diff options
| author |  Benjamin Barenblat <bbaren@google.com> | 2019-02-13 20:40:51 -0500 |
|---|---|---|
| committer | Benjamin Barenblat <bbaren@google.com> | 2019-02-13 20:40:51 -0500 |
| commit | 2ee22055c510a56c3d040fe023d0884b183bd68c (patch) | |
| tree | 595eeed2159e90da8284b9e2d545430a61a60d04 | |
| parent | 7ecbed522b4b4a9829eb9bd7b3f36db53788a77c (diff) | |
| parent | 8018e923c75eb5504310864f821972f794b7d554 (diff) | |
Updated version 8.8.0+1.gbp069dc3b from 'upstream/8.8.0+1.gbp069dc3b'
with Debian dir 4ca0cfbbc73543887b10ee2613b222f51702e276
| -rw-r--r-- | .gitignore | 22 | ||||
| -rw-r--r-- | CHANGELOG | 28 | ||||
| -rw-r--r-- | COPYING | 674 | ||||
| -rw-r--r-- | COPYING.LESSER | 165 | ||||
| -rw-r--r-- | LICENSE | 172 | ||||
| -rw-r--r-- | Make | 23 | ||||
| -rw-r--r-- | Makefile | 14 | ||||
| -rw-r--r-- | README | 55 | ||||
| -rw-r--r-- | README.md | 117 | ||||
| -rw-r--r-- | _CoqProject | 28 | ||||
| -rw-r--r-- | default.nix | 28 | ||||
| -rw-r--r-- | description | 15 | ||||
| -rw-r--r-- | meta.yml | 109 | ||||
| -rw-r--r-- | opam | 30 | ||||
| -rw-r--r-- | src/aac.ml4 | 79 | ||||
| -rw-r--r-- | src/aac_plugin.mlpack (renamed from aac.mlpack) | 1 | ||||
| -rw-r--r-- | src/aac_rewrite.ml (renamed from aac_rewrite.ml4) | 200 | ||||
| -rw-r--r-- | src/aac_rewrite.mli (renamed from aac_rewrite.mli) | 17 | ||||
| -rw-r--r--[-rwxr-xr-x] | src/coq.ml (renamed from coq.ml) | 143 | ||||
| -rw-r--r-- | src/coq.mli (renamed from coq.mli) | 128 | ||||
| -rw-r--r-- | src/helper.ml (renamed from helper.ml) | 4 | ||||
| -rw-r--r-- | src/helper.mli (renamed from helper.mli) | 2 | ||||
| -rw-r--r-- | src/matcher.ml (renamed from matcher.ml) | 10 | ||||
| -rw-r--r-- | src/matcher.mli (renamed from matcher.mli) | 0 | ||||
| -rw-r--r-- | src/print.ml (renamed from print.ml) | 19 | ||||
| -rw-r--r-- | src/print.mli (renamed from print.mli) | 2 | ||||
| -rw-r--r-- | src/search_monad.ml (renamed from search_monad.ml) | 0 | ||||
| -rw-r--r-- | src/search_monad.mli (renamed from search_monad.mli) | 0 | ||||
| -rw-r--r-- | src/theory.ml (renamed from theory.ml) | 168 | ||||
| -rw-r--r-- | src/theory.mli (renamed from theory.mli) | 54 | ||||
| -rw-r--r-- | theories/AAC.v (renamed from AAC.v) | 254 | ||||
| -rw-r--r-- | theories/Caveats.v (renamed from Caveats.v) | 16 | ||||
| -rw-r--r-- | theories/Instances.v (renamed from Instances.v) | 41 | ||||
| -rw-r--r-- | theories/Tutorial.v (renamed from Tutorial.v) | 30 | ||||
| -rw-r--r-- | theories/Utils.v | 257 |
35 files changed, 1221 insertions, 1684 deletions
@@ -1,3 +1,19 @@ -doc -html -.pc +*.aux +*.a +*.cma +*.cmi +*.cmo +*.cmx +*.cmxa +*.cmxs +*.glob +*.native +*.o +*.d +*.vio +*.vo +.coq-native + +.merlin +Makefile.coq +Makefile.coq.conf diff --git a/CHANGELOG b/CHANGELOG deleted file mode 100644 index 84b2aae..0000000 --- a/CHANGELOG +++ /dev/null @@ -1,28 +0,0 @@ -AAC_tactics 0.2-pl2 : ------------------ - -- Improved the handling of nullifiable patterns. - -AAC_tactics 0.2.1 : ------------------ - -- backport of some debian patches (thanks to S. Glondu) - -AAC_tactics 0.2 : ------------------ - -- Several operators can share a given unit (like max and plus sharing zero) -- Added some support to rewrite in inequations (using inequations) -- Better priting functions for aac_instances -- Overhauled inference of morphisms and operators : - * Lift the previous requirement to have at leat one AC and one A operator - * Binary operations are infered before morphisms (hence List.assoc can be recognized as being Associative) -- Should now be able to handle goal with evars (but this is not unification modulo AC) -- Added several new instances of Associative and Commutative operators -- The old syntax to declare AC and A operators is no longer supported -- The tactics do not abstract the proof they built (was troublesome if evars appeared) - -AAC_tactics 0.1 : ------------------ -Initial release - diff --git a/COPYING b/COPYING deleted file mode 100644 index 94a9ed0..0000000 --- a/COPYING +++ /dev/null @@ -1,674 +0,0 @@ - GNU GENERAL PUBLIC LICENSE - Version 3, 29 June 2007 - - Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/> - Everyone is permitted to copy and distribute verbatim copies - of this license document, but changing it is not allowed. - - Preamble - - The GNU General Public License is a free, copyleft license for -software and other kinds of works. - - The licenses for most software and other practical works are designed -to take away your freedom to share and change the works. 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Combined Libraries. - - You may place library facilities that are a work based on the -Library side by side in a single library together with other library -facilities that are not Applications and are not covered by this -License, and convey such a combined library under terms of your -choice, if you do both of the following: - - a) Accompany the combined library with a copy of the same work based - on the Library, uncombined with any other library facilities, - conveyed under the terms of this License. - - b) Give prominent notice with the combined library that part of it - is a work based on the Library, and explaining where to find the - accompanying uncombined form of the same work. - - 6. Revised Versions of the GNU Lesser General Public License. - - The Free Software Foundation may publish revised and/or new versions -of the GNU Lesser General Public License from time to time. Such new -versions will be similar in spirit to the present version, but may -differ in detail to address new problems or concerns. - - Each version is given a distinguishing version number. If the -Library as you received it specifies that a certain numbered version -of the GNU Lesser General Public License "or any later version" -applies to it, you have the option of following the terms and -conditions either of that published version or of any later version -published by the Free Software Foundation. If the Library as you -received it does not specify a version number of the GNU Lesser -General Public License, you may choose any version of the GNU Lesser -General Public License ever published by the Free Software Foundation. - - If the Library as you received it specifies that a proxy can decide -whether future versions of the GNU Lesser General Public License shall -apply, that proxy's public statement of acceptance of any version is -permanent authorization for you to choose that version for the -Library. @@ -1,4 +1,6 @@ -The aac_tactics plugin library is free software: you can redistribute +Copyright (C) 2009-2018 Thomas Braibant, Damien Pous, Fabian Kunze + +The AAC tactics plugin library is free software: you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. @@ -8,6 +10,168 @@ WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. -You should have received a copy of the GNU Lesser General Public -License along with this library. If not, see -<http://www.gnu.org/licenses/>. + GNU LESSER GENERAL PUBLIC LICENSE + Version 3, 29 June 2007 + + Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/> + Everyone is permitted to copy and distribute verbatim copies + of this license document, but changing it is not allowed. + + + This version of the GNU Lesser General Public License incorporates +the terms and conditions of version 3 of the GNU General Public +License, supplemented by the additional permissions listed below. + + 0. Additional Definitions. + + As used herein, "this License" refers to version 3 of the GNU Lesser +General Public License, and the "GNU GPL" refers to version 3 of the GNU +General Public License. + + "The Library" refers to a covered work governed by this License, +other than an Application or a Combined Work as defined below. + + An "Application" is any work that makes use of an interface provided +by the Library, but which is not otherwise based on the Library. +Defining a subclass of a class defined by the Library is deemed a mode +of using an interface provided by the Library. + + A "Combined Work" is a work produced by combining or linking an +Application with the Library. The particular version of the Library +with which the Combined Work was made is also called the "Linked +Version". + + The "Minimal Corresponding Source" for a Combined Work means the +Corresponding Source for the Combined Work, excluding any source code +for portions of the Combined Work that, considered in isolation, are +based on the Application, and not on the Linked Version. + + The "Corresponding Application Code" for a Combined Work means the +object code and/or source code for the Application, including any data +and utility programs needed for reproducing the Combined Work from the +Application, but excluding the System Libraries of the Combined Work. + + 1. Exception to Section 3 of the GNU GPL. + + You may convey a covered work under sections 3 and 4 of this License +without being bound by section 3 of the GNU GPL. + + 2. Conveying Modified Versions. + + If you modify a copy of the Library, and, in your modifications, a +facility refers to a function or data to be supplied by an Application +that uses the facility (other than as an argument passed when the +facility is invoked), then you may convey a copy of the modified +version: + + a) under this License, provided that you make a good faith effort to + ensure that, in the event an Application does not supply the + function or data, the facility still operates, and performs + whatever part of its purpose remains meaningful, or + + b) under the GNU GPL, with none of the additional permissions of + this License applicable to that copy. + + 3. Object Code Incorporating Material from Library Header Files. + + The object code form of an Application may incorporate material from +a header file that is part of the Library. You may convey such object +code under terms of your choice, provided that, if the incorporated +material is not limited to numerical parameters, data structure +layouts and accessors, or small macros, inline functions and templates +(ten or fewer lines in length), you do both of the following: + + a) Give prominent notice with each copy of the object code that the + Library is used in it and that the Library and its use are + covered by this License. + + b) Accompany the object code with a copy of the GNU GPL and this license + document. + + 4. Combined Works. + + You may convey a Combined Work under terms of your choice that, +taken together, effectively do not restrict modification of the +portions of the Library contained in the Combined Work and reverse +engineering for debugging such modifications, if you also do each of +the following: + + a) Give prominent notice with each copy of the Combined Work that + the Library is used in it and that the Library and its use are + covered by this License. + + b) Accompany the Combined Work with a copy of the GNU GPL and this license + document. + + c) For a Combined Work that displays copyright notices during + execution, include the copyright notice for the Library among + these notices, as well as a reference directing the user to the + copies of the GNU GPL and this license document. + + d) Do one of the following: + + 0) Convey the Minimal Corresponding Source under the terms of this + License, and the Corresponding Application Code in a form + suitable for, and under terms that permit, the user to + recombine or relink the Application with a modified version of + the Linked Version to produce a modified Combined Work, in the + manner specified by section 6 of the GNU GPL for conveying + Corresponding Source. + + 1) Use a suitable shared library mechanism for linking with the + Library. A suitable mechanism is one that (a) uses at run time + a copy of the Library already present on the user's computer + system, and (b) will operate properly with a modified version + of the Library that is interface-compatible with the Linked + Version. + + e) Provide Installation Information, but only if you would otherwise + be required to provide such information under section 6 of the + GNU GPL, and only to the extent that such information is + necessary to install and execute a modified version of the + Combined Work produced by recombining or relinking the + Application with a modified version of the Linked Version. (If + you use option 4d0, the Installation Information must accompany + the Minimal Corresponding Source and Corresponding Application + Code. If you use option 4d1, you must provide the Installation + Information in the manner specified by section 6 of the GNU GPL + for conveying Corresponding Source.) + + 5. Combined Libraries. + + You may place library facilities that are a work based on the +Library side by side in a single library together with other library +facilities that are not Applications and are not covered by this +License, and convey such a combined library under terms of your +choice, if you do both of the following: + + a) Accompany the combined library with a copy of the same work based + on the Library, uncombined with any other library facilities, + conveyed under the terms of this License. + + b) Give prominent notice with the combined library that part of it + is a work based on the Library, and explaining where to find the + accompanying uncombined form of the same work. + + 6. Revised Versions of the GNU Lesser General Public License. + + The Free Software Foundation may publish revised and/or new versions +of the GNU Lesser General Public License from time to time. Such new +versions will be similar in spirit to the present version, but may +differ in detail to address new problems or concerns. + + Each version is given a distinguishing version number. If the +Library as you received it specifies that a certain numbered version +of the GNU Lesser General Public License "or any later version" +applies to it, you have the option of following the terms and +conditions either of that published version or of any later version +published by the Free Software Foundation. If the Library as you +received it does not specify a version number of the GNU Lesser +General Public License, you may choose any version of the GNU Lesser +General Public License ever published by the Free Software Foundation. + + If the Library as you received it specifies that a proxy can decide +whether future versions of the GNU Lesser General Public License shall +apply, that proxy's public statement of acceptance of any version is +permanent authorization for you to choose that version for the +Library. @@ -1,23 +0,0 @@ --I . --R . AAC_tactics - -coq.mli -helper.mli -search_monad.mli -matcher.mli -theory.mli -print.mli -aac_rewrite.mli -coq.ml -helper.ml -search_monad.ml -matcher.ml -theory.ml -print.ml -aac_rewrite.ml4 -aac.mlpack - -AAC.v -Instances.v -Tutorial.v -Caveats.v @@ -1,16 +1,16 @@ all: Makefile.coq - +make -f Makefile.coq all + +$(MAKE) -f Makefile.coq all clean: Makefile.coq - +make -f Makefile.coq clean - rm -f Makefile.coq + +$(MAKE) -f Makefile.coq cleanall + rm -f Makefile.coq Makefile.coq.conf -Makefile.coq: Make - $(COQBIN)coq_makefile -f Make -o Makefile.coq +Makefile.coq: _CoqProject + $(COQBIN)coq_makefile -f _CoqProject -o Makefile.coq -Make: ; +_CoqProject Makefile: ; %: Makefile.coq - +make -f Makefile.coq $@ + +$(MAKE) -f Makefile.coq $@ .PHONY: all clean @@ -1,55 +0,0 @@ - - aac_tactics - =========== - - Thomas Braibant & Damien Pous - -Laboratoire d'Informatique de Grenoble (UMR 5217), INRIA, CNRS, France - - -FOREWORD -======== - -This plugin provides tactics for rewriting universally quantified -equations, modulo associativity and commutativity of some operators. - -INSTALLATION -============ - -opam repo add coq-released https://coq.inria.fr/opam/released -opam install coq-aac-tactics - -DOCUMENTATION -============= - -Please refer to Tutorial.v for a succinct introduction on how to use -this plugin. - -To understand the inner-working of the tactic, please refer to the -.mli files as the main source of information on each .ml -file. Alternatively, [make world] generates ocamldoc/coqdoc -documentation in directories doc/ and html/, respectively. - -File Instances.v defines several instances for frequent use-cases of -this plugin, that should allow you to use it out-of-the-shelf. Namely, -we have instances for: - -- Peano naturals (Import Instances.Peano) -- Z binary numbers (Import Instances.Z) -- N binary numbers (Import Instances.N) -- P binary numbers (Import Instances.P) -- Rationnal numbers (Import Instances.Q) -- Prop (Import Instances.Prop_ops) -- Booleans (Import Instances.Bool) -- Relations (Import Instances.Relations) -- All of the above (Import Instances.All) - - -ACKNOWLEDGEMENTS -================ - -We are grateful to Evelyne Contejean, Hugo Herbelin, Assia Mahboubi -and Matthieu Sozeau for highly instructive discussions. - -This plugin took inspiration from the plugin tutorial "constructors", -distributed under the LGPL 2.1, copyrighted by Matthieu Sozeau diff --git a/README.md b/README.md new file mode 100644 index 0000000..c70f1bf --- /dev/null +++ b/README.md @@ -0,0 +1,117 @@ +# AAC tactics + +[![Travis][travis-shield]][travis-link] +[![Contributing][contributing-shield]][contributing-link] +[![Code of Conduct][conduct-shield]][conduct-link] +[![Gitter][gitter-shield]][gitter-link] +[![DOI][doi-shield]][doi-link] + +[doi-shield]: https://zenodo.org/badge/DOI/10.1007/978-3-642-25379-9_14.svg +[doi-link]: https://doi.org/10.1007/978-3-642-25379-9_14 + +[travis-shield]: https://travis-ci.com/coq-community/aac-tactics.svg?branch=master +[travis-link]: https://travis-ci.com/coq-community/aac-tactics/builds + +[contributing-shield]: https://img.shields.io/badge/contributions-welcome-%23f7931e.svg +[contributing-link]: https://github.com/coq-community/manifesto/blob/master/CONTRIBUTING.md + +[conduct-shield]: https://img.shields.io/badge/%E2%9D%A4-code%20of%20conduct-%23f15a24.svg +[conduct-link]: https://github.com/coq-community/manifesto/blob/master/CODE_OF_CONDUCT.md + +[gitter-shield]: https://img.shields.io/badge/chat-on%20gitter-%23c1272d.svg +[gitter-link]: https://gitter.im/coq-community/Lobby + +This Coq plugin provides tactics for rewriting universally quantified +equations, modulo associativity and commutativity of some operator. +The tactics can be applied for custom operators by registering the +operators and their properties as type class instances. Many common +operator instances, such as for Z binary arithmetic and booleans, are +provided with the plugin. + + +More details about the project can be found in the paper +[Tactics for Reasoning modulo AC in Coq](https://arxiv.org/abs/1106.4448). + +## Meta + +- Author(s): + - Thomas Braibant (initial) + - Damien Pous (initial) + - Fabian Kunze +- Coq-community maintainer(s): + - Fabian Kunze ([**@fakusb**](https://github.com/fakusb)) + - Karl Palmskog ([**@palmskog**](https://github.com/palmskog)) +- License: [GNU Lesser General Public License v3.0 or later](LICENSE) +- Compatible Coq versions: Coq 8.9 (use the corresponding branch or release for other Coq versions) +- Compatible OCaml versions: all versions supported by Coq +- Additional dependencies: none + +## Building and installation instructions + +The easiest way to install the latest released version is via +[OPAM](https://opam.ocaml.org/doc/Install.html): + +```shell +opam repo add coq-released https://coq.inria.fr/opam/released +opam install coq-aac-tactics +``` + +To instead build and install manually, do: + +``` shell +git clone https://github.com/coq-community/aac-tactics +cd aac-tactics +make # or make -j <number-of-cores-on-your-machine> +make install +``` + +After installation, the included modules are available under +the `AAC_tactics` namespace. + +## Documentation + +The following example shows an application of the tactics for reasoning over Z binary numbers: +```coq +Require Import AAC_tactics.AAC. +Require AAC_tactics.Instances. +Require Import ZArith. + +Section ZOpp. + Import Instances.Z. + Variables a b c : Z. + Hypothesis H: forall x, x + Z.opp x = 0. + + Goal a + b + c + Z.opp (c + a) = b. + aac_rewrite H. + aac_reflexivity. + Qed. +End ZOpp. +``` + +The file [Tutorial.v](theories/Tutorial.v) provides a succinct introduction +and more examples of how to use this plugin. + +The file [Instances.v](theories/Instances.v) defines several type class instances +for frequent use-cases of this plugin, that should allow you to use it off-the-shelf. +Namely, it contains instances for: + +- Peano naturals (`Import Instances.Peano.`) +- Z binary numbers (`Import Instances.Z.`) +- N binary numbers (`Import Instances.N.`) +- P binary numbers (`Import Instances.P.`) +- Rational numbers (`Import Instances.Q.`) +- Prop (`Import Instances.Prop_ops.`) +- Booleans (`Import Instances.Bool.`) +- Relations (`Import Instances.Relations.`) +- all of the above (`Import Instances.All.`) + +To understand the inner workings of the tactics, please refer to +the `.mli` files as the main source of information on each `.ml` file. + +## Acknowledgements + +The initial authors are grateful to Evelyne Contejean, Hugo Herbelin, +Assia Mahboubi, and Matthieu Sozeau for highly instructive discussions. +The plugin took inspiration from the plugin tutorial "constructors" by +Matthieu Sozeau, distributed under the LGPL 2.1. + diff --git a/_CoqProject b/_CoqProject new file mode 100644 index 0000000..f803b8d --- /dev/null +++ b/_CoqProject @@ -0,0 +1,28 @@ +-Q theories AAC_tactics +-Q src AAC_tactics +-I src + +-arg -w -arg +default + +src/coq.mli +src/helper.mli +src/search_monad.mli +src/matcher.mli +src/theory.mli +src/print.mli +src/aac_rewrite.mli +src/coq.ml +src/helper.ml +src/search_monad.ml +src/matcher.ml +src/theory.ml +src/print.ml +src/aac_rewrite.ml +src/aac.ml4 +src/aac_plugin.mlpack + +theories/Utils.v +theories/AAC.v +theories/Instances.v +theories/Tutorial.v +theories/Caveats.v diff --git a/default.nix b/default.nix new file mode 100644 index 0000000..8cd0cac --- /dev/null +++ b/default.nix @@ -0,0 +1,28 @@ +{ pkgs ? (import <nixpkgs> {}), coq-version-or-url, shell ? false }: + +let + coq-version-parts = builtins.match "([0-9]+).([0-9]+)" coq-version-or-url; + coqPackages = + if coq-version-parts == null then + pkgs.mkCoqPackages (import (fetchTarball coq-version-or-url) {}) + else + pkgs."coqPackages_${builtins.concatStringsSep "_" coq-version-parts}"; +in + +with coqPackages; + +pkgs.stdenv.mkDerivation { + + name = "aac-tactics"; + + buildInputs = with coq.ocamlPackages; [ ocaml findlib camlp5 ] + ++ pkgs.lib.optionals shell [ merlin ocp-indent ocp-index ]; + + propagatedBuildInputs = [ + coq + ]; + + src = if shell then null else ./.; + + installFlags = "COQLIB=$(out)/lib/coq/${coq.coq-version}/"; +} diff --git a/description b/description deleted file mode 100644 index 7b7195d..0000000 --- a/description +++ /dev/null @@ -1,15 +0,0 @@ -Name: AACTactics -Title: AAC tactics -Description: This Coq plugin provides tactics for rewriting universally quantified equations, modulo associative (and possibly commutative) operators: -Keywords: reflexive tactic, rewriting, rewriting modulo associativity and commutativity, rewriting modulo AC, reflexive decision procedure -Category: Miscellaneous/Coq Extensions -Author: Thomas Braibant -Email: thomas.braibant@gmail.com -Homepage: http://sardes.inrialpes.fr/~braibant/ -Institution: INRIA/UJF/Ens Lyon -Author: Damien Pous -Email: damien.pous@inria.fr -Homepage: http://sardes.inrialpes.fr/~pous/ -Institution: CNRS -Require: -License: LGPL diff --git a/meta.yml b/meta.yml new file mode 100644 index 0000000..bc7f672 --- /dev/null +++ b/meta.yml @@ -0,0 +1,109 @@ +--- +fullname: AAC tactics +shortname: aac-tactics + +description: | + This Coq plugin provides tactics for rewriting universally quantified + equations, modulo associativity and commutativity of some operator. + The tactics can be applied for custom operators by registering the + operators and their properties as type class instances. Many common + operator instances, such as for Z binary arithmetic and booleans, are + provided with the plugin. + +paper: + doi: 10.1007/978-3-642-25379-9_14 + url: https://arxiv.org/abs/1106.4448 + title: Tactics for Reasoning modulo AC in Coq + +authors: +- name: Thomas Braibant + initial: true +- name: Damien Pous + initial: true +- name: Fabian Kunze + initial: false + +maintainers: +- name: Fabian Kunze + nickname: fakusb +- name: Karl Palmskog + nickname: palmskog + +opam-file-maintainer: palmskog@gmail.com + +license: + fullname: GNU Lesser General Public License v3.0 or later + identifier: LGPL-3.0-or-later + +plugin: true + +supported_coq_versions: + text: Coq 8.9 (use the corresponding branch or release for other Coq versions) + opam: '{>= "8.9" & < "8.10~"}' + +tested_coq_versions: +- version_or_url: 8.9 + +tested_coq_opam_version: 8.9 + +namespace: AAC_tactics + +keywords: +- name: reflexive tactic +- name: rewriting +- name: rewriting modulo associativity and commutativity +- name: rewriting modulo ac +- name: decision procedure + +categories: +- name: Miscellaneous/Coq Extensions +- name: Computer Science/Decision Procedures and Certified Algorithms/Decision procedures + +documentation: | + ## Documentation + + The following example shows an application of the tactics for reasoning over Z binary numbers: + ```coq + Require Import AAC_tactics.AAC. + Require AAC_tactics.Instances. + Require Import ZArith. + + Section ZOpp. + Import Instances.Z. + Variables a b c : Z. + Hypothesis H: forall x, x + Z.opp x = 0. + + Goal a + b + c + Z.opp (c + a) = b. + aac_rewrite H. + aac_reflexivity. + Qed. + End ZOpp. + ``` + + The file [Tutorial.v](theories/Tutorial.v) provides a succinct introduction + and more examples of how to use this plugin. + + The file [Instances.v](theories/Instances.v) defines several type class instances + for frequent use-cases of this plugin, that should allow you to use it off-the-shelf. + Namely, it contains instances for: + + - Peano naturals (`Import Instances.Peano.`) + - Z binary numbers (`Import Instances.Z.`) + - N binary numbers (`Import Instances.N.`) + - P binary numbers (`Import Instances.P.`) + - Rational numbers (`Import Instances.Q.`) + - Prop (`Import Instances.Prop_ops.`) + - Booleans (`Import Instances.Bool.`) + - Relations (`Import Instances.Relations.`) + - all of the above (`Import Instances.All.`) + + To understand the inner workings of the tactics, please refer to + the `.mli` files as the main source of information on each `.ml` file. + + ## Acknowledgements + + The initial authors are grateful to Evelyne Contejean, Hugo Herbelin, + Assia Mahboubi, and Matthieu Sozeau for highly instructive discussions. + The plugin took inspiration from the plugin tutorial "constructors" by + Matthieu Sozeau, distributed under the LGPL 2.1. +--- @@ -0,0 +1,30 @@ +opam-version: "1.2" +maintainer: "palmskog@gmail.com" + +homepage: "https://github.com/coq-community/aac-tactics" +dev-repo: "https://github.com/coq-community/aac-tactics.git" +bug-reports: "https://github.com/coq-community/aac-tactics/issues" +license: "LGPL-3.0-or-later" + +build: [make "-j%{jobs}%"] +install: [make "install"] +remove: ["rm" "-R" "%{lib}%/coq/user-contrib/AAC_tactics"] +depends: [ + "coq" {>= "8.9" & < "8.10~"} +] + +tags: [ + "category:Miscellaneous/Coq Extensions" + "category:Computer Science/Decision Procedures and Certified Algorithms/Decision procedures" + "keyword:reflexive tactic" + "keyword:rewriting" + "keyword:rewriting modulo associativity and commutativity" + "keyword:rewriting modulo ac" + "keyword:decision procedure" + "logpath:AAC_tactics" +] +authors: [ + "Thomas Braibant" + "Damien Pous" + "Fabian Kunze" +] diff --git a/src/aac.ml4 b/src/aac.ml4 new file mode 100644 index 0000000..e879a69 --- /dev/null +++ b/src/aac.ml4 @@ -0,0 +1,79 @@ +(***************************************************************************) +(* This is part of aac_tactics, it is distributed under the terms of the *) +(* GNU Lesser General Public License version 3 *) +(* (see file LICENSE for more details) *) +(* *) +(* Copyright 2009-2010: Thomas Braibant, Damien Pous. *) +(***************************************************************************) + +(** aac -- Reasoning modulo associativity and commutativity *) + +DECLARE PLUGIN "aac_plugin" + + +open Ltac_plugin +open Pcoq.Prim +open Pcoq.Constr +open Stdarg +open Aac_rewrite +open Extraargs +open Genarg + +ARGUMENT EXTEND aac_args +TYPED AS ((string * int) list ) +PRINTED BY pr_aac_args +| [ "at" integer(n) aac_args(q) ] -> [ add "at" n q ] +| [ "subst" integer(n) aac_args(q) ] -> [ add "subst" n q ] +| [ "in_right" aac_args(q) ] -> [ add "in_right" 0 q ] +| [ ] -> [ [] ] +END + +let pr_constro _ _ _ = fun b -> + match b with + | None -> Pp.str "" + | Some o -> Pp.str "<constr>" + +ARGUMENT EXTEND constro +TYPED AS (constr option) +PRINTED BY pr_constro +| [ "[" constr(c) "]" ] -> [ Some c ] +| [ ] -> [ None ] +END + +TACTIC EXTEND _aac_reflexivity_ +| [ "aac_reflexivity" ] -> [ Proofview.V82.tactic aac_reflexivity ] +END + +TACTIC EXTEND _aac_normalise_ +| [ "aac_normalise" ] -> [ Proofview.V82.tactic aac_normalise ] +END + +TACTIC EXTEND _aac_rewrite_ +| [ "aac_rewrite" orient(l2r) constr(c) aac_args(args) constro(extra)] -> + [ Proofview.V82.tactic (fun gl -> aac_rewrite ?extra ~args ~l2r ~strict:true c gl) ] +END + +TACTIC EXTEND _aac_pattern_ +| [ "aac_pattern" orient(l2r) constr(c) aac_args(args) constro(extra)] -> + [ Proofview.V82.tactic (fun gl -> aac_rewrite ?extra ~args ~l2r ~strict:true ~abort:true c gl) ] +END + +TACTIC EXTEND _aac_instances_ +| [ "aac_instances" orient(l2r) constr(c) aac_args(args) constro(extra)] -> + [ Proofview.V82.tactic (fun gl -> aac_rewrite ?extra ~args ~l2r ~strict:true ~show:true c gl) ] +END + +TACTIC EXTEND _aacu_rewrite_ +| [ "aacu_rewrite" orient(l2r) constr(c) aac_args(args) constro(extra)] -> + [ Proofview.V82.tactic (fun gl -> aac_rewrite ?extra ~args ~l2r ~strict:false c gl) ] +END + +TACTIC EXTEND _aacu_pattern_ +| [ "aacu_pattern" orient(l2r) constr(c) aac_args(args) constro(extra)] -> + [ Proofview.V82.tactic (fun gl -> aac_rewrite ?extra ~args ~l2r ~strict:false ~abort:true c gl) ] +END + +TACTIC EXTEND _aacu_instances_ +| [ "aacu_instances" orient(l2r) constr(c) aac_args(args) constro(extra)] -> + [ Proofview.V82.tactic (fun gl -> aac_rewrite ?extra ~args ~l2r ~strict:false ~show:true c gl) ] +END diff --git a/aac.mlpack b/src/aac_plugin.mlpack index 80cb22c..ae61b0d 100644 --- a/aac.mlpack +++ b/src/aac_plugin.mlpack @@ -5,3 +5,4 @@ Matcher Theory Print Aac_rewrite +Aac diff --git a/aac_rewrite.ml4 b/src/aac_rewrite.ml index 1f57c0b..697c15c 100644 --- a/aac_rewrite.ml4 +++ b/src/aac_rewrite.ml @@ -6,15 +6,10 @@ (* Copyright 2009-2010: Thomas Braibant, Damien Pous. *) (***************************************************************************) -(** aac_rewrite -- rewriting modulo *) - -open Pcoq.Prim -open Pcoq.Constr -open Stdarg -open Constrarg - -DECLARE PLUGIN "aac" - +(** aac_rewrite -- rewriting modulo A or AC*) + +open Ltac_plugin + module Control = struct let debug = false let printing = false @@ -29,57 +24,20 @@ let time_tac msg tac = let tac_or_exn tac exn msg = fun gl -> try tac gl with e -> - pr_constr "last goal" (Tacmach.pf_concl gl); + let env = Tacmach.pf_env gl in + let sigma = Tacmach.project gl in + pr_constr env sigma "last goal" (Tacmach.pf_concl gl); exn msg e let retype = Coq.retype -(* helper to be used with the previous function: raise a new anomaly - except if a another one was previously raised *) -let push_anomaly msg = function - | e when CErrors.is_anomaly e -> raise e - | _ -> Coq.anomaly msg - -module M = Matcher - -open Term +open EConstr open Names -open Coqlib open Proof_type -(** The various kind of relation we can encounter, as a hierarchy *) -type rew_relation = - | Bare of Coq.Relation.t - | Transitive of Coq.Transitive.t - | Equivalence of Coq.Equivalence.t -(** {!promote try to go higher in the aforementionned hierarchy} *) -let promote (rlt : Coq.Relation.t) (k : rew_relation -> Proof_type.tactic) = - try Coq.Equivalence.cps_from_relation rlt - (fun e -> k (Equivalence e)) - with - | Not_found -> - begin - try Coq.Transitive.cps_from_relation rlt - (fun trans -> k (Transitive trans)) - with - |Not_found -> k (Bare rlt) - end - - -(* - Various situations: - p == q |- left == right : rewrite <- -> - p <= q |- left <= right : rewrite -> - p <= q |- left == right : failure - p == q |- left <= right : rewrite <- -> - - Not handled - p <= q |- left >= right : failure -*) - -(** aac_lift : the ideal type beyond AAC.v/Lift +(** aac_lift : the ideal type beyond AAC_rewrite.v/Lift A base relation r, together with an equivalence relation, and the proof that the former lifts to the later. Howver, we have to @@ -89,7 +47,7 @@ type aac_lift = { r : Coq.Relation.t; e : Coq.Equivalence.t; - lift : Term.constr + lift : constr } type rewinfo = @@ -115,7 +73,7 @@ let infer_lifting (rlt: Coq.Relation.t) (k : lift:aac_lift -> Proof_type.tactic) e |] ) in - Coq.cps_resolve_one_typeclass ~error:"Cannot infer a lifting" + Coq.cps_resolve_one_typeclass ~error:(Pp.strbrk "Cannot infer a lifting") lift_ty (fun lift goal -> let x = rlt.Coq.Relation.carrier in let r = rlt.Coq.Relation.r in @@ -189,12 +147,12 @@ let by_aac_reflexivity zero (* This convert is required to deal with evars in a proper way *) let convert_to = mkApp (r, [| mkApp (eval,[| t |]); mkApp (eval, [|t'|])|]) in - let convert = Proofview.V82.of_tactic (Tactics.convert_concl convert_to Term.VMcast) in + let convert = Proofview.V82.of_tactic (Tactics.convert_concl convert_to Constr.VMcast) in let apply_tac = Proofview.V82.of_tactic (Tactics.apply decision_thm) in (Tacticals.tclTHENLIST [ retype decision_thm; retype convert_to; convert ; - tac_or_exn apply_tac Coq.user_error "unification failure"; + tac_or_exn apply_tac Coq.user_error (Pp.strbrk "unification failure"); tac_or_exn (time_tac "vm_norm" (Proofview.V82.of_tactic (Tactics.normalise_in_concl))) Coq.anomaly "vm_compute failure"; Tacticals.tclORELSE (Proofview.V82.of_tactic Tactics.reflexivity) (Tacticals.tclFAIL 0 (Pp.str "Not an equality modulo A/AC")) @@ -220,7 +178,7 @@ let by_aac_normalise zero lift ir t t' = (* This convert is required to deal with evars in a proper way *) let convert_to = mkApp (rlt.Coq.Relation.r, [| mkApp (eval,[| t |]); mkApp (eval, [|t'|])|]) in - let convert = Proofview.V82.of_tactic (Tactics.convert_concl convert_to Term.VMcast) in + let convert = Proofview.V82.of_tactic (Tactics.convert_concl convert_to Constr.VMcast) in let apply_tac = Proofview.V82.of_tactic (Tactics.apply normalise_thm) in (Tacticals.tclTHENLIST [ retype normalise_thm; retype convert_to; @@ -233,13 +191,13 @@ let by_aac_normalise zero lift ir t t' = (** A handler tactic, that reifies the goal, and infer the liftings, and then call its continuation *) let aac_conclude - (k : Term.constr -> aac_lift -> Theory.Trans.ir -> Matcher.Terms.t -> Matcher.Terms.t -> Proof_type.tactic) = fun goal -> + (k : constr -> aac_lift -> Theory.Trans.ir -> Matcher.Terms.t -> Matcher.Terms.t -> Proof_type.tactic) = fun goal -> - let (equation : Term.types) = Tacmach.pf_concl goal in + let (equation : types) = Tacmach.pf_concl goal in let envs = Theory.Trans.empty_envs () in let left, right,r = match Coq.match_as_equation goal equation with - | None -> Coq.user_error "The goal is not an applied relation" + | None -> Coq.user_error @@ Pp.strbrk "The goal is not an applied relation" | Some x -> x in try infer_lifting r (fun ~lift goal -> @@ -247,7 +205,9 @@ let aac_conclude let tleft,tright, goal = Theory.Trans.t_of_constr goal eq envs (left,right) in let goal, ir = Theory.Trans.ir_of_envs goal eq envs in let concl = Tacmach.pf_concl goal in - let _ = pr_constr "concl "concl in + let env = Tacmach.pf_env goal in + let sigma = Tacmach.project goal in + let _ = pr_constr env sigma "concl "concl in let evar_map = Tacmach.project goal in Tacticals.tclTHEN (Refiner.tclEVARS evar_map) @@ -255,22 +215,19 @@ let aac_conclude goal )goal with - | Not_found -> Coq.user_error "No lifting from the goal's relation to an equivalence" + | Not_found -> Coq.user_error @@ Pp.strbrk "No lifting from the goal's relation to an equivalence" -open Libnames open Tacexpr -open Tacinterp let aac_normalise = fun goal -> let ids = Tacmach.pf_ids_of_hyps goal in - let loc = Loc.ghost in let mp = MPfile (DirPath.make (List.map Id.of_string ["AAC"; "AAC_tactics"])) in let norm_tac = KerName.make2 mp (Label.make "internal_normalize") in - let norm_tac = Misctypes.ArgArg (loc, norm_tac) in + let norm_tac = Locus.ArgArg (None, norm_tac) in Tacticals.tclTHENLIST [ aac_conclude by_aac_normalise; - Proofview.V82.of_tactic (Tacinterp.eval_tactic (TacArg (loc, TacCall (loc, norm_tac, [])))); + Proofview.V82.of_tactic (Tacinterp.eval_tactic (TacArg (None, TacCall (None, (norm_tac, []))))); Proofview.V82.of_tactic (Tactics.keep ids) ] goal @@ -279,7 +236,7 @@ let aac_reflexivity = fun goal -> (fun zero lift ir t t' -> let x,r = Coq.Relation.split (lift.r) in let r_reflexive = (Coq.Classes.mk_reflexive x r) in - Coq.cps_resolve_one_typeclass ~error:"The goal's relation is not reflexive" + Coq.cps_resolve_one_typeclass ~error:(Pp.strbrk "The goal's relation is not reflexive") r_reflexive (fun reflexive -> let lift_reflexivity = @@ -297,7 +254,9 @@ let aac_reflexivity = fun goal -> (Tacticals.tclTHEN (retype lift_reflexivity) (Proofview.V82.of_tactic (Tactics.apply lift_reflexivity))) (fun goal -> let concl = Tacmach.pf_concl goal in - let _ = pr_constr "concl "concl in + let env = Tacmach.pf_env goal in + let sigma = Tacmach.project goal in + let _ = pr_constr env sigma "concl "concl in by_aac_reflexivity zero lift.e ir t t' goal) ) ) goal @@ -309,7 +268,7 @@ let lift_transitivity in_left (step:constr) preorder lifting (using_eq : Coq.Equ let concl = Tacmach.pf_concl goal in let (left, right, _ ) = match Coq.match_as_equation goal concl with | Some x -> x - | None -> Coq.user_error "The goal is not an equation" + | None -> Coq.user_error @@ Pp.strbrk "The goal is not an equation" in let lift_transitivity = let thm = @@ -336,13 +295,13 @@ let lift_transitivity in_left (step:constr) preorder lifting (using_eq : Coq.Equ ] goal -(** The core tactic for aac_rewrite *) +(** The core tactic for aac_rewrite. Env and sigma are for the constr *) let core_aac_rewrite ?abort rewinfo subst (by_aac_reflexivity : Matcher.Terms.t -> Matcher.Terms.t -> Proof_type.tactic) - (tr : constr) t left : tactic = - pr_constr "transitivity through" tr; + env sigma (tr : constr) t left : tactic = + pr_constr env sigma "transitivity through" tr; let tran_tac = lift_transitivity rewinfo.in_left tr rewinfo.rlt rewinfo.lifting.lift rewinfo.eqt in @@ -382,12 +341,12 @@ let choose_subst subterm sol m= (** rewrite the constr modulo AC from left to right in the left member of the goal *) -let aac_rewrite ?abort rew ?(l2r=true) ?(show = false) ?(in_left=true) ?strict ~occ_subterm ~occ_sol ?extra : Proof_type.tactic = fun goal -> +let aac_rewrite_wrap ?abort rew ?(l2r=true) ?(show = false) ?(in_left=true) ?strict ~occ_subterm ~occ_sol ?extra : Proof_type.tactic = fun goal -> let envs = Theory.Trans.empty_envs () in - let (concl : Term.types) = Tacmach.pf_concl goal in + let (concl : types) = Tacmach.pf_concl goal in let (_,_,rlt) as concl = match Coq.match_as_equation goal concl with - | None -> Coq.user_error "The goal is not an applied relation" + | None -> Coq.user_error @@ Pp.strbrk "The goal is not an applied relation" | Some (left, right, rlt) -> left,right,rlt in let check_type x = @@ -400,7 +359,7 @@ let aac_rewrite ?abort rew ?(l2r=true) ?(show = false) ?(in_left=true) ?strict fun rewinfo -> let goal = match extra with - | Some t -> Theory.Trans.add_symbol goal rewinfo.morph_rlt envs t + | Some t -> Theory.Trans.add_symbol goal rewinfo.morph_rlt envs (EConstr.to_constr (Tacmach.project goal) t) | None -> goal in let pattern, subject, goal = @@ -428,40 +387,35 @@ let aac_rewrite ?abort rew ?(l2r=true) ?(show = false) ?(in_left=true) ?strict let subst = Matcher.Subst.to_list subst in let subst = List.map (fun (x,y) -> x, conv y) subst in let by_aac_reflexivity = (by_aac_reflexivity rewinfo.subject rewinfo.eqt ir) in - core_aac_rewrite ?abort rewinfo subst by_aac_reflexivity tr_step_raw tr_step subject + let env = Tacmach.pf_env goal in + let sigma = Tacmach.project goal in + (* I'm not sure whether this is the right env/sigma for printing tr_step_raw *) + core_aac_rewrite ?abort rewinfo subst by_aac_reflexivity env sigma tr_step_raw tr_step subject with | NoSolutions -> Tacticals.tclFAIL 0 (Pp.str (if occ_subterm = None && occ_sol = None - then "No matching occurence modulo AC found" + then "No matching occurrence modulo AC found" else "No such solution")) ) ) goal +let get k l = try Some (List.assoc k l) with Not_found -> None + +let get_lhs l = try ignore (List.assoc "in_right" l); false with Not_found -> true + +let aac_rewrite ~args = + aac_rewrite_wrap ~occ_subterm:(get "at" args) ~occ_sol:(get "subst" args) ~in_left:(get_lhs args) + -open Coq.Rewrite -open Tacmach -open Tacticals -open Tacexpr -open Tacinterp -open Extraargs -open Genarg let rec add k x = function | [] -> [k,x] | k',_ as ky::q -> - if k'=k then Coq.user_error ("redondant argument ("^k^")") + if k'=k then Coq.user_error @@ Pp.strbrk ("redondant argument ("^k^")") else ky::add k x q -let get k l = try Some (List.assoc k l) with Not_found -> None - -let get_lhs l = try List.assoc "in_right" l; false with Not_found -> true - -let aac_rewrite ~args = - aac_rewrite ~occ_subterm:(get "at" args) ~occ_sol:(get "subst" args) ~in_left:(get_lhs args) - - let pr_aac_args _ _ _ l = List.fold_left (fun acc -> function @@ -469,61 +423,3 @@ let pr_aac_args _ _ _ l = | (k,i) -> Pp.(++) (Pp.(++) (Pp.str k) (Pp.int i)) acc ) (Pp.str "") l -ARGUMENT EXTEND aac_args -TYPED AS ((string * int) list ) -PRINTED BY pr_aac_args -| [ "at" integer(n) aac_args(q) ] -> [ add "at" n q ] -| [ "subst" integer(n) aac_args(q) ] -> [ add "subst" n q ] -| [ "in_right" aac_args(q) ] -> [ add "in_right" 0 q ] -| [ ] -> [ [] ] -END - -let pr_constro _ _ _ = fun b -> - match b with - | None -> Pp.str "" - | Some o -> Pp.str "<constr>" - -ARGUMENT EXTEND constro -TYPED AS (constr option) -PRINTED BY pr_constro -| [ "[" constr(c) "]" ] -> [ Some c ] -| [ ] -> [ None ] -END - -TACTIC EXTEND _aac_reflexivity_ -| [ "aac_reflexivity" ] -> [ Proofview.V82.tactic aac_reflexivity ] -END - -TACTIC EXTEND _aac_normalise_ -| [ "aac_normalise" ] -> [ Proofview.V82.tactic aac_normalise ] -END - -TACTIC EXTEND _aac_rewrite_ -| [ "aac_rewrite" orient(l2r) constr(c) aac_args(args) constro(extra)] -> - [ Proofview.V82.tactic (fun gl -> aac_rewrite ?extra ~args ~l2r ~strict:true c gl) ] -END - -TACTIC EXTEND _aac_pattern_ -| [ "aac_pattern" orient(l2r) constr(c) aac_args(args) constro(extra)] -> - [ Proofview.V82.tactic (fun gl -> aac_rewrite ?extra ~args ~l2r ~strict:true ~abort:true c gl) ] -END - -TACTIC EXTEND _aac_instances_ -| [ "aac_instances" orient(l2r) constr(c) aac_args(args) constro(extra)] -> - [ Proofview.V82.tactic (fun gl -> aac_rewrite ?extra ~args ~l2r ~strict:true ~show:true c gl) ] -END - -TACTIC EXTEND _aacu_rewrite_ -| [ "aacu_rewrite" orient(l2r) constr(c) aac_args(args) constro(extra)] -> - [ Proofview.V82.tactic (fun gl -> aac_rewrite ?extra ~args ~l2r ~strict:false c gl) ] -END - -TACTIC EXTEND _aacu_pattern_ -| [ "aacu_pattern" orient(l2r) constr(c) aac_args(args) constro(extra)] -> - [ Proofview.V82.tactic (fun gl -> aac_rewrite ?extra ~args ~l2r ~strict:false ~abort:true c gl) ] -END - -TACTIC EXTEND _aacu_instances_ -| [ "aacu_instances" orient(l2r) constr(c) aac_args(args) constro(extra)] -> - [ Proofview.V82.tactic (fun gl -> aac_rewrite ?extra ~args ~l2r ~strict:false ~show:true c gl) ] -END diff --git a/aac_rewrite.mli b/src/aac_rewrite.mli index d195075..80134af 100644 --- a/aac_rewrite.mli +++ b/src/aac_rewrite.mli @@ -6,4 +6,19 @@ (* Copyright 2009-2010: Thomas Braibant, Damien Pous. *) (***************************************************************************) -(** Definition of the tactics, and corresponding Coq grammar entries.