path: root/CHANGES

Changes from V8.3 to V8.4
=========================

Logic

- Standard eta-conversion now supported (dependent product only). (DOC TO DO)
- Guard condition improvement: subterm property is propagated through beta-redex
  blocked by pattern-matching, as in "(match v with C .. => fun x => u end) x";
  this allows for instance to use "rewrite ... in ..." without breaking
  the guard condition.

Specification language and notations

- Maximal implicit arguments can now be set locally by { }. The registration
  traverses fixpoints and lambdas. Because there is conversion in types,
  maximal implicit arguments are not taken into account in partial
  applications (use eta expanded form with explicit { } instead).
- Added support for recursive notations with binders (allows for instance
  to write "exists x y z, P").
- Structure/Record printing can be disable by "Unset Printing Records".
  In addition, it can be controlled on type by type basis using
  "Add Printing Record" or "Add Printing Constructor".
- In a pattern containing a "match", a final "| _ => _" branch could be used
  now instead of enumerating all remaining constructors. Moreover, the pattern
  "match _ with _ => _ end" now allows to match any "match". A "in" annotation
  can also be added to restrict to a precise inductive type.
- Pattern-matching compilation algorithm: in "match x, y with ... end",
  possible dependencies of x (or of the indices of its type) in the type
  of y are now taken into account.

Tactics

- New proof engine.
- Scripts can now be structured thanks to bullets - * + and to subgoal
  delimitation via { }. Note: for use with ProofGeneral, a cvs version of
  ProofGeneral no older than mid-July 2011 is currently required. DOC TODO.
- Support for tactical "info" is suspended.
- Support for command "Show Script" is suspended.
- New tactics constr_eq, is_evar and has_evar.
- Removed the two-argument variant of "decide equality".
- New experimental tactical "timeout <n> <tac>". Since <n> is a time
  in second for the moment, this feature should rather be avoided
  in scripts meant to be machine-independent.
- Fix in "destruct": removal of unexpected local definitions in context might
  result in some rare incompatibilities (solvable by adapting name hypotheses).
- Introduction pattern "_" made more robust.
- Tactic (and Eval command) vm_compute can now be interrupted via Ctrl-C.
- Unification in "apply" supports unification of patterns of the form
  ?f x y = g(x,y) (compatibility ensured by using
  "Unset Tactic Pattern Unification"). It also supports (full) betaiota.
- Tactic autorewrite does no longer instantiate pre-existing
  existential variables (theoretical source of possible incompatibility).
- Tactic "dependent rewrite" now supports equality in "sig".
- Tactic omega now understands Zpred (wish #1912) and can prove any goal
  from a context containing an arithmetical contradiction (wish #2236).
- Using "auto with nocore" disables the use of the "core" database (wish #2188).
  This pseudo-database "nocore" can also be used with trivial and eauto.
- Tactics "set", "destruct" and "induction" accepts incomplete terms and
  use the goal to complete the pattern assuming it is no ambiguous.
- When used on arguments with a dependent type, tactics such as
  "destruct", "induction", "case", "elim", etc. now try to abstract
  automatically the dependencies over the arguments of the types
  (based on initial ideas from Chung-Kil Hur, extension to nested
   dependencies suggested by Dan Grayson)
- Tactic "injection" now failing on an equality showing no constructors while
  it was formerly generalizing again the goal over the given equality.
- In Ltac, the "context [...]" syntax has now a variant "appcontext [...]"
  allowing to match partial applications in larger applications.
- When applying destruct or inversion on a fixpoint hiding an inductive
  type, recursive calls to the fixpoint now remain folded by default (rare
  source of incompatibility generally solvable by adding a call to simpl).

Vernacular commands

- It is now mandatory to have a space (or tabulation or newline or end-of-file)
  after a "." ending a sentence.
- In SearchAbout, the [ ] delimiters are now optional.
- New command "Add/Remove Search Blacklist <substring> ..." :
  a Search or SearchAbout or similar query will never mention lemmas
  whose qualified names contain any of the declared substrings.
  The default blacklisted substrings are "_admitted" "_subproof" "Private_". DOC TODO
- When the output file of "Print Universes" ends in ".dot" or ".gv",
  the universe graph is printed in the DOT language, and can be
  processed by Graphviz tools.
- New command "Print Sorted Universes".
- The undocumented and obsolete option "Set/Unset Boxed Definitions" has
  been removed, as well as syntaxes like "Boxed Fixpoint foo".
- A new option "Set Default Timeout n / Unset Default Timeout".
- Qed now uses information from the reduction tactics used in proof script
  to avoid conversion at Qed time to go into a very long computation.
- New command "Show Goal ident" to display the statement of a goal, even
  a closed one (available from Proof General).

Module System

- During subtyping checks, an opaque constant in a module type could now
  be implemented by anything of the right type, even if bodies differ.
  Said otherwise, with respect to subtyping, an opaque constant behaves
  just as a parameter. Coqchk was already implementing this, but not coqtop.
- The inlining done during application of functors can now be controlled
  more precisely, by the annotations (no inline) or (inline at level XX).
  With the latter annotation, only functor parameters whose levels
  are lower or equal than XX will be inlined.
  The level of a parameter can be fixed by "Parameter Inline(30) foo".
  When levels aren't given, the default value is 100. One can also use
  the flag "Set Inline Level ..." to set a level. TODO: DOC!
- Print Assumptions should now handle correctly opaque modules (#2168)
- Print Module (Type) now tries to print more details, such as types and
  bodies of the module elements. Note that Print Module Type could be
  used on a module to display only its interface. The option
  "Set Short Module Printing" could be used to switch back to the earlier
  behavior were only field names were displayed.

