarSetProof T j k) -> RstarSetProof T i k. -Implicit Arguments starTransS [I T i j k]. +Arguments starTransS [I T i j k]. Definition RstarInv {A : Set} (rel : relation A) : A -> A -> Type := (flip (RstarSetProof (flip rel))). diff --git a/test-suite/bugs/closed/2584.v b/test-suite/bugs/closed/2584.v index ef2e4e355..b5a723b47 100644 --- a/test-suite/bugs/closed/2584.v +++ b/test-suite/bugs/closed/2584.v @@ -8,7 +8,7 @@ Inductive res (A: Type) : Type := | OK: A -> res A | Error: err -> res A. -Implicit Arguments Error [A]. +Arguments Error [A]. Set Printing Universes. diff --git a/test-suite/bugs/closed/2667.v b/test-suite/bugs/closed/2667.v index 0631e5358..0e6d0108c 100644 --- a/test-suite/bugs/closed/2667.v +++ b/test-suite/bugs/closed/2667.v @@ -1,11 +1,11 @@ -(* Check that extra arguments to Arguments Scope do not disturb use of *) +(* Check that extra arguments to Arguments do not disturb use of *) (* scopes in constructors *) Inductive stmt : Type := Sskip: stmt | Scall : nat -> stmt. Bind Scope Cminor with stmt. (* extra argument is ok because of possible coercion to funclass *) -Arguments Scope Scall [_ Cminor ]. +Arguments Scall _ _%Cminor : extra scopes. (* extra argument is ok because of possible coercion to funclass *) Fixpoint f (c: stmt) : Prop := match c with Scall _ => False | _ => False end. diff --git a/test-suite/bugs/closed/2729.v b/test-suite/bugs/closed/2729.v index 7929b8810..c9d65c12c 100644 --- a/test-suite/bugs/closed/2729.v +++ b/test-suite/bugs/closed/2729.v @@ -82,8 +82,8 @@ Inductive SequenceBase (pu : PatchUniverse) (p : pu_type from mid) (qs : SequenceBase pu mid to), SequenceBase pu from to. -Implicit Arguments Nil [pu cxt]. -Implicit Arguments Cons [pu from mid to]. +Arguments Nil [pu cxt]. +Arguments Cons [pu from mid to]. Program Fixpoint insertBase {pu : PatchUniverse} {from mid to : NameSet} diff --git a/test-suite/bugs/closed/2830.v b/test-suite/bugs/closed/2830.v index bb607b785..07a5cf91a 100644 --- a/test-suite/bugs/closed/2830.v +++ b/test-suite/bugs/closed/2830.v @@ -49,9 +49,9 @@ Record ageable_facts (A:Type) (level: A -> nat) (age1:A -> option A) := ; af_level2 : forall x y, age1 x = Some y -> level x = S (level y) }. -Implicit Arguments af_unage [[A] [level] [age1]]. -Implicit Arguments af_level1 [[A] [level] [age1]]. -Implicit Arguments af_level2 [[A] [level] [age1]]. +Arguments af_unage {A level age1}. +Arguments af_level1 {A level age1}. +Arguments af_level2 {A level age1}. Class ageable (A:Type) := mkAgeable { level : A -> nat @@ -77,7 +77,7 @@ Coercion app_pred : pred >-> Funclass. Global Opaque pred. Definition derives {A} `{ageable A} (P Q:pred A) := forall a:A, P a -> Q a. -Implicit Arguments derives. +Arguments derives : default implicits. Program Definition andp {A} `{ageable A} (P Q:pred A) : pred A := fun a:A => P a /\ Q a. @@ -170,7 +170,7 @@ Class Functor `(C:Category) `(D:Category) (im : C -> D) := { fmap g ∘ fmap f ≈ fmap (g ∘ f) }. Coercion functor_im : Functor >-> Funclass. -Implicit Arguments fmap [Object Hom C Object0 Hom0 D im a b]. +Arguments fmap [Object Hom C Object0 Hom0 D im] _ [a b]. Add Parametric Morphism `(C:Category) `(D:Category) (Im:C->D) (F:Functor C D Im) (a b:C) : (@fmap _ _ C _ _ D Im F a b) diff --git a/test-suite/bugs/closed/3068.v b/test-suite/bugs/closed/3068.v index 79671ce93..9811733dc 100644 --- a/test-suite/bugs/closed/3068.v +++ b/test-suite/bugs/closed/3068.v @@ -33,7 +33,7 @@ Section Counted_list. End Counted_list. -Implicit Arguments counted_def_nth [A n]. +Arguments counted_def_nth [A n]. Section Finite_nat_set. diff --git a/test-suite/bugs/closed/3513.v b/test-suite/bugs/closed/3513.v index 1f0f3b0da..a1d0b9107 100644 --- a/test-suite/bugs/closed/3513.v +++ b/test-suite/bugs/closed/3513.v @@ -21,7 +21,7 @@ Section ILogic_Fun. Local Instance ILFun_Ops : ILogicOps (@ILFunFrm T _ Frm _) := admit. Definition ILFun_ILogic : ILogic (@ILFunFrm T _ Frm _) := admit. End ILogic_Fun. -Implicit Arguments ILFunFrm [[ILOps] [e]]. +Arguments ILFunFrm _ {e} _ {ILOps}. Instance ILogicOps_Prop : ILogicOps Prop | 2 := {| lentails P Q := (P : Prop) -> Q; ltrue := True; land P Q := P /\ Q; diff --git a/test-suite/bugs/closed/3647.v b/test-suite/bugs/closed/3647.v index f5a22bd50..e91c004c7 100644 --- a/test-suite/bugs/closed/3647.v +++ b/test-suite/bugs/closed/3647.v @@ -26,7 +26,7 @@ Record morphism T T' `{e : type T} `{e' : type T'} := mkMorph { morph :> T -> T'; morph_resp : setoid_resp morph}. -Implicit Arguments mkMorph [T T' e e0 e' e1]. +Arguments mkMorph [T T' e0 e e1 e']. Infix "-s>" := morphism (at level 45, right associativity). Section Morphisms. Context {S T U V} `{eS : type S} `{eT : type T} `{eU : type U} `{eV : type V}. @@ -334,8 +334,8 @@ Section ILogic_Fun. End ILogic_Fun. -Implicit Arguments ILFunFrm [[ILOps] [e]]. -Implicit Arguments mkILFunFrm [T Frm ILOps]. +Arguments ILFunFrm _ {e} _ {ILOps}. +Arguments mkILFunFrm [T] _ [Frm ILOps]. Program Definition ILFun_eq {T R} {ILOps: ILogicOps R} {ILogic: ILogic R} (P : T -> R) : @ILFunFrm T _ R ILOps := diff --git a/test-suite/bugs/closed/3732.v b/test-suite/bugs/closed/3732.v index 09f1149c2..13d62b8ff 100644 --- a/test-suite/bugs/closed/3732.v +++ b/test-suite/bugs/closed/3732.v @@ -16,7 +16,7 @@ Section machine. | Inj : forall G, Prop -> propX G | ExistsX : forall G A, propX (A :: G) -> propX G. - Implicit Arguments Inj [G]. + Arguments Inj [G]. Definition PropX := propX nil. Fixpoint last (G : list Type) : Type. diff --git a/test-suite/bugs/closed/4095.v b/test-suite/bugs/closed/4095.v index 8d7dfbd49..bc9380f90 100644 --- a/test-suite/bugs/closed/4095.v +++ b/test-suite/bugs/closed/4095.v @@ -23,7 +23,7 @@ Section ILogic_Fun. Local Instance ILFun_Ops : ILogicOps (@ILFunFrm T _ Frm _) := admit. Definition ILFun_ILogic : ILogic (@ILFunFrm T _ Frm _) := admit. End ILogic_Fun. -Implicit Arguments ILFunFrm [[ILOps] [e]]. +Arguments ILFunFrm _ {e} _ {ILOps}. Instance ILogicOps_Prop : ILogicOps Prop | 2 := {| lentails P Q := (P : Prop) -> Q; ltrue := True; land P Q := P /\ Q; diff --git a/test-suite/bugs/closed/4865.v b/test-suite/bugs/closed/4865.v index c5bf3289b..da4e53aab 100644 --- a/test-suite/bugs/closed/4865.v +++ b/test-suite/bugs/closed/4865.v @@ -48,5 +48,5 @@ Fail