*) +(** aac_rewrite -- rewriting modulo A or AC*) + +val aac_reflexivity : Coq.goal_sigma -> Proof_type.goal list Evd.sigma +val aac_normalise : Coq.goal_sigma -> Proof_type.goal list Evd.sigma + +val aac_rewrite : + args:(string * int) list -> + ?abort:bool -> + EConstr.constr -> + ?l2r:bool -> + ?show:bool -> + ?strict:bool -> ?extra:EConstr.t -> Proof_type.tactic + +val add : string -> 'a -> (string * 'a) list -> (string * 'a) list + +val pr_aac_args : 'a -> 'b -> 'c -> (string * int) list -> Pp.t @@ -7,12 +7,10 @@ (***************************************************************************) (** Interface with Coq *) -type constr = Term.constr -open Term +open Constr +open EConstr open Names -open Coqlib -open Sigma.Notations open Context.Rel.Declaration (* The contrib name is used to locate errors when loading constrs *) @@ -21,9 +19,11 @@ let contrib_name = "aac_tactics" (* Getting constrs (primitive Coq terms) from existing Coq libraries. *) let find_constant contrib dir s = - Universes.constr_of_global (Coqlib.find_reference contrib dir s) + UnivGen.constr_of_global (Coqlib.find_reference contrib dir s) -let init_constant dir s = find_constant contrib_name dir s +let init_constant_constr dir s = find_constant contrib_name dir s + +let init_constant dir s = EConstr.of_constr (find_constant contrib_name dir s) (* A clause specifying that the [let] should not try to fold anything in the goal *) @@ -42,25 +42,17 @@ let cps_mk_letin (k : constr -> Proof_type.tactic) : Proof_type.tactic = fun goal -> - let name = (Names.id_of_string name) in - let name = Tactics.fresh_id [] name goal in + let name = (Id.of_string name) in + let name = Tactics.fresh_id Id.Set.empty name goal in let letin = (Proofview.V82.of_tactic (Tactics.letin_tac None (Name name) c None nowhere)) in Tacticals.tclTHENLIST [retype c; letin; (k (mkVar name))] goal -(** {2 General functions} *) +(** {1 General functions} *) -type goal_sigma = Proof_type.goal Tacmach.sigma +type goal_sigma = Proof_type.goal Evd.sigma let goal_update (goal : goal_sigma) evar_map : goal_sigma= let it = Tacmach.sig_it goal in Tacmach.re_sig it evar_map - -let fresh_evar goal ty : constr * goal_sigma = - let env = Tacmach.pf_env goal in - let evar_map = Tacmach.project goal in - let evar_map = Sigma.Unsafe.of_evar_map evar_map in - let Sigma (x,em,_) = Evarutil.new_evar env evar_map ty in - let em = Sigma.to_evar_map em in - x,( goal_update goal em) let resolve_one_typeclass goal ty : constr*goal_sigma= let env = Tacmach.pf_env goal in @@ -68,65 +60,55 @@ let resolve_one_typeclass goal ty : constr*goal_sigma= let em,c = Typeclasses.resolve_one_typeclass env evar_map ty in c, (goal_update goal em) -let general_error = - "Cannot resolve a typeclass : please report" - -let cps_resolve_one_typeclass ?error : Term.types -> (Term.constr -> Proof_type.tactic) -> Proof_type.tactic = fun t k goal -> +let cps_resolve_one_typeclass ?error : types -> (constr -> Proof_type.tactic) -> Proof_type.tactic = fun t k goal -> Tacmach.pf_apply (fun env em -> let em ,c = try Typeclasses.resolve_one_typeclass env em t with Not_found -> begin match error with | None -> CErrors.anomaly (Pp.str "Cannot resolve a typeclass : please report") - | Some x -> CErrors.error x + | Some x -> CErrors.user_err x end in Tacticals.tclTHENLIST [Refiner.tclEVARS em; k c] goal ) goal -let nf_evar goal c : Term.constr= +let nf_evar goal c : constr= let evar_map = Tacmach.project goal in - Evarutil.nf_evar evar_map c + Evarutil.nf_evar evar_map c + + (* TODO: refactor following similar functions*) let evar_unit (gl : goal_sigma) (x : constr) : constr * goal_sigma = let env = Tacmach.pf_env gl in let evar_map = Tacmach.project gl in - let evar_map = Sigma.Unsafe.of_evar_map evar_map in - let Sigma (x,em,_) = Evarutil.new_evar env evar_map x in - let em = Sigma.to_evar_map em in + let (em,x) = Evarutil.new_evar env evar_map x in x,(goal_update gl em) let evar_binary (gl: goal_sigma) (x : constr) = let env = Tacmach.pf_env gl in let evar_map = Tacmach.project gl in let ty = mkArrow x (mkArrow x x) in - let evar_map = Sigma.Unsafe.of_evar_map evar_map in - let Sigma (x,em,_) = Evarutil.new_evar env evar_map ty in - let em = Sigma.to_evar_map em in + let (em,x) = Evarutil.new_evar env evar_map ty in x,( goal_update gl em) let evar_relation (gl: goal_sigma) (x: constr) = let env = Tacmach.pf_env gl in let evar_map = Tacmach.project gl in - let ty = mkArrow x (mkArrow x (mkSort prop_sort)) in - let evar_map = Sigma.Unsafe.of_evar_map evar_map in - let Sigma (r, em, _) = Evarutil.new_evar env evar_map ty in - let em = Sigma.to_evar_map em in + let ty = mkArrow x (mkArrow x (mkSort Sorts.prop)) in + let (em,r) = Evarutil.new_evar env evar_map ty in r,( goal_update gl em) let cps_evar_relation (x: constr) k = fun goal -> Tacmach.pf_apply (fun env em -> - let ty = mkArrow x (mkArrow x (mkSort prop_sort)) in - let em = Sigma.Unsafe.of_evar_map em in - let Sigma (r, em, _) = Evarutil.new_evar env em ty in - let em = Sigma.to_evar_map em in + let ty = mkArrow x (mkArrow x (mkSort Sorts.prop)) in + let (em, r) = Evarutil.new_evar env em ty in Tacticals.tclTHENLIST [Refiner.tclEVARS em; k r] goal ) goal -(* decomp_term : constr -> (constr, types) kind_of_term *) -let decomp_term c = kind_of_term (strip_outer_cast c) +let decomp_term sigma c = kind sigma (Termops.strip_outer_cast sigma c) let lapp c v = mkApp (Lazy.force c, v) @@ -180,7 +162,7 @@ end module Pos = struct - let path = ["Coq" ; "PArith"; "BinPos"] + let path = ["Coq" ; "Numbers"; "BinNums"] let typ = lazy (init_constant path "positive") let xI = lazy (init_constant path "xI") let xO = lazy (init_constant path "xO") @@ -227,7 +209,7 @@ end (** Lists from the standard library*) module List = struct - let path = ["Coq"; "Lists"; "List"] + let path = ["Coq"; "Init"; "Datatypes"] let typ = lazy (init_constant path "list") let nil = lazy (init_constant path "nil") let cons = lazy (init_constant path "cons") @@ -335,10 +317,10 @@ end remains typable*) let match_as_equation ?(context = Context.Rel.empty) goal equation : (constr*constr* Std.Relation.t) option = let env = Tacmach.pf_env goal in - let env = Environ.push_rel_context context env in + let env = EConstr.push_rel_context context env in let evar_map = Tacmach.project goal in begin - match decomp_term equation with + match decomp_term evar_map equation with | App(c,ca) when Array.length ca >= 2 -> let n = Array.length ca in let left = ca.(n-2) in @@ -364,8 +346,10 @@ let tclDEBUG msg tac = fun gl -> let _ = Feedback.msg_debug (Pp.str msg) in tac gl -let tclPRINT tac = fun gl -> - let _ = Feedback.msg_notice (Printer.pr_constr (Tacmach.pf_concl gl)) in +let tclPRINT tac = fun gl -> + let env = Tacmach.pf_env gl in + let sigma = Tacmach.project gl in + let _ = Feedback.msg_notice (Printer.pr_econstr_env env sigma (Tacmach.pf_concl gl)) in tac gl @@ -376,7 +360,7 @@ let anomaly msg = CErrors.anomaly ~label:"[aac_tactics]" (Pp.str msg) let user_error msg = - CErrors.error ("[aac_tactics] " ^ msg) + CErrors.user_err Pp.(str "[aac_tactics] " ++ msg) let warning msg = Feedback.msg_warning (Pp.str ("[aac_tactics]" ^ msg)) @@ -394,34 +378,35 @@ module Rewrite = struct type hypinfo = { - hyp : Term.constr; (** the actual constr corresponding to the hypothese *) - hyptype : Term.constr; (** the type of the hypothesis *) - context : Context.Rel.t; (** the quantifications of the hypothese *) - body : Term.constr; (** the body of the type of the hypothesis*) + hyp : constr; (** the actual constr corresponding to the hypothese *) + hyptype : constr; (** the type of the hypothesis *) + context : EConstr.rel_context; (** the quantifications of the hypothese *) + body : constr; (** the body of the type of the hypothesis*) rel : Std.Relation.t; (** the relation *) - left : Term.constr; (** left hand side *) - right : Term.constr; (** right hand side *) + left : constr; (** left hand side *) + right : constr; (** right hand side *) l2r : bool; (** rewriting from left to right *) } let get_hypinfo c ~l2r ?check_type (k : hypinfo -> Proof_type.tactic) : Proof_type.tactic = fun goal -> let ctype = Tacmach.pf_unsafe_type_of goal c in - let (rel_context, body_type) = Term.decompose_prod_assum ctype in + let evar_map = Tacmach.project goal in + let (rel_context, body_type) = decompose_prod_assum evar_map ctype in let rec check f e = - match decomp_term e with - | Term.Rel i -> f (get_type (Context.Rel.lookup i rel_context)) - | _ -> Term.fold_constr (fun acc x -> acc && check f x) true e + match decomp_term evar_map e with + | Rel i -> f (get_type (Context.Rel.lookup i rel_context)) + | _ -> fold evar_map (fun acc x -> acc && check f x) true e in begin match check_type with | None -> () | Some f -> if not (check f body_type) - then user_error "Unable to deal with higher-order or heterogeneous patterns"; + then user_error @@ Pp.strbrk "Unable to deal with higher-order or heterogeneous patterns"; end; begin - match match_as_equation ~context:rel_context goal body_type with + match match_as_equation ~context:rel_context goal body_type with | None -> - user_error "The hypothesis is not an applied relation" + user_error @@ Pp.strbrk "The hypothesis is not an applied relation" | Some (hleft,hright,hrlt) -> k { hyp = c; @@ -453,11 +438,11 @@ let get_hypinfo c ~l2r ?check_type (k : hypinfo -> Proof_type.tactic) : Proo (* Fresh evars for everyone (should be the good way to do this recompose in Coq v8.4) *) let recompose_prod - (context : Context.Rel.t) - (subst : (int * Term.constr) list) + (context : rel_context) + (subst : (int * constr) list) env em - : Evd.evar_map * Term.constr list = + : Evd.evar_map * constr list = (* the last index of rel relevant for the rewriting *) let min_n = List.fold_left (fun acc (x,_) -> min acc x) @@ -474,12 +459,10 @@ let recompose_prod let em,x = try em, List.assoc n subst with | Not_found -> - let em = Sigma.Unsafe.of_evar_map em in - let Sigma (r, em, _) = Evarutil.new_evar env em (Vars.substl acc (get_type t)) in - let em = Sigma.to_evar_map em in + let (em, r) = Evarutil.new_evar env em (Vars.substl acc (get_type t)) in (em, r) in - (Environ.push_rel t env), em,x::acc + (EConstr.push_rel t env), em,x::acc else env,em,acc in @@ -487,11 +470,11 @@ let recompose_prod em, acc (* no fresh evars : instead, use a lambda abstraction around an - application to handle non-instanciated variables. *) + application to handle non-instantiated variables. *) let recompose_prod' - (context : Context.Rel.t) - (subst : (int *Term.constr) list) + (context : rel_context) + (subst : (int *constr) list) c = let rec popn pop n l = @@ -509,7 +492,7 @@ let recompose_prod' aux sign (n+1) next (term::app) (None :: ctxt) with | Not_found -> - let term = Term.mkRel next in + let term = mkRel next in aux sign (n+1) (next+1) (term::app) (Some decl :: ctxt) in let app,ctxt = aux context 1 1 [] [] in @@ -536,8 +519,8 @@ let recompose_prod' update sign (decl :: res) (n+1) in let ctxt = update ctxt [] 0 in - let c = Term.applistc c (List.rev app) in - let c = Term.it_mkLambda_or_LetIn c (ctxt) in + let c = applist (c,List.rev app) in + let c = it_mkLambda_or_LetIn c ctxt in c (* Version de Matthieu @@ -566,22 +549,22 @@ let recompose_prod' context subst c = let build (h : hypinfo) - (subst : (int *Term.constr) list) - (k :Term.constr -> Proof_type.tactic) + (subst : (int *constr) list) + (k :constr -> Proof_type.tactic) : Proof_type.tactic = fun goal -> let c = recompose_prod' h.context subst h.hyp in Tacticals.tclTHENLIST [k c] goal let build_with_evar (h : hypinfo) - (subst : (int *Term.constr) list) - (k :Term.constr -> Proof_type.tactic) + (subst : (int *constr) list) + (k :constr -> Proof_type.tactic) : Proof_type.tactic = fun goal -> Tacmach.pf_apply (fun env em -> let evar_map, acc = recompose_prod h.context subst env em in - let c = Term.applistc h.hyp (List.rev acc) in + let c = applist (h.hyp,List.rev acc) in Tacticals.tclTHENLIST [Refiner.tclEVARS evar_map; k c] goal ) goal @@ -597,7 +580,7 @@ let rewrite ?(abort=false)hypinfo subst k = Locus.AllOccurrences true (* tell if existing evars must be frozen for instantiation *) false - (rew,Misctypes.NoBindings) + (rew,Tactypes.NoBindings) true end else @@ -23,27 +23,26 @@ (** {2 Getting Coq terms from the environment} *) -val init_constant : string list -> string -> Term.constr +val init_constant_constr : string list -> string -> Constr.t +val init_constant : string list -> string -> EConstr.constr (** {2 General purpose functions} *) -type goal_sigma = Proof_type.goal Tacmach.sigma -val goal_update : goal_sigma -> Evd.evar_map -> goal_sigma -val resolve_one_typeclass : Proof_type.goal Tacmach.sigma -> Term.types -> Term.constr * goal_sigma -val cps_resolve_one_typeclass: ?error:string -> Term.types -> (Term.constr -> Proof_type.tactic) -> Proof_type.tactic -val nf_evar : goal_sigma -> Term.constr -> Term.constr -val fresh_evar :goal_sigma -> Term.types -> Term.constr* goal_sigma -val evar_unit :goal_sigma ->Term.constr -> Term.constr* goal_sigma -val evar_binary: goal_sigma -> Term.constr -> Term.constr* goal_sigma -val evar_relation: goal_sigma -> Term.constr -> Term.constr* goal_sigma -val cps_evar_relation : Term.constr -> (Term.constr -> Proof_type.tactic) -> Proof_type.tactic +type goal_sigma = Proof_type.goal Evd.sigma +val resolve_one_typeclass : Proof_type.goal Evd.sigma -> EConstr.types -> EConstr.constr * goal_sigma +val cps_resolve_one_typeclass: ?error:Pp.t -> EConstr.types -> (EConstr.constr -> Proof_type.tactic) -> Proof_type.tactic +val nf_evar : goal_sigma -> EConstr.constr -> EConstr.constr +val evar_unit :goal_sigma ->EConstr.constr -> EConstr.constr* goal_sigma +val evar_binary: goal_sigma -> EConstr.constr -> EConstr.constr* goal_sigma +val evar_relation: goal_sigma -> EConstr.constr -> EConstr.constr* goal_sigma +val cps_evar_relation : EConstr.constr -> (EConstr.constr -> Proof_type.tactic) -> Proof_type.tactic (** [cps_mk_letin name v] binds the constr [v] using a letin tactic *) -val cps_mk_letin : string -> Term.constr -> ( Term.constr -> Proof_type.tactic) -> Proof_type.tactic +val cps_mk_letin : string -> EConstr.constr -> ( EConstr.constr -> Proof_type.tactic) -> Proof_type.tactic -val retype : Term.constr -> Proof_type.tactic +val retype : EConstr.constr -> Proof_type.tactic -val decomp_term : Term.constr -> (Term.constr , Term.types) Term.kind_of_term -val lapp : Term.constr lazy_t -> Term.constr array -> Term.constr +val decomp_term : Evd.evar_map -> EConstr.constr -> (EConstr.constr , EConstr.types, EConstr.ESorts.t, EConstr.EInstance.t) Constr.kind_of_term +val lapp : EConstr.constr lazy_t -> EConstr.constr array -> EConstr.constr (** {2 Bindings with Coq' Standard Library} *) @@ -51,81 +50,82 @@ val lapp : Term.constr lazy_t -> Term.constr array -> Term.constr module List: sig (** [of_list ty l] *) - val of_list:Term.constr ->Term.constr list ->Term.constr + val of_list:EConstr.constr ->EConstr.constr list ->EConstr.constr (** [type_of_list ty] *) - val type_of_list:Term.constr ->Term.constr + val type_of_list:EConstr.constr ->EConstr.constr end (** Coq pairs *) module Pair: sig - val typ:Term.constr lazy_t - val pair:Term.constr lazy_t - val of_pair : Term.constr -> Term.constr -> Term.constr * Term.constr -> Term.constr + val typ:EConstr.constr lazy_t + val pair:EConstr.constr lazy_t + val of_pair : EConstr.constr -> EConstr.constr -> EConstr.constr * EConstr.constr -> EConstr.constr end module Bool : sig - val typ : Term.constr lazy_t - val of_bool : bool -> Term.constr + val typ : EConstr.constr lazy_t + val of_bool : bool -> EConstr.constr end module Comparison : sig - val typ : Term.constr lazy_t - val eq : Term.constr lazy_t - val lt : Term.constr lazy_t - val gt : Term.constr lazy_t + val typ : EConstr.constr lazy_t + val eq : EConstr.constr lazy_t + val lt : EConstr.constr lazy_t + val gt : EConstr.constr lazy_t end module Leibniz : sig - val eq_refl : Term.types -> Term.constr -> Term.constr + val eq_refl : EConstr.types -> EConstr.constr -> EConstr.constr end module Option : sig - val some : Term.constr -> Term.constr -> Term.constr - val none : Term.constr -> Term.constr - val of_option : Term.constr -> Term.constr option -> Term.constr + val typ : EConstr.constr lazy_t + val some : EConstr.constr -> EConstr.constr -> EConstr.constr + val none : EConstr.constr -> EConstr.constr + val of_option : EConstr.constr -> EConstr.constr option -> EConstr.constr end (** Coq positive numbers (pos) *) module Pos: sig - val typ:Term.constr lazy_t - val of_int: int ->Term.constr + val typ:EConstr.constr lazy_t + val of_int: int ->EConstr.constr end (** Coq unary numbers (peano) *) module Nat: sig - val typ:Term.constr lazy_t - val of_int: int ->Term.constr + val typ:EConstr.constr lazy_t + val of_int: int ->EConstr.constr end (** Coq typeclasses *) module Classes: sig - val mk_morphism: Term.constr -> Term.constr -> Term.constr -> Term.constr - val mk_equivalence: Term.constr -> Term.constr -> Term.constr - val mk_reflexive: Term.constr -> Term.constr -> Term.constr - val mk_transitive: Term.constr -> Term.constr -> Term.constr + val mk_morphism: EConstr.constr -> EConstr.constr -> EConstr.constr -> EConstr.constr + val mk_equivalence: EConstr.constr -> EConstr.constr -> EConstr.constr + val mk_reflexive: EConstr.constr -> EConstr.constr -> EConstr.constr + val mk_transitive: EConstr.constr -> EConstr.constr -> EConstr.constr end module Relation : sig - type t = {carrier : Term.constr; r : Term.constr;} - val make : Term.constr -> Term.constr -> t - val split : t -> Term.constr * Term.constr + type t = {carrier : EConstr.constr; r : EConstr.constr;} + val make : EConstr.constr -> EConstr.constr -> t + val split : t -> EConstr.constr * EConstr.constr end module Transitive : sig type t = { - carrier : Term.constr; - leq : Term.constr; - transitive : Term.constr; + carrier : EConstr.constr; + leq : EConstr.constr; + transitive : EConstr.constr; } - val make : Term.constr -> Term.constr -> Term.constr -> t - val infer : goal_sigma -> Term.constr -> Term.constr -> t * goal_sigma + val make : EConstr.constr -> EConstr.constr -> EConstr.constr -> t + val infer : goal_sigma -> EConstr.constr -> EConstr.constr -> t * goal_sigma val from_relation : goal_sigma -> Relation.t -> t * goal_sigma val cps_from_relation : Relation.t -> (t -> Proof_type.tactic) -> Proof_type.tactic val to_relation : t -> Relation.t @@ -134,22 +134,22 @@ end module Equivalence : sig type t = { - carrier : Term.constr; - eq : Term.constr; - equivalence : Term.constr; + carrier : EConstr.constr; + eq : EConstr.constr; + equivalence : EConstr.constr; } - val make : Term.constr -> Term.constr -> Term.constr -> t - val infer : goal_sigma -> Term.constr -> Term.constr -> t * goal_sigma + val make : EConstr.constr -> EConstr.constr -> EConstr.constr -> t + val infer : goal_sigma -> EConstr.constr -> EConstr.constr -> t * goal_sigma val from_relation : goal_sigma -> Relation.t -> t * goal_sigma val cps_from_relation : Relation.t -> (t -> Proof_type.tactic) -> Proof_type.tactic val to_relation : t -> Relation.t - val split : t -> Term.constr * Term.constr * Term.constr + val split : t -> EConstr.constr * EConstr.constr * EConstr.constr end (** [match_as_equation ?context goal c] try to decompose c as a relation applied to two terms. An optionnal rel-context can be provided to ensure that the term remains typable *) -val match_as_equation : ?context:Context.Rel.t -> goal_sigma -> Term.constr -> (Term.constr * Term.constr * Relation.t) option +val match_as_equation : ?context:EConstr.rel_context -> goal_sigma -> EConstr.constr -> (EConstr.constr * EConstr.constr * Relation.t) option (** {2 Some tacticials} *) @@ -166,7 +166,7 @@ val tclPRINT : Proof_type.tactic -> Proof_type.tactic (** {2 Error related mechanisms} *) val anomaly : string -> 'a -val user_error : string -> 'a +val user_error : Pp.t -> 'a val warning : string -> unit @@ -188,13 +188,13 @@ module Rewrite : sig *) type hypinfo = { - hyp : Term.constr; (** the actual constr corresponding to the hypothese *) - hyptype : Term.constr; (** the type of the hypothesis *) - context : Context.Rel.t; (** the quantifications of the hypothese *) - body : Term.constr; (** the body of the hypothese*) + hyp : EConstr.constr; (** the actual constr corresponding to the hypothese *) + hyptype : EConstr.constr; (** the type of the hypothesis *) + context : EConstr.rel_context; (** the quantifications of the hypothese *) + body : EConstr.constr; (** the body of the hypothese*) rel : Relation.t; (** the relation *) - left : Term.constr; (** left hand side *) - right : Term.constr; (** right hand side *) + left : EConstr.constr; (** left hand side *) + right : EConstr.constr; (** right hand side *) l2r : bool; (** rewriting from left to right *) } @@ -202,7 +202,7 @@ type hypinfo = build the related hypinfo, in CPS style. Moreover, an optionnal function can be provided to check the type of every free variable of the body of the hypothesis. *) -val get_hypinfo :Term.constr -> l2r:bool -> ?check_type:(Term.types -> bool) -> (hypinfo -> Proof_type.tactic) -> Proof_type.tactic +val get_hypinfo :EConstr.constr -> l2r:bool -> ?check_type:(EConstr.types -> bool) -> (hypinfo -> Proof_type.tactic) -> Proof_type.tactic (** {2 Rewriting with bindings} @@ -219,14 +219,14 @@ val get_hypinfo :Term.constr -> l2r:bool -> ?check_type:(Term.types -> bool) -> *) (** build the constr to rewrite, in CPS style, with lambda abstractions *) -val build : hypinfo -> (int * Term.constr) list -> (Term.constr -> Proof_type.tactic) -> Proof_type.tactic +val build : hypinfo -> (int * EConstr.constr) list -> (EConstr.constr -> Proof_type.tactic) -> Proof_type.tactic (** build the constr to rewrite, in CPS style, with evars *) -val build_with_evar : hypinfo -> (int * Term.constr) list -> (Term.constr -> Proof_type.tactic) -> Proof_type.tactic +val build_with_evar : hypinfo -> (int * EConstr.constr) list -> (EConstr.constr -> Proof_type.tactic) -> Proof_type.tactic (** [rewrite ?abort hypinfo subst] builds the rewriting tactic associated with the given [subst] and [hypinfo], and feeds it to the given continuation. If [abort] is set to [true], we build [tclIDTAC] instead. *) -val rewrite : ?abort:bool -> hypinfo -> (int * Term.constr) list -> (Proof_type.tactic -> Proof_type.tactic) -> Proof_type.tactic +val rewrite : ?abort:bool -> hypinfo -> (int * EConstr.constr) list -> (Proof_type.tactic -> Proof_type.tactic) -> Proof_type.tactic end diff --git a/helper.ml b/src/helper.ml index 636b17f..c1cae2a 100644 --- a/helper.ml +++ b/src/helper.ml @@ -27,10 +27,10 @@ module Debug (X : CONTROL) = struct r else f x - let pr_constr msg constr = + let pr_constr env evd msg constr = if printing then ( Feedback.msg_notice (Pp.str (Printf.sprintf "=====%s====" msg)); - Feedback.msg_notice (Printer.pr_constr constr); + Feedback.msg_notice (Printer.pr_econstr_env env evd constr); ) diff --git a/helper.mli b/src/helper.mli index f4e4454..400e847 100644 --- a/helper.mli +++ b/src/helper.mli @@ -28,6 +28,6 @@ sig (** {!pr_constr} print a Coq constructor, that can be labelled by a string *) - val pr_constr : string -> Term.constr -> unit + val pr_constr : Environ.env -> Evd.evar_map -> string -> EConstr.constr -> unit end diff --git a/matcher.ml b/src/matcher.ml index 1dcb1d2..cc66961 100644 --- a/matcher.ml +++ b/src/matcher.ml @@ -255,7 +255,7 @@ end (** This function has to deal with the arities *) - let rec merge (l : nf_term mset) (l' : nf_term mset) : nf_term mset= + let merge (l : nf_term mset) (l' : nf_term mset) : nf_term mset= merge_ac nf_term_compare l l' let extract_A units s t = @@ -349,7 +349,7 @@ end (** {2 Conversion functions} *) (* rebuilds a tree out of a list, under the assumption that the list is not empty *) - let rec binary_of_list f comb l = + let binary_of_list f comb l = let l = List.rev l in let rec aux = function | [] -> assert false @@ -455,7 +455,7 @@ end | Dot (s,l,r) -> Dot (s, aux l, aux r) | Var i -> begin match find t i with - | None -> CErrors.error "aac_tactics: instantiate failure" + | None -> CErrors.user_err (Pp.strbrk "aac_tactics: instantiate failure") | Some x -> t_of_term x end in aux x @@ -1094,7 +1094,7 @@ let unit_warning p ~nullif ~unitif = begin Feedback.msg_warning (Pp.str - "[aac_tactics] This pattern can be instanciated to match units, some solutions can be missing"); + "[aac_tactics] This pattern can be instantiated to match units, some solutions can be missing"); end ;; @@ -1127,7 +1127,7 @@ let unit_warning p ~nullif ~unitif = pattern uninstantiated. We do so in order to allow interaction with the user, to choose the env. - Strange patterms like x*y*x can be instanciated by nothing, inside + Strange patterms like x*y*x can be instantiated by nothing, inside a product. Therefore, we need to check that all the term is not going into the context. With proper support for interaction with the user, we should lift these tests. However, at the moment, they diff --git a/matcher.mli b/src/matcher.mli index a6b6f46..a6b6f46 100644 --- a/matcher.mli +++ b/src/matcher.mli @@ -11,18 +11,19 @@ open Pp open Matcher open Context.Rel.Declaration +open Names -type named_env = (Names.name * Terms.t) list +type named_env = (Name.t * Terms.t) list (** {pp_env} prints a substitution mapping names to terms, using the provided printer *) -let pp_env pt : named_env -> Pp.std_ppcmds = fun env -> +let pp_env pt : named_env -> Pp.t = fun env -> List.fold_left (fun acc (v,t) -> begin match v with - | Names.Name s -> str (Printf.sprintf "%s: " (Names.string_of_id s)) + | Names.Name s -> str (Printf.sprintf "%s: " (Id.to_string s)) | Names.Anonymous -> str ("_") end ++ pt t ++ str "; " ++ acc @@ -33,7 +34,7 @@ let pp_env pt : named_env -> Pp.std_ppcmds = fun env -> (** {pp_envm} prints a collection of possible environments, and number them. This number must remain compatible with the parameters given to {!aac_rewrite} *) -let pp_envm pt : named_env Search_monad.m -> Pp.std_ppcmds = fun m -> +let pp_envm pt : named_env Search_monad.m -> Pp.t = fun m -> let _,s = Search_monad.fold (fun env (n,acc) -> @@ -50,10 +51,10 @@ let trivial_substitution envm = (** {pp_all} prints a collection of possible contexts and related possibles substitutions, giving a number to each. This number must remain compatible with the parameters of {!aac_rewrite} *) -let pp_all pt : (int * Terms.t * named_env Search_monad.m) Search_monad.m -> Pp.std_ppcmds = fun m -> +let pp_all pt : (int * Terms.t * named_env Search_monad.m) Search_monad.m -> Pp.t = fun m -> let _,s = Search_monad.fold (fun (size,context,envm) (n,acc) -> - let s = str (Printf.sprintf "occurence %i: transitivity through " n) in + let s = str (Printf.sprintf "occurrence %i: transitivity through " n) in let s = s ++ pt context ++ str "\n" in let s = if trivial_substitution envm then s else s ++ str (Printf.sprintf "%i possible(s) substitution(s)" (Search_monad.count envm) ) @@ -67,7 +68,7 @@ let pp_all pt : (int * Terms.t * named_env Search_monad.m) Search_monad.m -> Pp. rename the variables, and rebuilds raw Coq terms (for the context, and the terms in the environment). In order to do so, it requires the information gathered by the {!Theory.Trans} module.*) -let print rlt ir m (context : Context.Rel.t) goal = +let print rlt ir m (context : EConstr.rel_context) goal = if Search_monad.count m = 0 then ( @@ -92,9 +93,11 @@ let print rlt ir m (context : Context.Rel.t) goal = ) in let m = Search_monad.sort (fun (x,_,_) (y,_,_) -> x - y) m in + let env = Tacmach.pf_env goal in + let sigma = Tacmach.project goal in let _ = Feedback.msg_notice (pp_all - (fun t -> Printer.pr_constr (Theory.Trans.raw_constr_of_t ir rlt context t) ) m + (fun t -> Printer.pr_letype_env env sigma (Theory.Trans.raw_constr_of_t ir rlt context t)) m ) in Tacticals.tclIDTAC goal diff --git a/print.mli b/src/print.mli index bbb9b20..5ca6e27 100644 --- a/print.mli +++ b/src/print.mli @@ -18,6 +18,6 @@ val print : Coq.Relation.t -> Theory.Trans.ir -> (int * Matcher.Terms.t * Matcher.Subst.t Search_monad.m) Search_monad.m -> - Context.Rel.t -> + EConstr.rel_context -> Proof_type.tactic diff --git a/search_monad.ml b/src/search_monad.ml index 09a6455..09a6455 100644 --- a/search_monad.ml +++ b/src/search_monad.ml diff --git a/search_monad.mli b/src/search_monad.mli index 7e2a910..7e2a910 100644 --- a/search_monad.mli +++ b/src/search_monad.mli diff --git a/theory.ml b/src/theory.ml index 20cb299..7871fe4 100644 --- a/theory.ml +++ b/src/theory.ml @@ -9,11 +9,10 @@ (** Constr from the theory of this particular development The inner-working of this module is highly correlated with the - particular structure of {b AAC.v}, therefore, it should + particular structure of {b AAC_rewrite.v}, therefore, it should be of little interest to most readers. *) -open Term -open Context +open EConstr module Control = struct let printing = true @@ -31,6 +30,7 @@ open Debug module HMap = Hashtbl.Make(Constr) let ac_theory_path = ["AAC_tactics"; "AAC"] +let ac_util_path = ["AAC_tactics"; "Utils"] module Stubs = struct let path = ac_theory_path@["Internal"] @@ -68,7 +68,7 @@ module Classes = struct module Associative = struct let path = ac_theory_path let typ = lazy (Coq.init_constant path "Associative") - let ty (rlt : Coq.Relation.t) (value : Term.constr) = + let ty (rlt : Coq.Relation.t) (value : constr) = mkApp (Lazy.force typ, [| rlt.Coq.Relation.carrier; rlt.Coq.Relation.r; value @@ -81,7 +81,7 @@ module Classes = struct module Commutative = struct let path = ac_theory_path let typ = lazy (Coq.init_constant path "Commutative") - let ty (rlt : Coq.Relation.t) (value : Term.constr) = + let ty (rlt : Coq.Relation.t) (value : constr) = mkApp (Lazy.force typ, [| rlt.Coq.Relation.carrier; rlt.Coq.Relation.r; value @@ -112,7 +112,7 @@ module Classes = struct module Unit = struct let path = ac_theory_path let typ = lazy (Coq.init_constant path "Unit") - let ty (rlt : Coq.Relation.t) (value : Term.constr) (unit : Term.constr)= + let ty (rlt : Coq.Relation.t) (value : constr) (unit : constr)= mkApp (Lazy.force typ, [| rlt.Coq.Relation.carrier; rlt.Coq.Relation.r; value; @@ -124,7 +124,7 @@ end (* Non empty lists *) module NEList = struct - let path = ac_theory_path @ ["Internal"] + let path = ac_util_path let typ = lazy (Coq.init_constant path "list") let nil = lazy (Coq.init_constant path "nil") let cons = lazy (Coq.init_constant path "cons") @@ -189,7 +189,7 @@ end module Sym = struct - type pack = {ar: Term.constr; value: Term.constr ; morph: Term.constr} + type pack = {ar: Constr.t; value: Constr.t ; morph: Constr.t} let path = ac_theory_path @ ["Internal";"Sym"] let typ = lazy (Coq.init_constant path "pack") let mkPack = lazy (Coq.init_constant path "mkPack") @@ -197,7 +197,7 @@ module Sym = struct let null = lazy (Coq.init_constant path "null") let mk_pack (rlt: Coq.Relation.t) s = let (x,r) = Coq.Relation.split rlt in - mkApp (Lazy.force mkPack, [|x;r; s.ar;s.value;s.morph|]) + mkApp (Lazy.force mkPack, [|x;r; EConstr.of_constr s.ar;EConstr.of_constr s.value;EConstr.of_constr s.morph|]) let null rlt = let x = rlt.Coq.Relation.carrier in let r = rlt.Coq.Relation.r in @@ -209,24 +209,24 @@ module Sym = struct end module Bin =struct - type pack = {value : Term.constr; - compat : Term.constr; - assoc : Term.constr; - comm : Term.constr option; + type pack = {value : Constr.t; + compat : Constr.t; + assoc : Constr.t; + comm : Constr.t option; } let path = ac_theory_path @ ["Internal";"Bin"] let typ = lazy (Coq.init_constant path "pack") let mkPack = lazy (Coq.init_constant path "mk_pack") - let mk_pack: Coq.Relation.t -> pack -> Term.constr = fun (rlt) s -> + let mk_pack: Coq.Relation.t -> pack -> constr = fun (rlt) s -> let (x,r) = Coq.Relation.split rlt in - let comm_ty = Classes.Commutative.ty rlt s.value in + let comm_ty = Classes.Commutative.ty rlt (EConstr.of_constr s.value) in mkApp (Lazy.force mkPack , [| x ; r; - s.value; - s.compat ; - s.assoc; - Coq.Option.of_option comm_ty s.comm + EConstr.of_constr s.value; + EConstr.of_constr s.compat ; + EConstr.of_constr s.assoc; + Coq.Option.of_option comm_ty (Option.map EConstr.of_constr s.comm) |]) let mk_ty : Coq.Relation.t -> constr = fun rlt -> let (x,r) = Coq.Relation.split rlt in @@ -242,13 +242,13 @@ module Unit = struct type unit_of = { - uf_u : Term.constr; (* u *) - uf_idx : Term.constr; - uf_desc : Term.constr; (* Unit R (e_bin uf_idx) u *) + uf_u : Constr.t; (* u *) + uf_idx : Constr.t; + uf_desc : Constr.t; (* Unit R (e_bin uf_idx) u *) } type pack = { - u_value : Term.constr; (* X *) + u_value : constr; (* X *) u_desc : (unit_of) list (* unit_of u_value *) } @@ -266,11 +266,11 @@ module Unit = struct r; e_bin ; u; - unit_of.uf_idx; - unit_of.uf_desc + EConstr.of_constr unit_of.uf_idx; + EConstr.of_constr unit_of.uf_desc |]) - let mk_pack rlt e_bin pack : Term.constr = + let mk_pack rlt e_bin pack : constr = let (x,r) = Coq.Relation.split rlt in let ty = ty_unit_of rlt e_bin pack.u_value in let mk_unit_of = mk_unit_of rlt e_bin pack.u_value in @@ -292,7 +292,7 @@ let anomaly msg = CErrors.anomaly ~label:"aac_tactics" (Pp.str msg) let user_error msg = - CErrors.error ("aac_tactics: " ^ msg) + CErrors.user_err Pp.(strbrk "aac_tactics: " ++ msg) module Trans = struct @@ -321,7 +321,7 @@ module Trans = struct | Bin of Bin.pack with_unit (* will only be used in the second pass : {!Parse}*) | Sym of Sym.pack - | Unit of constr (* to avoid confusion in bloom *) + | Unit of Constr.t (* to avoid confusion in bloom *) module PackHash = struct @@ -381,7 +381,7 @@ module Trans = struct module PackTable = Hashtbl.Make(PackHash) - (** discr is a map from {!Term.constr} to {!pack}. + (** discr is a map from {!constr} to {!pack}. [None] means that it is not possible to instantiate this partial application to an interesting class. @@ -423,9 +423,9 @@ module Trans = struct try PackTable.find envs.bloom pack with Not_found -> assert false - (********************************************) - (* (\* Gather the occuring AC/A symbols *\) *) - (********************************************) + (*********************************************) + (* (\* Gather the occurring AC/A symbols *\) *) + (*********************************************) (** This modules exhibit a function that memoize in the environment all the AC/A operators as well as the morphism that occur. This @@ -438,7 +438,7 @@ module Trans = struct units. Otherwise, we do not have the ability to rewrite [0 = a + a] in [a = ...]*) module Gather : sig - val gather : Coq.goal_sigma -> Coq.Relation.t -> envs -> Term.constr -> Coq.goal_sigma + val gather : Coq.goal_sigma -> Coq.Relation.t -> envs -> constr -> Coq.goal_sigma end = struct @@ -492,10 +492,10 @@ module Trans = struct None, goal in let bin = - {Bin.value = op; - Bin.compat = proper; - Bin.assoc = assoc; - Bin.comm = comm } + {Bin.value = EConstr.to_constr (Tacmach.project goal) op; + Bin.compat = EConstr.to_constr (Tacmach.project goal) proper; + Bin.assoc = EConstr.to_constr (Tacmach.project goal) assoc; + Bin.comm = Option.map (EConstr.to_constr (Tacmach.project goal)) comm } in Some (goal,bin) with |Not_found -> None @@ -509,25 +509,27 @@ module Trans = struct | Some (gl, unit,s) -> let unit_of = { - Unit.uf_u = unit; + Unit.uf_u = EConstr.to_constr (Tacmach.project goal) unit; (* TRICK : this term is not well-typed by itself, but it is okay the way we use it in the other functions *) - Unit.uf_idx = op; - Unit.uf_desc = s; + Unit.uf_idx = EConstr.to_constr (Tacmach.project goal) op; + Unit.uf_desc = EConstr.to_constr (Tacmach.project goal) s; } in Some (gl,Bin (bin_pack, Some (unit_of))) (** {is_morphism} try to infer the kind of operator we are dealing with *) - let is_morphism goal (rlt : Coq.Relation.t) (papp : Term.constr) (ar : int) : (Coq.goal_sigma * pack ) option = + let is_morphism goal (rlt : Coq.Relation.t) (papp : constr) (ar : int) : (Coq.goal_sigma * pack ) option = let typeof = Classes.Proper.mk_typeof rlt ar in let relof = Classes.Proper.mk_relof rlt ar in let m = Coq.Classes.mk_morphism typeof relof papp in try let m,goal = Coq.resolve_one_typeclass goal m in - let pack = {Sym.ar = (Coq.Nat.of_int ar); Sym.value= papp; Sym.morph= m} in + let pack = {Sym.ar = EConstr.to_constr (Tacmach.project goal) (Coq.Nat.of_int ar); + Sym.value= EConstr.to_constr (Tacmach.project goal) papp; + Sym.morph= EConstr.to_constr (Tacmach.project goal) m} in Some (goal, Sym pack) with | Not_found -> None @@ -541,7 +543,7 @@ module Trans = struct if n <= 1 then None else - let papp = Term.mkApp (t, Array.sub ca 0 (n-2) ) in + let papp = mkApp (t, Array.sub ca 0 (n-2) ) in let args = Array.sub ca (n-2) 2 in Some (papp, args ) @@ -550,16 +552,16 @@ module Trans = struct let nb_params = Array.length ca in let rec aux n = assert (n < nb_params && 0 < nb_params ); - let papp = Term.mkApp (t, Array.sub ca 0 n) in + let papp = mkApp (t, Array.sub ca 0 n) in match is_morphism goal rlt papp (nb_params - n) with | None -> (* here we have to memoize the failures *) - HMap.add envs.discr papp None; + HMap.add envs.discr (EConstr.to_constr (Tacmach.project goal) papp) None; if n < nb_params - 1 then aux (n+1) else goal | Some (goal, pack) -> let args = Array.sub ca (n) (nb_params -n)in let goal = Array.fold_left cont goal args in - memoize envs papp pack; + memoize envs (EConstr.to_constr (Tacmach.project goal) papp) pack; goal in if nb_params = 0 then goal else aux 0 @@ -572,7 +574,7 @@ module Trans = struct begin match is_aac papp goal with | None -> fold_morphism t ca | Some (goal, pack) -> - memoize envs papp pack; + memoize envs (EConstr.to_constr (Tacmach.project goal) papp) pack; Array.fold_left cont goal args end @@ -580,8 +582,8 @@ module Trans = struct have to memoize failures, here. *) let gather goal (rlt : Coq.Relation.t ) envs t : Coq.goal_sigma = let rec aux goal x = - match Coq.decomp_term x with - | App (t,ca) -> + match Coq.decomp_term (Tacmach.project goal) x with + | Constr.App (t,ca) -> fold goal rlt envs t ca (aux ) | _ -> goal in @@ -614,13 +616,15 @@ module Trans = struct This functions is prevented to go through [ar < 0] by the fact that a constant is a morphism. But not an eva. *) - let is_morphism goal (rlt : Coq.Relation.t) (papp : Term.constr) (ar : int) : (Coq.goal_sigma * pack ) option = + let is_morphism goal (rlt : Coq.Relation.t) (papp : constr) (ar : int) : (Coq.goal_sigma * pack ) option = let typeof = Classes.Proper.mk_typeof rlt ar in let relof = Classes.Proper.mk_relof rlt ar in let m = Coq.Classes.mk_morphism typeof relof papp in try let m,goal = Coq.resolve_one_typeclass goal m in - let pack = {Sym.ar = (Coq.Nat.of_int ar); Sym.value= papp; Sym.morph= m} in + let pack = {Sym.ar = EConstr.to_constr ~abort_on_undefined_evars:(false)(Tacmach.project goal) (Coq.Nat.of_int ar); + Sym.value= EConstr.to_constr ~abort_on_undefined_evars:(false)(Tacmach.project goal) papp; + Sym.morph= EConstr.to_constr ~abort_on_undefined_evars:(false)(Tacmach.project goal) m} in Some (goal, Sym pack) with | e -> None @@ -634,7 +638,7 @@ module Trans = struct let p_app = mkApp (t, Array.sub ca 0 (nb_params - ar)) in begin try - begin match HMap.find envs.discr p_app with + begin match HMap.find envs.discr (EConstr.to_constr ~abort_on_undefined_evars:(false) (Tacmach.project goal) p_app) with | None -> fold goal (ar-1) | Some pack -> @@ -649,7 +653,7 @@ module Trans = struct assert (0 <= ar && ar <= nb_params); match x with | Some (goal, pack) -> - HMap.add envs.discr p_app (Some pack); + HMap.add envs.discr (EConstr.to_constr ~abort_on_undefined_evars:(false) (Tacmach.project goal) p_app) (Some pack); add_bloom envs pack; (goal, pack, p_app, Array.sub ca (nb_params-ar) ar) | None -> @@ -657,29 +661,29 @@ module Trans = struct if ar = 0 then raise NotReflexive; begin (* to memoise the failures *) - HMap.add envs.discr p_app None; + HMap.add envs.discr (EConstr.to_constr ~abort_on_undefined_evars:(false) (Tacmach.project goal) p_app) None; (* will terminate, since [const] is capped, and it is easy to find an instance of a constant *) fold goal (ar-1) end in - try match HMap.find envs.discr (mkApp (t,ca))with + try match HMap.find envs.discr (EConstr.to_constr ~abort_on_undefined_evars:(false) (Tacmach.project goal) (mkApp (t,ca))) with | None -> fold goal (nb_params) | Some pack -> goal, pack, (mkApp (t,ca)), [| |] with Not_found -> fold goal (nb_params) let discriminate goal envs rlt x = try - match Coq.decomp_term x with - | App (t,ca) -> + match Coq.decomp_term (Tacmach.project goal) x with + | Constr.App (t,ca) -> discriminate goal envs rlt t ca | _ -> discriminate goal envs rlt x [| |] with - | NotReflexive -> user_error "The relation to which the goal was lifted is not Reflexive" + | NotReflexive -> user_error @@ Pp.strbrk "The relation to which the goal was lifted is not Reflexive" (* TODO: is it the only source of invalid use that fall into this catch_all ? *) | e -> - user_error "Cannot handle this kind of hypotheses (variables occuring under a function symbol which is not a proper morphism)." + user_error @@ Pp.strbrk "Cannot handle this kind of hypotheses (variables occurring under a function symbol which is not a proper morphism)." (** [t_of_constr goal rlt envs cstr] builds the abstract syntax tree of the term [cstr]. Doing so, it modifies the environment of @@ -688,8 +692,8 @@ module Trans = struct let t_of_constr goal (rlt: Coq.Relation.t ) envs : constr -> Matcher.Terms.t * Coq.goal_sigma = let r_goal = ref (goal) in let rec aux x = - match Coq.decomp_term x with - | Rel i -> Matcher.Terms.Var i + match Coq.decomp_term (Tacmach.project goal) x with + | Constr.Rel i -> Matcher.Terms.Var i | _ -> let goal, pack , p_app, ca = discriminate (!r_goal) envs rlt x in r_goal := goal; @@ -718,7 +722,7 @@ module Trans = struct end (* Parse *) let add_symbol goal rlt envs l = - let goal = Gather.gather goal rlt envs (Term.mkApp (l, [| Term.mkRel 0;Term.mkRel 0|])) in + let goal = Gather.gather goal rlt envs (EConstr.of_constr (Constr.mkApp (l, [| Constr.mkRel 0;Constr.mkRel 0|]))) in goal (* [t_of_constr] buils a the abstract syntax tree of a constr, @@ -740,7 +744,7 @@ module Trans = struct packer : (int, pack) Hashtbl.t; (* = bloom_back *) bin : (int * Bin.pack) list ; units : (int * Unit.pack) list; - sym : (int * Term.constr) list ; + sym : (int * constr) list ; matcher_units : Matcher.ext_units } @@ -751,7 +755,7 @@ module Trans = struct let nil = [] in let sym , (bin : (int * Bin.pack with_unit) list), - (units : (int * constr) list) = + (units : (int * Constr.t) list) = Hashtbl.fold (fun int pack (sym,bin,units) -> match pack with @@ -797,14 +801,14 @@ module Trans = struct if Constr.equal (unit_of.Unit.uf_u) u then {unit_of with - Unit.uf_idx = (Coq.Pos.of_int nop)} :: acc + Unit.uf_idx = EConstr.to_constr (Tacmach.project goal) (Coq.Pos.of_int nop)} :: acc else acc ) [] bin in (n,{ - Unit.u_value = u; + Unit.u_value = EConstr.of_constr u; Unit.u_desc = all_bin })::acc ) @@ -831,7 +835,7 @@ module Trans = struct (** [raw_constr_of_t_debruijn] rebuilds a term in the raw representation, without products on top, and maybe escaping free debruijn indices (in the case of a pattern for example). *) - let raw_constr_of_t_debruijn ir (t : Matcher.Terms.t) : Term.constr * int list = + let raw_constr_of_t_debruijn ir (t : Matcher.Terms.t) : constr * int list = let add_set,get = let r = ref [] in let rec add x = function @@ -849,25 +853,25 @@ module Trans = struct | Matcher.Terms.Plus (s,l,r) -> begin match Hashtbl.find ir.packer s with | Bin (s,_) -> - mkApp (s.Bin.value , [|(aux l);(aux r)|]) + mkApp (EConstr.of_constr s.Bin.value , [|(aux l);(aux r)|]) | _ -> Printf.printf "erreur:%i\n%!"s; assert false end | Matcher.Terms.Dot (s,l,r) -> begin match Hashtbl.find ir.packer s with | Bin (s,_) -> - mkApp (s.Bin.value, [|(aux l);(aux r)|]) + mkApp (EConstr.of_constr s.Bin.value, [|(aux l);(aux r)|]) | _ -> assert false end | Matcher.Terms.Sym (s,t) -> begin match Hashtbl.find ir.packer s with | Sym s -> - mkApp (s.Sym.value, Array.map aux t) + mkApp (EConstr.of_constr s.Sym.value, Array.map aux t) | _ -> assert false end | Matcher.Terms.Unit x -> begin match Hashtbl.find ir.packer x with - | Unit s -> s + | Unit s -> EConstr.of_constr s | _ -> assert false end | Matcher.Terms.Var i -> add_set i; @@ -877,7 +881,7 @@ module Trans = struct t , get ( ) (** [raw_constr_of_t] rebuilds a term in the raw representation *) - let raw_constr_of_t ir rlt (context:Context.Rel.t) t = + let raw_constr_of_t ir rlt (context:rel_context) t = (** cap rebuilds the products in front of the constr *) let rec cap c = function [] -> c | t::q -> @@ -906,16 +910,16 @@ module Trans = struct from the symbols (as ints) to indexes (as constr) *) type sigmas = { - env_sym : Term.constr; - env_bin : Term.constr; - env_units : Term.constr; (* the [idx -> X:constr] *) + env_sym : constr; + env_bin : constr; + env_units : constr; (* the [idx -> X:constr] *) } type sigma_maps = { - sym_to_pos : int -> Term.constr; - bin_to_pos : int -> Term.constr; - units_to_pos : int -> Term.constr; + sym_to_pos : int -> constr; + bin_to_pos : int -> constr; + units_to_pos : int -> constr; } @@ -935,12 +939,12 @@ module Trans = struct let compat,goal = Classes.Proper.infer goal rlt op 2 in let op = Coq.nf_evar goal op in { - Bin.value = op; - Bin.compat = compat; - Bin.assoc = assoc; + Bin.value = EConstr.to_constr (Tacmach.project goal) op; + Bin.compat = EConstr.to_constr (Tacmach.project goal) compat; + Bin.assoc = EConstr.to_constr (Tacmach.project goal) assoc; Bin.comm = None } - with Not_found -> user_error "Cannot infer a default A operator (required at least to be Proper and Associative)" + with Not_found -> user_error @@ Pp.strbrk "Cannot infer a default A operator (required at least to be Proper and Associative)" in let zero, goal = try diff --git a/theory.mli b/src/theory.mli index fe79a11..e7bfbfe 100644 --- a/theory.mli +++ b/src/theory.mli @@ -10,14 +10,14 @@ reification and translation functions. Note: this