Check g 0 0 1. (* 2nd 0 in bool *) Fixpoint arr n := match n with 0%nat => nat | S n => nat -> arr n end. Fixpoint lam n : arr n := match n with 0%nat => 0%nat | S n => fun x => lam n end. Notation "0" := true. -Arguments Scope lam [nat_scope nat_scope]. +Arguments lam _%nat_scope _%nat_scope : extra scopes. Check (lam 1 0). diff --git a/test-suite/bugs/closed/6631.v b/test-suite/bugs/closed/6631.v new file mode 100644 index 000000000..100dc13fc --- /dev/null +++ b/test-suite/bugs/closed/6631.v @@ -0,0 +1,7 @@ +Require Import Coq.derive.Derive. + +Derive f SuchThat (f = 1 + 1) As feq. +Proof. + transitivity 2; [refine (eq_refl 2)|]. + transitivity 2. + 2:abstract exact (eq_refl 2). diff --git a/test-suite/bugs/closed/6956.v b/test-suite/bugs/closed/6956.v new file mode 100644 index 000000000..ee21adbbf --- /dev/null +++ b/test-suite/bugs/closed/6956.v @@ -0,0 +1,13 @@ +(** Used to trigger an anomaly with VM compilation *) + +Set Universe Polymorphism. + +Inductive t A : nat -> Type := +| nil : t A 0 +| cons : forall (h : A) (n : nat), t A n -> t A (S n). + +Definition case0 {A} (P : t A 0 -> Type) (H : P (nil A)) v : P v := +match v with +| nil _ => H +| _ => fun devil => False_ind (@IDProp) devil +end. diff --git a/test-suite/bugs/closed/7092.v b/test-suite/bugs/closed/7092.v new file mode 100644 index 000000000..d90de8b93 --- /dev/null +++ b/test-suite/bugs/closed/7092.v @@ -0,0 +1,70 @@ +(* Examples matching fix/cofix in Ltac pattern-matching *) + +Goal True. +lazymatch (eval cbv delta [Nat.add] in Nat.add) with +| (fix F (n : nat) (v : ?A) {struct n} : @?P n v + := match n with + | O => @?O_case v + | S n' => @?S_case n' v F + end) + => + unify A nat; + unify P (fun _ _ : nat => nat); + unify O_case (fun v : nat => v); + unify S_case (fun (p : nat) (m : nat) (add : nat -> nat -> nat) + => S (add p m)) + end. +Abort. + +Fixpoint f l n := match n with 0 => 0 | S n => g n (cons n l) end +with g n l := match n with 0 => 1 | S n => f (cons 0 l) n end. + +Goal True. + +lazymatch (eval cbv delta [f] in f) with +| fix myf (l : ?L) (n : ?N) {struct n} : nat := + match n as _ with + | 0 => ?Z + | S n0 => @?S myf myg n0 l + end + with myg (n' : ?N') (l' : ?L') {struct n'} : nat := + match n' as _ with + | 0 => ?Z' + | S n0' => @?S' myf myg n0' l' + end + for myf => + unify L (list nat); + unify L' (list nat); + unify N nat; + unify N' nat; + unify Z 0; + unify Z' 1; + unify S (fun (f : L -> N -> nat) (g : N -> L -> nat) n l => g n (cons n l)); + unify S' (fun (f : L -> N -> nat) (g : N -> L -> nat) (n:N) l => f (cons 0 l) n) +end. + +Abort. + +CoInductive S1 := C1 : nat -> S2 -> S1 with S2 := C2 : bool -> S1 -> S2. + +CoFixpoint f' n l := C1 n (g' (cons n l) n n) +with g' l n p := C2 true (f' (S n) l). + +Goal True. + +lazymatch (eval cbv delta [f'] in f') with +| cofix myf (n : ?N) (l : ?L) : ?T := @?X n g l + with g (l' : ?L') (n' : ?N') (p' : ?N'') : ?T' := @?X' n' myf l' + for myf => + unify L (list nat); + unify L' (list nat); + unify N nat; + unify N' nat; + unify N'' nat; + unify T S1; + unify T' S2; + unify X (fun n g l => C1 n (g (cons n l) n n)); + unify X' (fun n f (l : list nat) => C2 true (f (S n) l)) +end. + +Abort. diff --git a/test-suite/bugs/opened/2456.v b/test-suite/bugs/opened/2456.v index 6cca5c9fb..5294adefd 100644 --- a/test-suite/bugs/opened/2456.v +++ b/test-suite/bugs/opened/2456.v @@ -6,7 +6,7 @@ Parameter Patch : nat -> nat -> Set. Inductive Catch (from to : nat) : Type := MkCatch : forall (p : Patch from to), Catch from to. -Implicit Arguments MkCatch [from to]. +Arguments MkCatch [from to]. Inductive CatchCommute5 : forall {from mid1 mid2 to : nat}, diff --git a/test-suite/bugs/opened/3295.v b/test-suite/bugs/opened/3295.v index 2a156e333..c09649de7 100644 --- a/test-suite/bugs/opened/3295.v +++ b/test-suite/bugs/opened/3295.v @@ -5,7 +5,7 @@ Class lops := lmk_ops { weq: relation car }. -Implicit Arguments car []. +Arguments car : clear implicits. Coercion car: lops >-> Sortclass. @@ -23,7 +23,7 @@ Class ops := mk_ops { dot: forall n m p, mor n m -> mor m p -> mor n p }. Coercion mor: ops >-> Funclass. -Implicit Arguments ob []. +Arguments ob : clear implicits. Instance dot_weq `{ops} n m p: Proper (weq ==> weq ==> weq) (dot n m p). Proof. diff --git a/test-suite/complexity/injection.v b/test-suite/complexity/injection.v index 08f489d75..a76fa19d3 100644 --- a/test-suite/complexity/injection.v +++ b/test-suite/complexity/injection.v @@ -47,7 +47,7 @@ Parameter mkJoinmap : forall (key: Type) (t: Type) (j: joinable t), joinmap key j. Parameter ADMIT: forall p: Prop, p. -Implicit Arguments ADMIT [p]. +Arguments ADMIT [p]. Module Share. Parameter jb : joinable bool. diff --git a/test-suite/coq-makefile/coqdoc1/run.sh b/test-suite/coq-makefile/coqdoc1/run.sh index dc5a500db..88237815b 100755 --- a/test-suite/coq-makefile/coqdoc1/run.sh +++ b/test-suite/coq-makefile/coqdoc1/run.sh @@ -9,7 +9,15 @@ make html mlihtml make install DSTROOT="$PWD/tmp" make install-doc DSTROOT="$PWD/tmp" #make debug -(for d in `find tmp -name user-contrib` ; do pushd $d >/dev/null && find . && popd >/dev/null; done) | sort -u > actual + +# to learn about <(cmd) see https://www.gnu.org/software/bash/manual/html_node/Process-Substitution.html +( + while IFS= read -r -d '' d + do + pushd "$d" >/dev/null && find . && popd >/dev/null + done < <(find tmp -name user-contrib -print0) +) | sort -u > actual + sort -u > desired <<EOT . ./test diff --git a/test-suite/coq-makefile/coqdoc2/run.sh b/test-suite/coq-makefile/coqdoc2/run.sh index dc5a500db..5811dd17e 100755 --- a/test-suite/coq-makefile/coqdoc2/run.sh +++ b/test-suite/coq-makefile/coqdoc2/run.sh @@ -9,7 +9,13 @@ make html mlihtml make install DSTROOT="$PWD/tmp" make install-doc DSTROOT="$PWD/tmp" #make debug -(for d in `find tmp -name user-contrib` ; do pushd $d >/dev/null && find . && popd >/dev/null; done) | sort -u > actual +( + while IFS= read -r -d '' d + do + pushd "$d" >/dev/null && find . && popd >/dev/null + done < <(find tmp -name user-contrib -print0) +) | sort -u > actual + sort -u > desired <<EOT . ./test diff --git a/test-suite/coq-makefile/findlib-package/run.sh b/test-suite/coq-makefile/findlib-package/run.sh index 5b24df639..5cab400cc 100755 --- a/test-suite/coq-makefile/findlib-package/run.sh +++ b/test-suite/coq-makefile/findlib-package/run.sh @@ -7,7 +7,8 @@ export OCAMLPATH=$OCAMLPATH:$PWD/findlib if which cygpath 2>/dev/null; then # the only way I found to pass OCAMLPATH on win is to have it contain # only one entry - export OCAMLPATH=`cygpath -w $PWD/findlib` + OCAMLPATH=$(cygpath -w "$PWD"/findlib) + export OCAMLPATH fi make -C findlib/foo clean coq_makefile -f _CoqProject -o Makefile diff --git a/test-suite/coq-makefile/mlpack1/run.sh b/test-suite/coq-makefile/mlpack1/run.sh index 03df9cf05..bbd2fc460 100755 --- a/test-suite/coq-makefile/mlpack1/run.sh +++ b/test-suite/coq-makefile/mlpack1/run.sh @@ -8,7 +8,7 @@ make make html mlihtml make install DSTROOT="$PWD/tmp" #make debug -(cd `find tmp -name user-contrib` && find .) | sort > actual +(cd "$(find tmp -name user-contrib)" && find .) | sort > actual sort > desired <<EOT . ./test diff --git a/test-suite/coq-makefile/mlpack2/run.sh b/test-suite/coq-makefile/mlpack2/run.sh index 03df9cf05..bbd2fc460 100755 --- a/test-suite/coq-makefile/mlpack2/run.sh +++ b/test-suite/coq-makefile/mlpack2/run.sh @@ -8,7 +8,7 @@ make make html mlihtml make install DSTROOT="$PWD/tmp" #make debug -(cd `find tmp -name user-contrib` && find .) | sort > actual +(cd "$(find tmp -name user-contrib)" && find .) | sort > actual sort > desired <<EOT . ./test diff --git a/test-suite/coq-makefile/multiroot/run.sh b/test-suite/coq-makefile/multiroot/run.sh index d3bb53106..45bf1481d 100755 --- a/test-suite/coq-makefile/multiroot/run.sh +++ b/test-suite/coq-makefile/multiroot/run.sh @@ -11,7 +11,12 @@ make html mlihtml make install DSTROOT="$PWD/tmp" make install-doc DSTROOT="$PWD/tmp" #make debug -(for d in `find tmp -name user-contrib` ; do pushd $d >/dev/null && find . && popd >/dev/null; done) | sort -u > actual +( + while IFS= read -r -d '' d + do + pushd "$d" >/dev/null && find . && popd >/dev/null + done < <(find tmp -name user-contrib -print0) +) | sort -u > actual sort > desired <<EOT . ./test diff --git a/test-suite/coq-makefile/native1/run.sh b/test-suite/coq-makefile/native1/run.sh index 89bafe9ad..8f9ab9a71 100755 --- a/test-suite/coq-makefile/native1/run.sh +++ b/test-suite/coq-makefile/native1/run.sh @@ -1,17 +1,17 @@ #!/usr/bin/env bash -NATIVECOMP=`grep "let no_native_compiler = false" ../../../config/coq_config.ml`||true -if [[ `which ocamlopt` && $NATIVECOMP ]]; then +NATIVECOMP=$(grep "let no_native_compiler = false" ../../../config/coq_config.ml)||true +if [[ $(which ocamlopt) && $NATIVECOMP ]]; then . ../template/init.sh - + coq_makefile -f _CoqProject -o Makefile cat Makefile.conf make make html mlihtml make install DSTROOT="$PWD/tmp" #make debug -(cd `find tmp -name user-contrib` && find .) | sort > actual +(cd "$(find tmp -name user-contrib)" && find .) | sort > actual sort > desired <<EOT . ./test diff --git a/test-suite/coq-makefile/plugin1/run.sh b/test-suite/coq-makefile/plugin1/run.sh index 5433d9e92..1e2bd979b 100755 --- a/test-suite/coq-makefile/plugin1/run.sh +++ b/test-suite/coq-makefile/plugin1/run.sh @@ -9,7 +9,7 @@ make make html mlihtml make install DSTROOT="$PWD/tmp" #make debug -(cd `find tmp -name user-contrib` && find .) | sort > actual +(cd "$(find tmp -name user-contrib)" && find .) | sort > actual sort > desired <<EOT . ./test diff --git a/test-suite/coq-makefile/plugin2/run.sh b/test-suite/coq-makefile/plugin2/run.sh index 5433d9e92..1e2bd979b 100755 --- a/test-suite/coq-makefile/plugin2/run.sh +++ b/test-suite/coq-makefile/plugin2/run.sh @@ -9,7 +9,7 @@ make make html mlihtml make install DSTROOT="$PWD/tmp" #make debug -(cd `find tmp -name user-contrib` && find .) | sort > actual +(cd "$(find tmp -name user-contrib)" && find .) | sort > actual sort > desired <<EOT . ./test diff --git a/test-suite/coq-makefile/plugin3/run.sh b/test-suite/coq-makefile/plugin3/run.sh index 5433d9e92..1e2bd979b 100755 --- a/test-suite/coq-makefile/plugin3/run.sh +++ b/test-suite/coq-makefile/plugin3/run.sh @@ -9,7 +9,7 @@ make make html mlihtml make install DSTROOT="$PWD/tmp" #make debug -(cd `find tmp -name user-contrib` && find .) | sort > actual +(cd "$(find tmp -name user-contrib)" && find .) | sort > actual sort > desired <<EOT . ./test diff --git a/test-suite/coq-makefile/quick2vo/run.sh b/test-suite/coq-makefile/quick2vo/run.sh index 9e681223b..dda51dd2e 100755 --- a/test-suite/coq-makefile/quick2vo/run.sh +++ b/test-suite/coq-makefile/quick2vo/run.sh @@ -1,11 +1,11 @@ #!/usr/bin/env bash -a=`uname` +a=$(uname) . ../template/init.sh coq_makefile -f _CoqProject -o Makefile # vio2vo is broken on Windows (#6720) -if [ "$a" = "Darwin" -o "$a" = "Linux" ]; then +if [ "$a" = "Darwin" ] || [ "$a" = "Linux" ]; then make quick2vo J=2 test -f theories/test.vo make validate diff --git a/test-suite/coq-makefile/template/init.sh b/test-suite/coq-makefile/template/init.sh index e19d168cf..2e066d30d 100755 --- a/test-suite/coq-makefile/template/init.sh +++ b/test-suite/coq-makefile/template/init.sh @@ -1,10 +1,11 @@ +#!/bin/sh . ../template/path-init.sh rm -rf _test mkdir _test find . -maxdepth 1 -not -name . -not -name _test -exec cp -r '{}' -t _test ';' -cd _test +cd _test || exit 1 mkdir -p src mkdir -p theories/sub diff --git a/test-suite/coq-makefile/template/path-init.sh b/test-suite/coq-makefile/template/path-init.sh index dd19ab2b1..c79b56652 100755 --- a/test-suite/coq-makefile/template/path-init.sh +++ b/test-suite/coq-makefile/template/path-init.sh @@ -1,3 +1,4 @@ +#!/bin/sh set -e set -o pipefail diff --git a/test-suite/coq-makefile/timing/precomputed-time-tests/run.sh b/test-suite/coq-makefile/timing/precomputed-time-tests/run.sh index a918cceb6..9f3b648aa 100755 --- a/test-suite/coq-makefile/timing/precomputed-time-tests/run.sh +++ b/test-suite/coq-makefile/timing/precomputed-time-tests/run.sh @@ -4,7 +4,8 @@ set -x set -e cd "$(dirname "${BASH_SOURCE[0]}")" -export COQLIB="$(cd ../../../.. && pwd)" +COQLIB="$(cd ../../../.. && pwd)" +export COQLIB -./001-correct-diff-sorting-order/run.sh || exit $? -./002-single-file-sorting/run.sh || exit $? +./001-correct-diff-sorting-order/run.sh +./002-single-file-sorting/run.sh diff --git a/test-suite/coq-makefile/timing/run.sh b/test-suite/coq-makefile/timing/run.sh index aa6b0a9a4..11a04d5c2 100755 --- a/test-suite/coq-makefile/timing/run.sh +++ b/test-suite/coq-makefile/timing/run.sh @@ -40,7 +40,7 @@ INFINITY_REPLACEMENT="+.%" # assume that if the before time is zero, we expected TO_SED_IN_BOTH=( -e s"/${INFINITY}/${INFINITY_REPLACEMENT}/g" # Whether or not something shows up as ∞ depends on whether a time registers as 0.s or as 0.001s, so we can't rely on this being consistent - -e s":|\s*N/A\s*$:| ${INFINITY_REPLACEMENT}:g" # Whether or not something shows up as N/A depends on whether a time registers as 0.s or as 0.001s, so we can't rely on this being consistent + -e s':|\s*N/A\s*$:| '"${INFINITY_REPLACEMENT}"':g' # Whether or not something shows up as N/A depends on whether a time registers as 0.s or as 0.001s, so we can't rely on this being consistent -e s'/ *$//g' # the number of trailing spaces depends on how many digits percentages end up being; since this varies across runs, we remove trailing spaces -e s'/[0-9]*\.[0-9]*//g' # the precise timing numbers vary, so we strip them out -e s'/^-*$/------/g' # When none of the numbers get over 100 (or 1000, in per-file), the width of the table is different, so we normalize the number of dashes for table separators @@ -58,16 +58,14 @@ TO_SED_IN_PER_LINE=( -e s'/+/-/g' # some code lines don't really change, but this can show up as either -0m00.01s or +0m00.01s, so we need to normalize the signs ) -for ext in "" .desired; do - for file in time-of-build-before.log time-of-build-after.log time-of-build-both.log; do - cat ${file}${ext} | grep -v 'warning: undefined variable' | sed "${TO_SED_IN_BOTH[@]}" "${TO_SED_IN_PER_FILE[@]}" > ${file}${ext}.processed - done -done for file in time-of-build-before.log time-of-build-after.log time-of-build-both.log; do - echo "cat $file" - cat "$file" - echo - diff -u $file.desired.processed $file.processed || exit $? + for ext in "" .desired; do + grep -v 'warning: undefined variable' < ${file}${ext} | sed "${TO_SED_IN_BOTH[@]}" "${TO_SED_IN_PER_FILE[@]}" > ${file}${ext}.processed + done + echo "cat $file" + cat "$file" + echo + diff -u $file.desired.processed $file.processed || exit $? done cd ../per-file-before @@ -92,13 +90,12 @@ echo "cat A.v.timing.diff" cat A.v.timing.diff echo +file=A.v.timing.diff + for ext in "" .desired; do - for file in A.v.timing.diff; do - cat ${file}${ext} | sed "${TO_SED_IN_BOTH[@]}" "${TO_SED_IN_PER_LINE[@]}" | sort > ${file}${ext}.processed - done -done -for file in A.v.timing.diff; do - diff -u $file.desired.processed $file.processed || exit $? + sed "${TO_SED_IN_BOTH[@]}" "${TO_SED_IN_PER_LINE[@]}" < "${file}${ext}" | sort > "${file}${ext}.processed" done +diff -u "$file.desired.processed" "$file.processed" || exit $? + exit 0 diff --git a/test-suite/coq-makefile/uninstall1/run.sh b/test-suite/coq-makefile/uninstall1/run.sh index 5354f794f..fc95d84b9 100755 --- a/test-suite/coq-makefile/uninstall1/run.sh +++ b/test-suite/coq-makefile/uninstall1/run.sh @@ -11,7 +11,12 @@ make install-doc DSTROOT="$PWD/tmp" make uninstall DSTROOT="$PWD/tmp" make uninstall-doc DSTROOT="$PWD/tmp" #make debug -(for d in `find tmp -name user-contrib` ; do pushd $d >/dev/null && find . && popd >/dev/null; done) | sort -u > actual +( + while IFS= read -r -d '' d + do + pushd "$d" >/dev/null && find . && popd >/dev/null + done < <(find tmp -name user-contrib -print0) +) | sort -u > actual sort -u > desired <<EOT . EOT diff --git a/test-suite/coq-makefile/uninstall2/run.sh b/test-suite/coq-makefile/uninstall2/run.sh index 5354f794f..fc95d84b9 100755 --- a/test-suite/coq-makefile/uninstall2/run.sh +++ b/test-suite/coq-makefile/uninstall2/run.sh @@ -11,7 +11,12 @@ make install-doc DSTROOT="$PWD/tmp" make uninstall DSTROOT="$PWD/tmp" make uninstall-doc DSTROOT="$PWD/tmp" #make debug -(for d in `find tmp -name user-contrib` ; do pushd $d >/dev/null && find . && popd >/dev/null; done) | sort -u > actual +( + while IFS= read -r -d '' d + do + pushd "$d" >/dev/null && find . && popd >/dev/null + done < <(find tmp -name user-contrib -print0) +) | sort -u > actual sort -u > desired <<EOT . EOT diff --git a/test-suite/coq-makefile/vio2vo/run.sh b/test-suite/coq-makefile/vio2vo/run.sh index 85656da41..e555d62f3 100755 --- a/test-suite/coq-makefile/vio2vo/run.sh +++ b/test-suite/coq-makefile/vio2vo/run.sh @@ -1,12 +1,12 @@ #!/usr/bin/env bash -a=`uname` +a=$(uname) . ../template/init.sh coq_makefile -f _CoqProject -o Makefile make quick # vio2vo is broken on Windows (#6720) -if [ "$a" = "Darwin" -o "$a" = "Linux" ]; then +if [ "$a" = "Darwin" ] || [ "$a" = "Linux" ]; then make vio2vo J=2 test -f theories/test.vo make validate diff --git a/test-suite/failure/check.v b/test-suite/failure/check.v index a148ebe8e..0ef4b417a 100644 --- a/test-suite/failure/check.v +++ b/test-suite/failure/check.v @@ -1,3 +1,3 @@ -Implicit Arguments eq [A]. +Arguments eq [A]. Fail Check (bool = true). diff --git a/test-suite/ide/bug7088.fake b/test-suite/ide/bug7088.fake new file mode 100644 index 000000000..e2a2aa52a --- /dev/null +++ b/test-suite/ide/bug7088.fake @@ -0,0 +1,13 @@ +ADD { Arguments id T x : rename. } +ADD { Lemma foo : True. } +ADD here { Proof. } +ADD { exact 3. } +ADD { Qed. } +WAIT +EDIT_AT here +ADD { Arguments id FOO BAR : rename. } +ADD { exact I. } +ADD { Qed. } +ADD { Arguments id T x : assert. } +JOIN + diff --git a/test-suite/misc/deps-checksum.sh b/test-suite/misc/deps-checksum.sh index e07612b84..a15a8fbee 100755 --- a/test-suite/misc/deps-checksum.sh +++ b/test-suite/misc/deps-checksum.sh @@ -1,3 +1,4 @@ +#!/bin/sh rm -f misc/deps/A/*.vo misc/deps/B/*.vo $coqc -R misc/deps/A A misc/deps/A/A.v $coqc -R misc/deps/B A misc/deps/B/A.v diff --git a/test-suite/misc/deps-order.sh b/test-suite/misc/deps-order.sh index 299f49469..6bb2ba2da 100755 --- a/test-suite/misc/deps-order.sh +++ b/test-suite/misc/deps-order.sh @@ -1,17 +1,18 @@ +#!