module is highly correlated with the definitions of {i - AAC.v}. + AAC_rewrite.v}. This module interfaces with the above Coq module; it provides facilities to interpret a term with arbitrary operators as an abstract syntax tree, and to convert an AST into a Coq term (either using the Coq "raw" terms, as written in the starting goal, or using the reified Coq datatypes we define in {i - AAC.v}). + AAC_rewrite.v}). *) (** Both in OCaml and Coq, we represent finite multisets using @@ -26,7 +26,7 @@ [mk_mset ty l] constructs a Coq multiset from an OCaml multiset [l] of Coq terms of type [ty] *) -val mk_mset:Term.constr -> (Term.constr * int) list ->Term.constr +val mk_mset:EConstr.constr -> (EConstr.constr * int) list ->EConstr.constr (** {2 Packaging modules} *) @@ -34,16 +34,16 @@ val mk_mset:Term.constr -> (Term.constr * int) list ->Term.constr module Sigma: sig (** [add ty n x map] adds the value [x] of type [ty] with key [n] in [map] *) - val add: Term.constr ->Term.constr ->Term.constr ->Term.constr ->Term.constr + val add: EConstr.constr ->EConstr.constr ->EConstr.constr ->EConstr.constr ->EConstr.constr (** [empty ty] create an empty map of type [ty] *) - val empty: Term.constr ->Term.constr + val empty: EConstr.constr ->EConstr.constr (** [of_list ty null l] translates an OCaml association list into a Coq one *) - val of_list: Term.constr -> Term.constr -> (int * Term.constr ) list -> Term.constr + val of_list: EConstr.constr -> EConstr.constr -> (int * EConstr.constr ) list -> EConstr.constr (** [to_fun ty null map] converts a Coq association list into a Coq function (with default value [null]) *) - val to_fun: Term.constr ->Term.constr ->Term.constr ->Term.constr + val to_fun: EConstr.constr ->EConstr.constr ->EConstr.constr ->EConstr.constr end @@ -51,16 +51,16 @@ end module Sym: sig (** mimics the Coq record [Sym.pack] *) - type pack = {ar: Term.constr; value: Term.constr ; morph: Term.constr} + type pack = {ar: Constr.t; value: Constr.t ; morph: Constr.t} - val typ: Term.constr lazy_t + val typ: EConstr.constr lazy_t (** [mk_pack rlt (ar,value,morph)] *) - val mk_pack: Coq.Relation.t -> pack -> Term.constr + val mk_pack: Coq.Relation.t -> pack -> EConstr.constr (** [null] builds a dummy (identity) symbol, given an {!Coq.Relation.t} *) - val null: Coq.Relation.t -> Term.constr + val null: Coq.Relation.t -> EConstr.constr end @@ -68,20 +68,20 @@ end (** We need to export some Coq stubs out of this module. They are used by the main tactic, see {!Rewrite} *) module Stubs : sig - val lift : Term.constr Lazy.t - val lift_proj_equivalence : Term.constr Lazy.t - val lift_transitivity_left : Term.constr Lazy.t - val lift_transitivity_right : Term.constr Lazy.t - val lift_reflexivity : Term.constr Lazy.t + val lift : EConstr.constr Lazy.t + val lift_proj_equivalence : EConstr.constr Lazy.t + val lift_transitivity_left : EConstr.constr Lazy.t + val lift_transitivity_right : EConstr.constr Lazy.t + val lift_reflexivity : EConstr.constr Lazy.t (** The evaluation fonction, used to convert a reified coq term to a raw coq term *) - val eval: Term.constr lazy_t + val eval: EConstr.constr lazy_t (** The main lemma of our theory, that is [compare (norm u) (norm v) = Eq -> eval u == eval v] *) - val decide_thm:Term.constr lazy_t + val decide_thm:EConstr.constr lazy_t - val lift_normalise_thm : Term.constr lazy_t + val lift_normalise_thm : EConstr.constr lazy_t end (** {2 Building reified terms} @@ -136,11 +136,11 @@ module Trans : sig evars; this is why we give back the [goal], accordingly updated. *) - val t_of_constr : Coq.goal_sigma -> Coq.Relation.t -> envs -> (Term.constr * Term.constr) -> Matcher.Terms.t * Matcher.Terms.t * Coq.goal_sigma + val t_of_constr : Coq.goal_sigma -> Coq.Relation.t -> envs -> (EConstr.constr * EConstr.constr) -> Matcher.Terms.t * Matcher.Terms.t * Coq.goal_sigma (** [add_symbol] adds a given binary symbol to the environment of known stuff. *) - val add_symbol : Coq.goal_sigma -> Coq.Relation.t -> envs -> Term.constr -> Coq.goal_sigma + val add_symbol : Coq.goal_sigma -> Coq.Relation.t -> envs -> Constr.t -> Coq.goal_sigma (** {2 Reconstruction: from AST back to Coq terms } @@ -160,16 +160,16 @@ module Trans : sig reconstruct the named products on top of it. In particular, this allow us to print the context put around the left (or right) hand side of a pattern. *) - val raw_constr_of_t : ir -> Coq.Relation.t -> (Context.Rel.t) ->Matcher.Terms.t -> Term.constr + val raw_constr_of_t : ir -> Coq.Relation.t -> EConstr.rel_context -> Matcher.Terms.t -> EConstr.constr (** {2 Building reified terms} *) (** The reification environments, as Coq constrs *) type sigmas = { - env_sym : Term.constr; - env_bin : Term.constr; - env_units : Term.constr; (* the [idx -> X:constr] *) + env_sym : EConstr.constr; + env_bin : EConstr.constr; + env_units : EConstr.constr; (* the [idx -> X:constr] *) } @@ -188,10 +188,10 @@ module Trans : sig reify each term successively.*) type reifier - val mk_reifier : Coq.Relation.t -> Term.constr -> ir -> (sigmas * reifier -> Proof_type.tactic) -> Proof_type.tactic + val mk_reifier : Coq.Relation.t -> EConstr.constr -> ir -> (sigmas * reifier -> Proof_type.tactic) -> Proof_type.tactic (** [reif_constr_of_t reifier t] rebuilds the term [t] in the reified form. *) - val reif_constr_of_t : reifier -> Matcher.Terms.t -> Term.constr + val reif_constr_of_t : reifier -> Matcher.Terms.t -> EConstr.constr end @@ -32,6 +32,9 @@ Require Import FMapPositive FMapFacts. Require Import RelationClasses Equality. Require Export Morphisms. +From AAC_tactics +Require Import Utils. + Set Implicit Arguments. Set Asymmetric Patterns. @@ -88,7 +91,6 @@ Instance aac_lift_proper {X} {R : relation X} {E} {HE: Equivalence E} Module Internal. - (** * Utilities for the evaluation function *) Section copy. @@ -113,7 +115,7 @@ Section copy. Qed. Lemma copy_xH : forall x, R (copy 1 x) x. Proof. intros; unfold copy; rewrite Prect_base. reflexivity. Qed. - Lemma copy_Psucc : forall n x, R (copy (Psucc n) x) (plus x (copy n x)). + Lemma copy_Psucc : forall n x, R (copy (Pos.succ n) x) (plus x (copy n x)). Proof. intros; unfold copy; rewrite Prect_succ. reflexivity. Qed. Global Instance copy_compat n: Proper (R ==> R) (copy n). @@ -126,248 +128,6 @@ Section copy. End copy. -(** * Utilities for positive numbers - which we use as: - - indices for morphisms and symbols - - multiplicity of terms in sums *) - -Local Notation idx := positive. - -Fixpoint eq_idx_bool i j := - match i,j with - | xH, xH => true - | xO i, xO j => eq_idx_bool i j - | xI i, xI j => eq_idx_bool i j - | _, _ => false - end. - -Fixpoint idx_compare i j := - match i,j with - | xH, xH => Eq - | xH, _ => Lt - | _, xH => Gt - | xO i, xO j => idx_compare i j - | xI i, xI j => idx_compare i j - | xI _, xO _ => Gt - | xO _, xI _ => Lt - end. - -Local Notation pos_compare := idx_compare (only parsing). - -(** Specification predicate for boolean binary functions *) -Inductive decide_spec {A} {B} (R : A -> B -> Prop) (x : A) (y : B) : bool -> Prop := -| decide_true : R x y -> decide_spec R x y true -| decide_false : ~(R x y) -> decide_spec R x y false. - -Lemma eq_idx_spec : forall i j, decide_spec (@eq _) i j (eq_idx_bool i j). -Proof. - induction i; destruct j; simpl; try (constructor; congruence). - case (IHi j); constructor; congruence. - case (IHi j); constructor; congruence. -Qed. - -(** weak specification predicate for comparison functions: only the 'Eq' case is specified *) -Inductive compare_weak_spec A: A -> A -> comparison -> Prop := -| pcws_eq: forall i, compare_weak_spec i i Eq -| pcws_lt: forall i j, compare_weak_spec i j Lt -| pcws_gt: forall i j, compare_weak_spec i j Gt. - -Lemma pos_compare_weak_spec: forall i j, compare_weak_spec i j (pos_compare i j). -Proof. induction i; destruct j; simpl; try constructor; case (IHi j); intros; constructor. Qed. - -Lemma idx_compare_reflect_eq: forall i j, idx_compare i j = Eq -> i=j. -Proof. intros i j. case (pos_compare_weak_spec i j); intros; congruence. Qed. - -(** * Dependent types utilities *) - -Local Notation cast T H u := (eq_rect _ T u _ H). - -Section dep. - Variable U: Type. - Variable T: U -> Type. - - Lemma cast_eq: (forall u v: U, {u=v}+{u<>v}) -> - forall A (H: A=A) (u: T A), cast T H u = u. - Proof. intros. rewrite <- Eqdep_dec.eq_rect_eq_dec; trivial. Qed. - - Variable f: forall A B, T A -> T B -> comparison. - Definition reflect_eqdep := forall A u B v (H: A=B), @f A B u v = Eq -> cast T H u = v. - - (* these lemmas have to remain transparent to get structural recursion - in the lemma [tcompare_weak_spec] below *) - Lemma reflect_eqdep_eq: reflect_eqdep -> - forall A u v, @f A A u v = Eq -> u = v. - Proof. intros H A u v He. apply (H _ _ _ _ eq_refl He). Defined. - - Lemma reflect_eqdep_weak_spec: reflect_eqdep -> - forall A u v, compare_weak_spec u v (@f A A u v). - Proof. - intros. case_eq (f u v); try constructor. - intro H'. apply reflect_eqdep_eq in H'. subst. constructor. assumption. - Defined. -End dep. - - - -(** * Utilities about (non-empty) lists and multisets *) - -Inductive nelist (A : Type) : Type := -| nil : A -> nelist A -| cons : A -> nelist A -> nelist A. - -Local Notation "x :: y" := (cons x y). - -Fixpoint nelist_map (A B: Type) (f: A -> B) l := - match l with - | nil x => nil ( f x) - | cons x l => cons ( f x) (nelist_map f l) - end. - -Fixpoint appne A l l' : nelist A := - match l with - nil x => cons x l' - | cons t q => cons t (appne A q l') - end. - -Local Notation "x ++ y" := (appne x y). - -(** finite multisets are represented with ordered lists with multiplicities *) -Definition mset A := nelist (A*positive). - -(** lexicographic composition of comparisons (this is a notation to keep it lazy) *) -Local Notation lex e f := (match e with Eq => f | _ => e end). - - -Section lists. - - (** comparison functions *) - - Section c. - Variables A B: Type. - Variable compare: A -> B -> comparison. - Fixpoint list_compare h k := - match h,k with - | nil x, nil y => compare x y - | nil x, _ => Lt - | _, nil x => Gt - | u::h, v::k => lex (compare u v) (list_compare h k) - end. - End c. - Definition mset_compare A B compare: mset A -> mset B -> comparison := - list_compare (fun un vm => - let '(u,n) := un in - let '(v,m) := vm in - lex (compare u v) (pos_compare n m)). - - Section list_compare_weak_spec. - Variable A: Type. - Variable compare: A -> A -> comparison. - Hypothesis Hcompare: forall u v, compare_weak_spec u v (compare u v). - (* this lemma has to remain transparent to get structural recursion - in the lemma [tcompare_weak_spec] below *) - Lemma list_compare_weak_spec: forall h k, - compare_weak_spec h k (list_compare compare h k). - Proof. - induction h as [|u h IHh]; destruct k as [|v k]; simpl; try constructor. - - case (Hcompare a a0 ); try constructor. - case (Hcompare u v ); try constructor. - case (IHh k); intros; constructor. - Defined. - End list_compare_weak_spec. - - Section mset_compare_weak_spec. - Variable A: Type. - Variable compare: A -> A -> comparison. - Hypothesis Hcompare: forall u v, compare_weak_spec u v (compare u v). - (* this lemma has to remain transparent to get structural recursion - in the lemma [tcompare_weak_spec] below *) - Lemma mset_compare_weak_spec: forall h k, - compare_weak_spec h k (mset_compare compare h k). - Proof. - apply list_compare_weak_spec. - intros [u n] [v m]. - case (Hcompare u v); try constructor. - case (pos_compare_weak_spec n m); try constructor. - Defined. - End mset_compare_weak_spec. - - (** (sorted) merging functions *) - - Section m. - Variable A: Type. - Variable compare: A -> A -> comparison. - Definition insert n1 h1 := - let fix insert_aux l2 := - match l2 with - | nil (h2,n2) => - match compare h1 h2 with - | Eq => nil (h1,Pplus n1 n2) - | Lt => (h1,n1):: nil (h2,n2) - | Gt => (h2,n2):: nil (h1,n1) - end - | (h2,n2)::t2 => - match compare h1 h2 with - | Eq => (h1,Pplus n1 n2):: t2 - | Lt => (h1,n1)::l2 - | Gt => (h2,n2)::insert_aux t2 - end - end - in insert_aux. - - Fixpoint merge_msets l1 := - match l1 with - | nil (h1,n1) => fun l2 => insert n1 h1 l2 - | (h1,n1)::t1 => - let fix merge_aux l2 := - match l2 with - | nil (h2,n2) => - match compare h1 h2 with - | Eq => (h1,Pplus n1 n2) :: t1 - | Lt => (h1,n1):: merge_msets t1 l2 - | Gt => (h2,n2):: l1 - end - | (h2,n2)::t2 => - match compare h1 h2 with - | Eq => (h1,Pplus n1 n2)::merge_msets t1 t2 - | Lt => (h1,n1)::merge_msets t1 l2 - | Gt => (h2,n2)::merge_aux t2 - end - end - in merge_aux - end. - - (** interpretation of a list with a constant and a binary operation *) - - Variable B: Type. - Variable map: A -> B. - Variable b2: B -> B -> B. - Fixpoint fold_map l := - match l with - | nil x => map x - | u::l => b2 (map u) (fold_map l) - end. - - (** mapping and merging *) - - Variable merge: A -> nelist B -> nelist B. - Fixpoint merge_map (l: nelist A): nelist B := - match l with - | nil x => nil (map x) - | u::l => merge u (merge_map l) - end. - - Variable ret : A -> B. - Variable bind : A -> B -> B. - Fixpoint fold_map' (l : nelist A) : B := - match l with - | nil x => ret x - | u::l => bind u (fold_map' l) - end. - - End m. -End lists. - (** * Packaging structures *) (** ** free symbols *) @@ -842,7 +602,7 @@ Section s. Qed. - Lemma copy_mset_succ n (l: mset T): eval (sum i (copy_mset (Psucc n) l)) == @Bin.value _ _ (e_bin i) (eval (sum i l)) (eval (sum i (copy_mset n l))). + Lemma copy_mset_succ n (l: mset T): eval (sum i (copy_mset (Pos.succ n) l)) == @Bin.value _ _ (e_bin i) (eval (sum i l)) (eval (sum i (copy_mset n l))). Proof. rewrite 2 copy_mset'. @@ -1118,7 +878,7 @@ End Internal. Local Ltac internal_normalize := let x := fresh in let y := fresh in intro x; intro y; vm_compute in x; vm_compute in y; unfold x; unfold y; - compute [Internal.eval Internal.fold_map Internal.copy Prect]; simpl. + compute [Internal.eval Utils.fold_map Internal.copy Prect]; simpl. (** * Lemmas for performing transitivity steps @@ -1138,4 +898,4 @@ Section t. End t. -Declare ML Module "aac". +Declare ML Module "aac_plugin". diff --git a/Caveats.v b/theories/Caveats.v index a7967cc..d7824cd 100644 --- a/Caveats.v +++ b/theories/Caveats.v @@ -13,7 +13,11 @@ with the path to the [aac_tactics] library *) +Require NArith Minus. + +From AAC_tactics Require Import AAC. +From AAC_tactics Require Instances. (** ** Limitations *) @@ -74,7 +78,7 @@ End parameters. type [T] to some other type [T']. *) Section morphism. - Require Import NArith Minus. + Import NArith Minus. Open Scope nat_scope. (** Typically, although [N_of_nat] is a proper morphism from @@ -122,11 +126,11 @@ End morphism. Section ineq. - Require Import ZArith. + Import ZArith. Import Instances.Z. Open Scope Z_scope. - Instance Zplus_incr: Proper (Zle ==> Zle ==> Zle) Zplus. + Instance Zplus_incr: Proper (Z.le ==> Z.le ==> Z.le) Zplus. Proof. intros ? ? H ? ? H'. apply Zplus_le_compat; assumption. Qed. Hypothesis H: forall x, x+x <= x. @@ -197,7 +201,7 @@ appearing in a goal are considered as constants, they will not be instantiated. *) Section evars. - Require Import ZArith. + Import ZArith. Import Instances.Z. Variable P: Prop. @@ -333,7 +337,7 @@ Goal a+b*c = c. *) Abort. -(** **** If the pattern is a unit or can be instanciated to be equal +(** **** If the pattern is a unit or can be instantiated to be equal to a unit: The heuristic is to make the unit appear at each possible position @@ -350,7 +354,7 @@ Goal a+b+c = c. (** 7 solutions, we miss solutions like [(a+b+c+0*(1+0*[]))]*) Abort. -(** *** Another example of the former case is the following, where the hypothesis can be instanciated to be equal to [1] *) +(** *** Another example of the former case is the following, where the hypothesis can be instantiated to be equal to [1] *) Hypothesis H : forall x y, (x+y)*x = x*x + y *x. Goal a*a+b*a + c = c. (** Here, only one solution if we use the aac_instance tactic *) diff --git a/Instances.v b/theories/Instances.v index 55dffbb..d007ceb 100644 --- a/Instances.v +++ b/theories/Instances.v @@ -12,6 +12,7 @@ Require ZArith Zminmax. Require QArith Qminmax. Require Relations. +From AAC_tactics Require Export AAC. (** Instances for aac_rewrite.