/bin/sh # Check that both coqdep and coqtop/coqc supports -R # Check that both coqdep and coqtop/coqc takes the later -R # See bugs 2242, 2337, 2339 rm -f misc/deps/lib/*.vo misc/deps/client/*.vo -tmpoutput=`mktemp /tmp/coqcheck.XXXXXX` -$coqdep -R misc/deps/lib lib -R misc/deps/client client misc/deps/client/bar.v 2>&1 | head -n 1 > $tmpoutput -diff -u --strip-trailing-cr misc/deps/deps.out $tmpoutput 2>&1 +tmpoutput=$(mktemp /tmp/coqcheck.XXXXXX) +$coqdep -R misc/deps/lib lib -R misc/deps/client client misc/deps/client/bar.v 2>&1 | head -n 1 > "$tmpoutput" +diff -u --strip-trailing-cr misc/deps/deps.out "$tmpoutput" 2>&1 R=$? times $coqc -R misc/deps/lib lib misc/deps/lib/foo.v 2>&1 $coqc -R misc/deps/lib lib -R misc/deps/client client misc/deps/client/foo.v 2>&1 $coqtop -R misc/deps/lib lib -R misc/deps/client client -load-vernac-source misc/deps/client/bar.v 2>&1 S=$? -if [ $R = 0 -a $S = 0 ]; then +if [ $R = 0 ] && [ $S = 0 ]; then printf "coqdep and coqtop agree\n" exit 0 else diff --git a/test-suite/misc/deps-utf8.sh b/test-suite/misc/deps-utf8.sh index 13e264c09..acb45b229 100755 --- a/test-suite/misc/deps-utf8.sh +++ b/test-suite/misc/deps-utf8.sh @@ -1,15 +1,16 @@ +#!/bin/sh # Check reading directories matching non pure ascii idents # See bug #5715 (utf-8 working on macos X and linux) # Windows is still not compliant -a=`uname` -if [ "$a" = "Darwin" -o "$a" = "Linux" ]; then +a=$(uname) +if [ "$a" = "Darwin" ] || [ "$a" = "Linux" ]; then rm -f misc/deps/théorèmes/*.v -tmpoutput=`mktemp /tmp/coqcheck.XXXXXX` +tmpoutput=$(mktemp /tmp/coqcheck.XXXXXX) $coqc -R misc/deps AlphaBêta misc/deps/αβ/γδ.v R=$? $coqtop -R misc/deps AlphaBêta -load-vernac-source misc/deps/αβ/εζ.v S=$? -if [ $R = 0 -a $S = 0 ]; then +if [ $R = 0 ] && [ $S = 0 ]; then exit 0 else exit 1 diff --git a/test-suite/misc/exitstatus.sh b/test-suite/misc/exitstatus.sh index cea1de862..a327f4248 100755 --- a/test-suite/misc/exitstatus.sh +++ b/test-suite/misc/exitstatus.sh @@ -1,7 +1,8 @@ +#!/bin/sh $coqtop -load-vernac-source misc/exitstatus/illtyped.v N=$? $coqc misc/exitstatus/illtyped.v P=$? -printf "On ill-typed input, coqtop returned $N.\n" -printf "On ill-typed input, coqc returned $P.\n" -if [ $N = 1 -a $P = 1 ]; then exit 0; else exit 1; fi +printf "On ill-typed input, coqtop returned %s.\n" "$N" +printf "On ill-typed input, coqc returned %s.\n" "$P" +if [ $N = 1 ] && [ $P = 1 ]; then exit 0; else exit 1; fi diff --git a/test-suite/misc/printers.sh b/test-suite/misc/printers.sh index 28e7dc362..ef3f056d8 100755 --- a/test-suite/misc/printers.sh +++ b/test-suite/misc/printers.sh @@ -1,3 +1,2 @@ -printf "Drop. #use\"include\";; #quit;;\n" | $coqtopbyte 2>&1 | egrep "Error|Unbound" -if [ $? = 0 ]; then exit 1; else exit 0; fi - +#!/bin/sh +if printf "Drop. #use\"include\";; #quit;;\n" | $coqtopbyte 2>&1 | grep -E "Error|Unbound" ; then exit 1; else exit 0; fi diff --git a/test-suite/misc/universes.sh b/test-suite/misc/universes.sh index d87a86035..ef61ca624 100755 --- a/test-suite/misc/universes.sh +++ b/test-suite/misc/universes.sh @@ -1,8 +1,9 @@ +#!/bin/sh # Sort universes for the whole standard library EXPECTED_UNIVERSES=4 # Prop is not counted $coqc -R misc/universes Universes misc/universes/all_stdlib 2>&1 $coqc -R misc/universes Universes misc/universes/universes 2>&1 mv universes.txt misc/universes -N=`awk '{print $3}' misc/universes/universes.txt | sort -u | wc -l` -printf "Found %s/%s universes\n" $N $EXPECTED_UNIVERSES +N=$(awk '{print $3}' misc/universes/universes.txt | sort -u | wc -l) +printf "Found %s/%s universes\n" "$N" "$EXPECTED_UNIVERSES" if [ "$N" -eq $EXPECTED_UNIVERSES ]; then exit 0; else exit 1; fi diff --git a/test-suite/modules/PO.v b/test-suite/modules/PO.v index 8ba8525c6..be3310491 100644 --- a/test-suite/modules/PO.v +++ b/test-suite/modules/PO.v @@ -1,8 +1,8 @@ Set Implicit Arguments. Unset Strict Implicit. -Implicit Arguments fst. -Implicit Arguments snd. +Arguments fst : default implicits. +Arguments snd : default implicits. Module Type PO. Parameter T : Set. diff --git a/test-suite/modules/Przyklad.v b/test-suite/modules/Przyklad.v index 7214287a6..ece1b47b4 100644 --- a/test-suite/modules/Przyklad.v +++ b/test-suite/modules/Przyklad.v @@ -1,7 +1,7 @@ Definition ifte (T : Set) (A B : Prop) (s : {A} + {B}) (th el : T) := if s then th else el. -Implicit Arguments ifte. +Arguments ifte : default implicits. Lemma Reflexivity_provable : forall (A : Set) (a : A) (s : {a = a} + {a <> a}), diff --git a/test-suite/output/Notations3.out b/test-suite/output/Notations3.out index 1987b6a6e..304353f55 100644 --- a/test-suite/output/Notations3.out +++ b/test-suite/output/Notations3.out @@ -223,3 +223,11 @@ fun S : nat => [[S | S.S]] : Set exists2 '{{y, z}} : nat * nat, y > z & z > y : Prop +foo = +fun l : list nat => match l with + | _ :: (_ :: _) as l1 => l1 + | _ => l + end + : list nat -> list nat + +Argument scope is [list_scope] diff --git a/test-suite/output/Notations3.v b/test-suite/output/Notations3.v index c165f9553..d2d136946 100644 --- a/test-suite/output/Notations3.v +++ b/test-suite/output/Notations3.v @@ -278,10 +278,12 @@ Set Printing Notations. (* Check insensitivity of "match" clauses to order *) +Module IfPat. Notation "'if' t 'is' n .+ 1 'then' p 'else' q" := (match t with S n => p | 0 => q end) (at level 200). Check fun x => if x is n.+1 then n else 1. +End IfPat. (* Examples with binding patterns *) @@ -338,11 +340,13 @@ Check ∀ '(((x,y),true)|((x,y),false)), x>y. (* Check Georges' printability of a "if is then else" notation *) +Module IfPat2. Notation "'if' c 'is' p 'then' u 'else' v" := (match c with p => u | _ => v end) (at level 200, p pattern at level 100). Check fun p => if p is S n then n else 0. Check fun p => if p is Lt then 1 else 0. +End IfPat2. (* Check that mixed binders and terms defaults to ident and not pattern *) Module F. @@ -364,3 +368,15 @@ Check {'(x,y)|x+y=0}. (* Check exists2 with a pattern *) Check ex2 (fun x => let '(y,z) := x in y>z) (fun x => let '(y,z) := x in z>y). + +Module Issue7110. +Open Scope list_scope. +Notation "[ :: x1 , x2 , .. , xn & s ]" := (x1 :: x2 :: .. (xn :: s) ..) + (at level 0). +Definition foo (l : list nat) := + match l with + | a :: (b :: l) as l1 => l1 + | _ => l +end. +Print foo. +End Issue7110. diff --git a/test-suite/output/Projections.out b/test-suite/output/Projections.out new file mode 100644 index 000000000..e9c28faf1 --- /dev/null +++ b/test-suite/output/Projections.out @@ -0,0 +1,2 @@ +fun S : store => S.