*) @@ -58,18 +59,18 @@ Module Z. Instance aac_Zmult_Comm : Commutative eq Zmult := Zmult_comm. Instance aac_Zmult_Assoc : Associative eq Zmult := Zmult_assoc. - Instance aac_Zmin_Comm : Commutative eq Zmin := Zmin_comm. - Instance aac_Zmin_Assoc : Associative eq Zmin := Zmin_assoc. + Instance aac_Zmin_Comm : Commutative eq Z.min := Z.min_comm. + Instance aac_Zmin_Assoc : Associative eq Z.min := Z.min_assoc. - Instance aac_Zmax_Comm : Commutative eq Zmax := Zmax_comm. - Instance aac_Zmax_Assoc : Associative eq Zmax := Zmax_assoc. + Instance aac_Zmax_Comm : Commutative eq Z.max := Z.max_comm. + Instance aac_Zmax_Assoc : Associative eq Z.max := Z.max_assoc. Instance aac_one : Unit eq Zmult 1 := Build_Unit eq Zmult 1 Zmult_1_l Zmult_1_r. Instance aac_zero_Zplus : Unit eq Zplus 0 := Build_Unit eq Zplus 0 Zplus_0_l Zplus_0_r. (* We also provide liftings from le to eq *) - Instance preorder_Zle : PreOrder Zle := Build_PreOrder _ Zle_refl Zle_trans. - Instance lift_le_eq : AAC_lift Zle eq := Build_AAC_lift eq_equivalence _. + Instance preorder_Zle : PreOrder Z.le := Build_PreOrder _ Z.le_refl Z.le_trans. + Instance lift_le_eq : AAC_lift Z.le eq := Build_AAC_lift eq_equivalence _. End Z. @@ -95,19 +96,19 @@ Module N. Instance aac_Nmult_Comm : Commutative eq Nmult := Nmult_comm. Instance aac_Nmult_Assoc : Associative eq Nmult := Nmult_assoc. - Instance aac_Nmin_Comm : Commutative eq Nmin := N.min_comm. - Instance aac_Nmin_Assoc : Associative eq Nmin := N.min_assoc. + Instance aac_Nmin_Comm : Commutative eq N.min := N.min_comm. + Instance aac_Nmin_Assoc : Associative eq N.min := N.min_assoc. - Instance aac_Nmax_Comm : Commutative eq Nmax := N.max_comm. - Instance aac_Nmax_Assoc : Associative eq Nmax := N.max_assoc. + Instance aac_Nmax_Comm : Commutative eq N.max := N.max_comm. + Instance aac_Nmax_Assoc : Associative eq N.max := N.max_assoc. Instance aac_one : Unit eq Nmult (1)%N := Build_Unit eq Nmult (1)%N Nmult_1_l Nmult_1_r. Instance aac_zero : Unit eq Nplus (0)%N := Build_Unit eq Nplus (0)%N Nplus_0_l Nplus_0_r. - Instance aac_zero_max : Unit eq Nmax 0 := Build_Unit eq Nmax 0 N.max_0_l N.max_0_r. + Instance aac_zero_max : Unit eq N.max 0 := Build_Unit eq N.max 0 N.max_0_l N.max_0_r. (* We also provide liftings from le to eq *) - Instance preorder_le : PreOrder Nle := Build_PreOrder Nle N.le_refl N.le_trans. - Instance lift_le_eq : AAC_lift Nle eq := Build_AAC_lift eq_equivalence _. + Instance preorder_le : PreOrder N.le := Build_PreOrder N.le N.le_refl N.le_trans. + Instance lift_le_eq : AAC_lift N.le eq := Build_AAC_lift eq_equivalence _. End N. @@ -120,19 +121,19 @@ Module P. Instance aac_Pmult_Comm : Commutative eq Pmult := Pmult_comm. Instance aac_Pmult_Assoc : Associative eq Pmult := Pmult_assoc. - Instance aac_Pmin_Comm : Commutative eq Pmin := Pos.min_comm. - Instance aac_Pmin_Assoc : Associative eq Pmin := Pos.min_assoc. + Instance aac_Pmin_Comm : Commutative eq Pos.min := Pos.min_comm. + Instance aac_Pmin_Assoc : Associative eq Pos.min := Pos.min_assoc. - Instance aac_Pmax_Comm : Commutative eq Pmax := Pos.max_comm. - Instance aac_Pmax_Assoc : Associative eq Pmax := Pos.max_assoc. + Instance aac_Pmax_Comm : Commutative eq Pos.max := Pos.max_comm. + Instance aac_Pmax_Assoc : Associative eq Pos.max := Pos.max_assoc. Instance aac_one : Unit eq Pmult 1 := Build_Unit eq Pmult 1 _ Pmult_1_r. intros; reflexivity. Qed. (* TODO : add this lemma in the stdlib *) - Instance aac_one_max : Unit eq Pmax 1 := Build_Unit eq Pmax 1 Pos.max_1_l Pos.max_1_r. + Instance aac_one_max : Unit eq Pos.max 1 := Build_Unit eq Pos.max 1 Pos.max_1_l Pos.max_1_r. (* We also provide liftings from le to eq *) - Instance preorder_le : PreOrder Ple := Build_PreOrder Ple Pos.le_refl Pos.le_trans. - Instance lift_le_eq : AAC_lift Ple eq := Build_AAC_lift eq_equivalence _. + Instance preorder_le : PreOrder Pos.le := Build_PreOrder Pos.le Pos.le_refl Pos.le_trans. + Instance lift_le_eq : AAC_lift Pos.le eq := Build_AAC_lift eq_equivalence _. End P. Module Q. diff --git a/Tutorial.v b/theories/Tutorial.v index 76006ca..e403d92 100644 --- a/Tutorial.v +++ b/theories/Tutorial.v @@ -12,9 +12,11 @@ lines, or add them to your .coqrc files, replacing "." with the path to the [aac_tactics] library. *) -Add Rec LoadPath "." as AAC_tactics. -Add ML Path ".". +Require Arith ZArith. + +From AAC_tactics Require Import AAC. +From AAC_tactics Require Instances. (** ** Introductory example @@ -29,12 +31,12 @@ Section introduction. Import Instances.Z. Variables a b c : Z. - Hypothesis H: forall x, x + Zopp x = 0. - Goal a + b + c + Zopp (c + a) = b. + Hypothesis H: forall x, x + Z.opp x = 0. + Goal a + b + c + Z.opp (c + a) = b. aac_rewrite H. aac_reflexivity. Qed. - Goal a + c + Zopp (b + a + Zopp b) = c. + Goal a + c + Z.opp (b + a + Z.opp b) = c. do 2 aac_rewrite H. reflexivity. Qed. @@ -223,7 +225,7 @@ End base. already declared in file [Instances.v].) *) Section Peano. - Require Import Arith. + Import Arith. Instance aac_plus_Assoc : Associative eq plus := plus_assoc. Instance aac_plus_Comm : Commutative eq plus := plus_comm. @@ -327,7 +329,7 @@ End Peano. Section AAC_normalise. Import Instances.Z. - Require Import ZArith. + Import ZArith. Open Scope Z_scope. Variable a b c d : Z. @@ -344,30 +346,30 @@ End AAC_normalise. Section Examples. Import Instances.Z. - Require Import ZArith. + Import ZArith. Open Scope Z_scope. (** *** Reverse triangle inequality *) - Lemma Zabs_triangle : forall x y, Zabs (x + y) <= Zabs x + Zabs y . - Proof Zabs_triangle. + Lemma Zabs_triangle : forall x y, Z.abs (x + y) <= Z.abs x + Z.abs y . + Proof Z.abs_triangle. Lemma Zplus_opp_r : forall x, x + -x = 0. Proof Zplus_opp_r. (** The following morphisms are required to perform the required rewrites *) - Instance Zminus_compat : Proper (Zge ==> Zle) Zopp. + Instance Zminus_compat : Proper (Z.ge ==> Z.le) Z.opp. Proof. intros x y. omega. Qed. - Instance Proper_Zplus : Proper (Zle ==> Zle ==> Zle) Zplus. + Instance Proper_Zplus : Proper (Z.le ==> Z.le ==> Z.le) Zplus. Proof. firstorder. Qed. - Goal forall a b, Zabs a - Zabs b <= Zabs (a - b). + Goal forall a b, Z.abs a - Z.abs b <= Z.abs (a - b). intros. unfold Zminus. aac_instances <- (Zminus_diag b). aac_rewrite <- (Zminus_diag b) at 3. unfold Zminus. - aac_rewrite Zabs_triangle. + aac_rewrite Z.abs_triangle. aac_rewrite Zplus_opp_r. aac_reflexivity. Qed. diff --git a/theories/Utils.v b/theories/Utils.v new file mode 100644 index 0000000..0f37ae1 --- /dev/null +++ b/theories/Utils.v @@ -0,0 +1,257 @@ +(***************************************************************************) +(* This is part of aac_tactics, it is distributed under the terms of the *) +(* GNU Lesser General Public License version 3 *) +(* (see file LICENSE for more details) *) +(* *) +(* Copyright 2009-2010: Thomas Braibant, Damien Pous. *) +(***************************************************************************) + + +Require Import Arith NArith. +Require Import List. +Require Import FMapPositive FMapFacts. +Require Import RelationClasses Equality. + +Set Implicit Arguments. +Set Asymmetric Patterns. + +(** * Utilities for positive numbers + which we use as: + - indices for morphisms and symbols + - multiplicity of terms in sums *) + +Notation idx := positive. + +Fixpoint eq_idx_bool i j := + match i,j with + | xH, xH => true + | xO i, xO j => eq_idx_bool i j + | xI i, xI j => eq_idx_bool i j + | _, _ => false + end. + +Fixpoint idx_compare i j := + match i,j with + | xH, xH => Eq + | xH, _ => Lt + | _, xH => Gt + | xO i, xO j => idx_compare i j + | xI i, xI j => idx_compare i j + | xI _, xO _ => Gt + | xO _, xI _ => Lt + end. + +Notation pos_compare := idx_compare (only parsing). + +(** Specification predicate for boolean binary functions *) +Inductive decide_spec {A} {B} (R : A -> B -> Prop) (x : A) (y : B) : bool -> Prop := +| decide_true : R x y -> decide_spec R x y true +| decide_false : ~(R x y) -> decide_spec R x y false. + +Lemma eq_idx_spec : forall i j, decide_spec (@eq _) i j (eq_idx_bool i j). +Proof. + induction i; destruct j; simpl; try (constructor; congruence). + case (IHi j); constructor; congruence. + case (IHi j); constructor; congruence. +Qed. + +(** weak specification predicate for comparison functions: only the 'Eq' case is specified *) +Inductive compare_weak_spec A: A -> A -> comparison -> Prop := +| pcws_eq: forall i, compare_weak_spec i i Eq +| pcws_lt: forall i j, compare_weak_spec i j Lt +| pcws_gt: forall i j, compare_weak_spec i j Gt. + +Lemma pos_compare_weak_spec: forall i j, compare_weak_spec i j (pos_compare i j). +Proof. induction i; destruct j; simpl; try constructor; case (IHi j); intros; constructor. Qed. + +Lemma idx_compare_reflect_eq: forall i j, idx_compare i j = Eq -> i=j. +Proof. intros i j. case (pos_compare_weak_spec i j); intros; congruence. Qed. + +(** * Dependent types utilities *) + +Notation cast T H u := (eq_rect _ T u _ H). + +Section dep. + Variable U: Type. + Variable T: U -> Type. + + Lemma cast_eq: (forall u v: U, {u=v}+{u<>v}) -> + forall A (H: A=A) (u: T A), cast T H u = u. + Proof. intros. rewrite <- Eqdep_dec.eq_rect_eq_dec; trivial. Qed. + + Variable f: forall A B, T A -> T B -> comparison. + Definition reflect_eqdep := forall A u B v (H: A=B), @f A B u v = Eq -> cast T H u = v. + + (* these lemmas have to remain transparent to get structural recursion + in the lemma [tcompare_weak_spec] below *) + Lemma reflect_eqdep_eq: reflect_eqdep -> + forall A u v, @f A A u v = Eq -> u = v. + Proof. intros H A u v He. apply (H _ _ _ _ eq_refl He). Defined. + + Lemma reflect_eqdep_weak_spec: reflect_eqdep -> + forall A u v, compare_weak_spec u v (@f A A u v). + Proof. + intros. case_eq (f u v); try constructor. + intro H'. apply reflect_eqdep_eq in H'. subst. constructor. assumption. + Defined. +End dep. + + +(** * Utilities about (non-empty) lists and multisets *) + +Inductive nelist (A : Type) : Type := +| nil : A -> nelist A +| cons : A -> nelist A -> nelist A. + +Notation "x :: y" := (cons x y). + +Fixpoint nelist_map (A B: Type) (f: A -> B) l := + match l with + | nil x => nil ( f x) + | cons x l => cons ( f x) (nelist_map f l) + end. + +Fixpoint appne A l l' : nelist A := + match l with + nil x => cons x l' + | cons t q => cons t (appne A q l') + end. + +Notation "x ++ y" := (appne x y). + +(** finite multisets are represented with ordered lists with multiplicities *) +Definition mset A := nelist (A*positive). + +(** lexicographic composition of comparisons (this is a notation to keep it lazy) *) +Notation lex e f := (match e with Eq => f | _ => e end). + + +Section lists. + + (** comparison functions *) + + Section c. + Variables A B: Type. + Variable compare: A -> B -> comparison. + Fixpoint list_compare h k := + match h,k with + | nil x, nil y => compare x y + | nil x, _ => Lt + | _, nil x => Gt + | u::h, v::k => lex (compare u v) (list_compare h k) + end. + End c. + Definition mset_compare A B compare: mset A -> mset B -> comparison := + list_compare (fun un vm => + let '(u,n) := un in + let '(v,m) := vm in + lex (compare u v) (pos_compare n m)). + + Section list_compare_weak_spec. + Variable A: Type. + Variable compare: A -> A -> comparison. + Hypothesis Hcompare: forall u v, compare_weak_spec u v (compare u v). + (* this lemma has to remain transparent to get structural recursion + in the lemma [tcompare_weak_spec] below *) + Lemma list_compare_weak_spec: forall h k, + compare_weak_spec h k (list_compare compare h k). + Proof. + induction h as [|u h IHh]; destruct k as [|v k]; simpl; try constructor. + + case (Hcompare a a0 ); try constructor. + case (Hcompare u v ); try constructor. + case (IHh k); intros; constructor. + Defined. + End list_compare_weak_spec. + + Section mset_compare_weak_spec. + Variable A: Type. + Variable compare: A -> A -> comparison. + Hypothesis Hcompare: forall u v, compare_weak_spec u v (compare u v). + (* this lemma has to remain transparent to get structural recursion + in the lemma [tcompare_weak_spec] below *) + Lemma mset_compare_weak_spec: forall h k, + compare_weak_spec h k (mset_compare compare h k). + Proof. + apply list_compare_weak_spec. + intros [u n] [v m]. + case (Hcompare u v); try constructor. + case (pos_compare_weak_spec n m); try constructor. + Defined. + End mset_compare_weak_spec. + + (** (sorted) merging functions *) + + Section m. + Variable A: Type. + Variable compare: A -> A -> comparison. + Definition insert n1 h1 := + let fix insert_aux l2 := + match l2 with + | nil (h2,n2) => + match compare h1 h2 with + | Eq => nil (h1,Pplus n1 n2) + | Lt => (h1,n1):: nil (h2,n2) + | Gt => (h2,n2):: nil (h1,n1) + end + | (h2,n2)::t2 => + match compare h1 h2 with + | Eq => (h1,Pplus n1 n2):: t2 + | Lt => (h1,n1)::l2 + | Gt => (h2,n2)::insert_aux t2 + end + end + in insert_aux. + + Fixpoint merge_msets l1 := + match l1 with + | nil (h1,n1) => fun l2 => insert n1 h1 l2 + | (h1,n1)::t1 => + let fix merge_aux l2 := + match l2 with + | nil (h2,n2) => + match compare h1 h2 with + | Eq => (h1,Pplus n1 n2) :: t1 + | Lt => (h1,n1):: merge_msets t1 l2 + | Gt => (h2,n2):: l1 + end + | (h2,n2)::t2 => + match compare h1 h2 with + | Eq => (h1,Pplus n1 n2)::merge_msets t1 t2 + | Lt => (h1,n1)::merge_msets t1 l2 + | Gt => (h2,n2)::merge_aux t2 + end + end + in merge_aux + end. + + (** interpretation of a list with a constant and a binary operation *) + + Variable B: Type. + Variable map: A -> B. + Variable b2: B -> B -> B. + Fixpoint fold_map l := + match l with + | nil x => map x + | u::l => b2 (map u) (fold_map l) + end. + + (** mapping and merging *) + + Variable merge: A -> nelist B -> nelist B. + Fixpoint merge_map (l: nelist A): nelist B := + match l with + | nil x => nil (map x) + | u::l => merge u (merge_map l) + end. + + Variable ret : A -> B. + Variable bind : A -> B -> B. + Fixpoint fold_map' (l : nelist A) : B := + match l with + | nil x => ret x + | u::l => bind u (fold_map' l) + end. + + End m. +End lists. |