(store_funcs) + : store -> host_func diff --git a/test-suite/output/Projections.v b/test-suite/output/Projections.v new file mode 100644 index 000000000..098a518dc --- /dev/null +++ b/test-suite/output/Projections.v @@ -0,0 +1,11 @@ + +Set Printing Projections. + +Class HostFunction := host_func : Type. + +Section store. + Context `{HostFunction}. + Record store := { store_funcs : host_func }. +End store. + +Check (fun (S:@store nat) => S.(store_funcs)). diff --git a/test-suite/output/bug5778.out b/test-suite/output/bug5778.out index 91ceb1b58..d6056c509 100644 --- a/test-suite/output/bug5778.out +++ b/test-suite/output/bug5778.out @@ -1,4 +1,4 @@ The command has indeed failed with message: -In nested Ltac calls to "c", "abs" and "abstract b ltac:(())", last call -failed. +In nested Ltac calls to "c", "abs", "abstract b ltac:(())", +"b", "a", "pose (I : I)" and "(I : I)", last term evaluation failed. The term "I" has type "True" which should be Set, Prop or Type. diff --git a/test-suite/output/bug6404.out b/test-suite/output/bug6404.out new file mode 100644 index 000000000..05464755f --- /dev/null +++ b/test-suite/output/bug6404.out @@ -0,0 +1,4 @@ +The command has indeed failed with message: +In nested Ltac calls to "c", "abs", "transparent_abstract (tactic3)", +"b", "a", "pose (I : I)" and "(I : I)", last term evaluation failed. +The term "I" has type "True" which should be Set, Prop or Type. diff --git a/test-suite/output/bug6404.v b/test-suite/output/bug6404.v new file mode 100644 index 000000000..bbe6b1a00 --- /dev/null +++ b/test-suite/output/bug6404.v @@ -0,0 +1,7 @@ +Ltac a _ := pose (I : I). +Ltac b _ := a (). +Ltac abs _ := transparent_abstract b (). +Ltac c _ := abs (). +Goal True. + Fail c (). +Abort. diff --git a/test-suite/output/ssr_clear.out b/test-suite/output/ssr_clear.out new file mode 100644 index 000000000..151595406 --- /dev/null +++ b/test-suite/output/ssr_clear.out @@ -0,0 +1,3 @@ +The command has indeed failed with message: +Ltac call to "move (ssrmovearg) (ssrclauses)" failed. +No assumption is named NO_SUCH_NAME diff --git a/test-suite/output/ssr_clear.v b/test-suite/output/ssr_clear.v new file mode 100644 index 000000000..573ec47e0 --- /dev/null +++ b/test-suite/output/ssr_clear.v @@ -0,0 +1,6 @@ +Require Import ssreflect. + +Example foo : True -> True. +Proof. +Fail move=> {NO_SUCH_NAME}. +Abort. diff --git a/test-suite/prerequisite/make_local.v b/test-suite/prerequisite/make_local.v index 8700a6c4e..6d9117c05 100644 --- a/test-suite/prerequisite/make_local.v +++ b/test-suite/prerequisite/make_local.v @@ -2,8 +2,7 @@ Definition f (A:Type) (a:A) := a. -Local Arguments Scope f [type_scope type_scope]. -Local Implicit Arguments f [A]. +Local Arguments f [A]%type_scope _%type_scope. (* Used in ImportedCoercion.v to test the locality flag *) diff --git a/test-suite/success/AdvancedTypeClasses.v b/test-suite/success/AdvancedTypeClasses.v index b4efa7edc..d0aa5c857 100644 --- a/test-suite/success/AdvancedTypeClasses.v +++ b/test-suite/success/AdvancedTypeClasses.v @@ -28,8 +28,8 @@ Class interp_pair (abs : Type) := { repr : term; link: abs = interp repr }. -Implicit Arguments repr [[interp_pair]]. -Implicit Arguments link [[interp_pair]]. +Arguments repr _ {interp_pair}. +Arguments link _ {interp_pair}. Lemma prod_interp `{interp_pair a, interp_pair b} : a * b = interp (Prod (repr a) (repr b)). simpl. intros. rewrite <- link. rewrite <- (link b). reflexivity. diff --git a/test-suite/success/ImplicitArguments.v b/test-suite/success/ImplicitArguments.v index 921433cad..9a19b595e 100644 --- a/test-suite/success/ImplicitArguments.v +++ b/test-suite/success/ImplicitArguments.v @@ -2,7 +2,7 @@ Inductive vector {A : Type} : nat -> Type := | vnil : vector 0 | vcons : A -> forall {n'}, vector n' -> vector (S n'). -Implicit Arguments vector []. +Arguments vector A : clear implicits. Require Import Coq.Program.Program. diff --git a/test-suite/success/Inductive.v b/test-suite/success/Inductive.v index 5b1482fd5..f07c0191f 100644 --- a/test-suite/success/Inductive.v +++ b/test-suite/success/Inductive.v @@ -73,7 +73,7 @@ CoInductive LList (A : Set) : Set := | LNil : LList A | LCons : A -> LList A -> LList A. -Implicit Arguments LNil [A]. +Arguments LNil [A]. Inductive Finite (A : Set) : LList A -> Prop := | Finite_LNil : Finite LNil diff --git a/test-suite/success/Inversion.v b/test-suite/success/Inversion.v index 45c71615f..ca8da3948 100644 --- a/test-suite/success/Inversion.v +++ b/test-suite/success/Inversion.v @@ -31,7 +31,7 @@ Inductive in_extension (I : Set) (r : rule I) : extension I -> Type := | in_first : forall e, in_extension r (add_rule r e) | in_rest : forall e r', in_extension r e -> in_extension r (add_rule r' e). -Implicit Arguments NL [I]. +Arguments NL [I]. Inductive super_extension (I : Set) (e : extension I) : extension I -> Type := diff --git a/test-suite/success/RecTutorial.v b/test-suite/success/RecTutorial.v index 841940492..29350d620 100644 --- a/test-suite/success/RecTutorial.v +++ b/test-suite/success/RecTutorial.v @@ -991,10 +991,10 @@ Proof. Qed. -Implicit Arguments Vector.cons [A n]. -Implicit Arguments Vector.nil [A]. -Implicit Arguments Vector.hd [A n]. -Implicit Arguments Vector.tl [A n]. +Arguments Vector.cons [A] _ [n]. +Arguments Vector.nil [A]. +Arguments Vector.hd [A n]. +Arguments Vector.tl [A n]. Definition Vid : forall (A : Type)(n:nat), Vector.t A n -> Vector.t A n. Proof. @@ -1064,7 +1064,7 @@ Fixpoint vector_nth (A:Set)(n:nat)(p:nat)(v:Vector.t A p){struct v} | S n', Vector.cons _ v' => vector_nth A n' _ v' end. -Implicit Arguments vector_nth [A p]. +Arguments vector_nth [A] _ [p]. Lemma nth_bitwise : forall (n:nat) (v1 v2: Vector.t bool n) i a b, @@ -1159,7 +1159,7 @@ infiniteproof map_iterate'. Qed. -Implicit Arguments LNil [A]. +Arguments LNil [A]. Lemma Lnil_not_Lcons : forall (A:Set)(a:A)(l:LList A), LNil <> (LCons a l). diff --git a/test-suite/success/Record.v b/test-suite/success/Record.v index 6f27c1d36..18ebcd638 100644 --- a/test-suite/success/Record.v +++ b/test-suite/success/Record.v @@ -5,7 +5,7 @@ Require Import Program. Require Import List. Record vector {A : Type} {n : nat} := { vec_list : list A ; vec_len : length vec_list = n }. -Implicit Arguments vector []. +Arguments vector : clear implicits. Coercion vec_list : vector >-> list. diff --git a/test-suite/success/Scopes.v b/test-suite/success/Scopes.v index ca3746716..2da630633 100644 --- a/test-suite/success/Scopes.v +++ b/test-suite/success/Scopes.v @@ -11,7 +11,7 @@ Check (A.opp 3). Record B := { f :> Z -> Z }. Variable a:B. -Arguments Scope a [Z_scope]. +Arguments a _%Z_scope : extra scopes. Check a 0. (* Check that casts activate scopes if ever possible *) diff --git a/test-suite/success/Typeclasses.v b/test-suite/success/Typeclasses.v index cd6eac35c..400479ae8 100644 --- a/test-suite/success/Typeclasses.v +++ b/test-suite/success/Typeclasses.v @@ -128,8 +128,8 @@ Record Monad {m : Type -> Type} := { Print Visibility. Print unit. -Implicit Arguments unit [[m] [m0] [α]]. -Implicit Arguments Monad []. +Arguments unit {m m0 α}. +Arguments Monad : clear implicits. Notation "'return' t" := (unit t). (* Test correct handling of existentials and defined fields. *) diff --git a/test-suite/success/apply.v b/test-suite/success/apply.v index 02e043bc3..b287b5fac 100644 --- a/test-suite/success/apply.v +++ b/test-suite/success/apply.v @@ -39,7 +39,7 @@ Qed. (* Check apply/eapply distinction in presence of open terms *) Parameter h : forall x y z : nat, x = z -> x = y. -Implicit Arguments h [[x] [y]]. +Arguments h {x y}. Goal 1 = 0 -> True. intro H. apply h in H || exact I. diff --git a/test-suite/success/dependentind.v b/test-suite/success/dependentind.v index f5bb884d2..55ae54ca0 100644 --- a/test-suite/success/dependentind.v +++ b/test-suite/success/dependentind.v @@ -42,7 +42,7 @@ Inductive ctx : Type := Bind Scope context_scope with ctx. Delimit Scope context_scope with ctx. -Arguments Scope snoc [context_scope]. +Arguments snoc _%context_scope. Notation " Γ , τ " := (snoc Γ τ) (at level 25, τ at next level, left associativity) : context_scope. diff --git a/test-suite/success/evars.v b/test-suite/success/evars.v index 627794832..5b13f35d5 100644 --- a/test-suite/success/evars.v +++ b/test-suite/success/evars.v @@ -386,7 +386,7 @@ Record iffT (X Y:Type) : Type := mkIff { iffLR : X->Y; iffRL : Y->X }. Record tri (R:Type->Type->Type) (S:Type->Type->Type) (T:Type->Type->Type) := mkTri { tri0 : forall a b c, R a b -> S a c -> T b c }. -Implicit Arguments mkTri [R S T]. +Arguments mkTri [R S T]. Definition tri_iffT : tri iffT iffT iffT := (mkTri (fun X0 X1 X2 E01 E02 => diff --git a/test-suite/success/implicit.v b/test-suite/success/implicit.v index a0981311b..23853890d 100644 --- a/test-suite/success/implicit.v +++ b/test-suite/success/implicit.v @@ -33,11 +33,11 @@ Definition eq1 := fun (A:Type) (x y:A) => x=y. Definition eq2 := fun (A:Type) (x y:A) => x=y. Definition eq3 := fun (A:Type) (x y:A) => x=y. -Implicit Arguments op' []. -Global Implicit Arguments op'' []. +Arguments op' : clear implicits. +Global Arguments op'' : clear implicits. -Implicit Arguments eq2 []. -Global Implicit Arguments eq3 []. +Arguments eq2 : clear implicits. +Global Arguments eq3 : clear implicits. Check (op 0 0). Check (op' nat 0 0). @@ -89,14 +89,14 @@ Fixpoint plus n m {struct n} := (* Check multiple implicit arguments signatures *) -Implicit Arguments eq_refl [[A] [x]] [[A]]. +Arguments eq_refl {A x}, {A}. Check eq_refl : 0 = 0. (* Check that notations preserve implicit (since 8.3) *) Parameter p : forall A, A -> forall n, n = 0 -> True. -Implicit Arguments p [A n]. +Arguments p [A] _ [n]. Notation Q := (p 0). Check Q eq_refl. diff --git a/tools/gallina-syntax.el b/tools/gallina-syntax.el index 662762b08..7c59fb6ae 100644 --- a/tools/gallina-syntax.el +++ b/tools/gallina-syntax.el @@ -432,7 +432,6 @@ ("Add Semi Ring" nil "Add Semi Ring #." t "Add\\s-+Semi\\s-+Ring") ("Add Setoid" nil "Add Setoid #." t "Add\\s-+Setoid") ("Admit Obligations" "oblsadmit" "Admit Obligations." nil "Admit\\s-+Obligations") - ("Arguments Scope" "argsc" "Arguments Scope @{id} [ @{_} ]" t "Arguments\\s-+Scope") ("Bind Scope" "bndsc" "Bind Scope @{scope} with @{type}" t "Bind\\s-+Scope") ("Canonical Structure" nil "Canonical Structure #." t "Canonical\\s-+Structure") ("Cd" nil "Cd #." nil "Cd") diff --git a/toplevel/coqloop.ml b/toplevel/coqloop.ml index 64d839f18..d0989cfcc 100644 --- a/toplevel/coqloop.ml +++ b/toplevel/coqloop.ml @@ -325,6 +325,24 @@ let cproof p1 p2 = let drop_last_doc = ref None +(* We try to behave better when goal printing raises an exception + [usually Ctrl-C] + + This is mostly a hack as we should protect printing in a more + generic way, but that'll do for now *) +let top_goal_print oldp newp = + try + let proof_changed = not (Option.equal cproof oldp newp) in + let print_goals = not !Flags.quiet && + proof_changed && Proof_global.there_are_pending_proofs () in + if print_goals then Feedback.msg_notice (pr_open_cur_subgoals ()) + with + | exn -> + let (e, info) = CErrors.push exn in + let loc = Loc.get_loc info in + let msg = CErrors.iprint (e, info) in + TopErr.print_error_for_buffer ?loc Feedback.Error msg top_buffer + (* Careful to keep this loop tail-rec *) let rec vernac_loop ~state = let open CAst in @@ -338,6 +356,13 @@ let rec vernac_loop ~state = try let input = top_buffer.tokens in match read_sentence ~state input with + | {v=VernacBacktrack(bid,_,_)} -> + let bid = Stateid.of_int bid in + let doc, res = Stm.edit_at ~doc:state.doc bid in + assert (res = `NewTip); + let state = { state with doc; sid = bid } in + vernac_loop ~state + | {v=VernacQuit} -> exit 0 | {v=VernacDrop} -> @@ -346,10 +371,7 @@ let rec vernac_loop ~state = else (Feedback.msg_warning (str "There is no ML toplevel."); vernac_loop ~state) | {v=VernacControl c; loc} -> let nstate = Vernac.process_expr ~state (make ?loc c) in - let proof_changed = not (Option.equal cproof nstate.proof state.proof) in - let print_goals = not !Flags.quiet && - proof_changed && Proof_global.there_are_pending_proofs () in - if print_goals then Feedback.msg_notice (pr_open_cur_subgoals ()); + top_goal_print state.proof nstate.proof; vernac_loop ~state:nstate with | Stm.End_of_input -> diff --git a/toplevel/coqtop.ml b/toplevel/coqtop.ml index a08cfa9f4..0dabed6b7 100644 --- a/toplevel/coqtop.ml +++ b/toplevel/coqtop.ml @@ -315,16 +315,24 @@ let check_vio_tasks opts = (* vio files *) let schedule_vio opts = - (* We must add update the loadpath here as the scheduling process - happens outside of the STM *) - let iload_path = build_load_path opts in - List.iter Mltop.add_coq_path iload_path; - if opts.vio_checking then Vio_checking.schedule_vio_checking opts.vio_files_j opts.vio_files else Vio_checking.schedule_vio_compilation opts.vio_files_j opts.vio_files +let do_vio opts = + (* We must initialize the loadpath here as the vio scheduling + process happens outside of the STM *) + if opts.vio_files <> [] || opts.vio_tasks <> [] then + let iload_path = build_load_path opts in + List.iter Mltop.add_coq_path iload_path; + + (* Vio compile pass *) + if opts.vio_files <> [] then schedule_vio opts; + (* Vio task pass *) + if opts.vio_tasks <> [] then check_vio_tasks opts + + (******************************************************************************) (* Color Options *) (******************************************************************************) @@ -483,10 +491,9 @@ let init_toplevel arglist = end else begin try compile_files opts; - (* Vio compile pass *) - if opts.vio_files <> [] then schedule_vio opts; - (* Vio task pass *) - check_vio_tasks opts; + (* Careful this will modify the load-path and state so after + this point some stuff may not be safe anymore. *) + do_vio opts; (* Allow the user to output an arbitrary state *) outputstate opts; None, opts diff --git a/toplevel/g_toplevel.ml4 b/toplevel/g_toplevel.ml4 index 7526f3071..d5d558b9b 100644 --- a/toplevel/g_toplevel.ml4 +++ b/toplevel/g_toplevel.ml4 @@ -9,10 +9,12 @@ (************************************************************************) open Pcoq +open Pcoq.Prim open Vernacexpr (* Vernaculars specific to the toplevel *) type vernac_toplevel = + | VernacBacktrack of int * int * int | VernacDrop | VernacQuit | VernacControl of vernac_control @@ -31,6 +33,8 @@ GEXTEND Gram vernac_toplevel: FIRST [ [ IDENT "Drop"; "." -> CAst.make VernacDrop | IDENT "Quit"; "." -> CAst.make VernacQuit + | IDENT "Backtrack"; n = natural ; m = natural ; p = natural; "." -> + CAst.make (VernacBacktrack (n,m,p)) | cmd = main_entry -> match cmd with | None -> raise Stm.End_of_input diff --git a/vernac/vernacentries.ml b/vernac/vernacentries.ml index 9ff4e3302..b44c7cccb 100644 --- a/vernac/vernacentries.ml +++ b/vernac/vernacentries.ml @@ -534,17 +534,14 @@ let vernac_assumption ~atts discharge kind l nl = if not status then Feedback.feedback Feedback.AddedAxiom let should_treat_as_cumulative cum poly = - if poly then - match cum with - | GlobalCumulativity | LocalCumulativity -> true - | GlobalNonCumulativity | LocalNonCumulativity -> false - else - match cum with - | GlobalCumulativity | GlobalNonCumulativity -> false - | LocalCumulativity -> - user_err Pp.(str "The Cumulative prefix can only be used in a polymorphic context.") - | LocalNonCumulativity -> - user_err Pp.(str "The NonCumulative prefix can only be used in a polymorphic context.") + match cum with + | Some VernacCumulative -> + if poly then true + else user_err Pp.(str "The Cumulative prefix can only be used in a polymorphic context.") + | Some VernacNonCumulative -> + if poly then false + else user_err Pp.(str "The NonCumulative prefix can only be used in a polymorphic context.") + | None -> poly && Flags.is_polymorphic_inductive_cumulativity () let vernac_record cum k poly finite struc binders sort nameopt cfs = let is_cumulative = should_treat_as_cumulative cum poly in @@ -565,7 +562,6 @@ let vernac_record cum k poly finite struc binders sort nameopt cfs = indicates whether the type is inductive, co-inductive or neither. *) let vernac_inductive ~atts cum lo finite indl = - let is_cumulative = should_treat_as_cumulative cum atts.polymorphic in if Dumpglob.dump () then List.iter (fun (((coe,(lid,_)), _, _, _, cstrs), _) -> match cstrs with @@ -602,6 +598,7 @@ let vernac_inductive ~atts cum lo finite indl = | _ -> user_err Pp.(str "Cannot handle mutually (co)inductive records.") in let indl = List.map unpack indl in + let is_cumulative = should_treat_as_cumulative cum atts.polymorphic in ComInductive.do_mutual_inductive indl is_cumulative atts.polymorphic lo finite let vernac_fixpoint ~atts discharge l = @@ -2008,7 +2005,6 @@ let interp ?proof ~atts ~st c = | VernacRestart -> CErrors.user_err (str "Restart cannot be used through the Load command") | VernacUndo _ -> CErrors.user_err (str "Undo cannot be used through the Load command") | VernacUndoTo _ -> CErrors.user_err (str "UndoTo cannot be used through the Load command") - | VernacBacktrack _ -> CErrors.user_err (str "Backtrack cannot be used through the Load command") (* Resetting *) | VernacResetName _ -> anomaly (str "VernacResetName not handled by Stm.") @@ -2025,7 +2021,6 @@ let interp ?proof ~atts ~st c = | VernacDelimiters (sc,lr) -> vernac_delimiters sc lr | VernacBindScope (sc,rl) -> vernac_bind_scope sc rl | VernacOpenCloseScope (b, s) -> vernac_open_close_scope ~atts (b,s) - | VernacArgumentsScope (qid,scl) -> vernac_arguments_scope ~atts qid scl | VernacInfix (mv,qid,sc) -> vernac_infix ~atts mv qid sc | VernacNotation (c,infpl,sc) -> vernac_notation ~atts c infpl sc @@ -2099,8 +2094,6 @@ let interp ?proof ~atts ~st c = vernac_hints ~atts dbnames hints | VernacSyntacticDefinition (id,c,b) -> vernac_syntactic_definition ~atts id c b - | VernacDeclareImplicits (qid,l) -> - vernac_declare_implicits ~atts qid l | VernacArguments (qid, args, more_implicits, nargs, flags) -> vernac_arguments ~atts qid args more_implicits nargs flags | VernacReserve bl -> vernac_reserve bl @@ -2168,7 +2161,7 @@ let check_vernac_supports_locality c l = | VernacDeclareMLModule _ | VernacCreateHintDb _ | VernacRemoveHints _ | VernacHints _ | VernacSyntacticDefinition _ - | VernacArgumentsScope _ | VernacDeclareImplicits _ | VernacArguments _ + | VernacArguments _ | VernacGeneralizable _ | VernacSetOpacity _ | VernacSetStrategy _ | VernacSetOption _ | VernacUnsetOption _ diff --git a/vernac/vernacprop.ml b/vernac/vernacprop.ml index a837b77a3..0fdd2faaf 100644 --- a/vernac/vernacprop.ml +++ b/vernac/vernacprop.ml @@ -31,7 +31,6 @@ let rec has_Fail = function let is_navigation_vernac_expr = function | VernacResetInitial | VernacResetName _ - | VernacBacktrack _ | VernacBackTo _ | VernacBack _ -> true | _ -> false |