Libraries

- Extension of the abstract part of Numbers, which now provide axiomatizations
  and results about many more integer functions, such as pow, gcd, lcm, sqrt, log2
  and bitwise functions. These functions are implemented for nat N BigN Z BigZ.
  See in particular file NPeano for new functions about nat.
- The definition of types positive, N, Z is now in file BinNums.v
- Major reorganization of ZArith. The initial file ZArith/BinInt.v now contains
  an internal module Z implementing the Numbers interface for integers.
  This module Z regroups:
  * all functions over type Z : Z.add, Z.mul, ...
  * the minimal proofs of specifications for these functions : Z.add_0_l, ...
  * an instantation of all derived properties proved generically in Numbers :
    Z.add_comm, Z.add_assoc, ...
  A large part of ZArith is now simply compatibility notations, for instance
  Zplus_comm is an alias for Z.add_comm. The direct use of module Z is now
  recommended instead of relying on these compatibility notations.
- Similar major reorganization of NArith, via a module N in NArith/BinNat.v
- Concerning the positive datatype, BinPos.v is now in a specific directory
  PArith, and contains an internal submodule Pos. We regroup there functions
  such as Pos.add Pos.mul etc as well as many results about them. These results
  are here proved directly (no Number interface for strictly positive numbers).
- Note that in spite of the compatibility layers, all these reorganizations
  may induce some marginal incompatibilies in scripts. In particular:
  * the "?=" notation for positive now refers to a binary function Pos.compare,
    instead of the infamous ternary Pcompare (now Pos.compare_cont).
  * some hypothesis names generated by the system may changed (typically for
    a "destruct Z_le_gt_dec") since naming is done after the short name of
    the head predicate (here now "le" in module Z instead of "Zle", etc).
  * the internals of Z.add has changed, now relying of Z.pos_sub.
- Also note these new notations:
  * "<?" "<=?" "=?" for boolean tests such as Z.ltb Z.leb Z.eqb.
  * "÷" for the alternative integer division Z.quot implementing the Truncate
    convention (former ZOdiv), while the notation for the Coq usual division
    Z.div implementing the Flooring convention remains "/". Their corresponding
    modulo functions are Z.rem (no notations) for Z.quot and Z.modulo (infix
    "mod" notation) for Z.div.
- Lemmas about conversions between these datatypes are also organized
  in modules, see for instance modules Z2Nat, N2Z, etc.
- When creating BigN, the macro-generated part NMake_gen is much smaller.
  The generic part NMake has been reworked and improved. Some changes
  may introduce incompatibilities. In particular, the order of the arguments
  for BigN.shiftl and BigN.shiftr is now reversed: the number to shift now
  comes first. By default, the power function now takes two BigN.
- Creation of Vector, an independant library for list indiced by their length.
  Vectors' names overwrite lists' one so you shouldn't "Import" the library.
  All old names change: functions' name become the CaML one and for example
  Vcons become Vector.cons. You can use notations by importing
  Vector.VectorNotations.
- Removal of TheoryList. Requiring List instead should work most of the time.
- New syntax "rew Heq in H" and "rew <- Heq in H" for eq_rect and 
  eq_rect_r (available by importing module EqNotations).
- Wf.iter_nat is now Peano.nat_iter (with an implicit type argument)

Internal infrastructure

- Opaque proofs are now loaded lazily by default. This allows to be almost as
  fast as -dont-load-proofs, while being safer (no creation of axioms) and
  avoiding feature restrictions (Print and Print Assumptions work ok).
- Revised hash-consing code allowing more sharing of memory
- Experimental support added for camlp4 (the one provided alongside ocaml),
  simply pass option -usecamlp4 to ./configure. By default camlp5 is used.
- Revised build system: no more stages in Makefile thanks to some recursive
  aspect of recent gnu make, use of vo.itarget files containing .v to compile
  for both make and ocamlbuild, etc.
- Support of cross-compilation via mingw from unix toward Windows,
  contact P. Letouzey for more informations.
- new Makefile rules mli-doc to make html of mli in dev/doc/html and
  full-stdlib to get a HUGE pdf with all the stdlib.

Extraction

- By default, opaque terms are now truly considered opaque by extraction:
  instead of accessing their body, they are now considered as axioms.
  The previous behaviour can be reactivated via the option
  "Set Extraction AccessOpaque".
- The pretty-printer for Haskell now produces layout-independant code
- A new command "Separate Extraction cst1 cst2 ..." that mixes a
  minimal extracted environment a la "Recursive Extraction" and the
  production of several files (one per coq source) a la "Extraction Library".
  DOC TODO.
- New option "Set/Unset Extraction KeepSingleton" for preventing the
  extraction to optimize singleton container types. DOC TODO
- The extraction now identifies and properly rejects a particular case of
  universe polymorphism it cannot handle yet (the pair (I,I) being Prop).
- Support of anonymous fields in record (#2555).

CoqIDE

- Coqide now runs coqtop as separated process, making it more robust:
  coqtop subprocess can be interrupted, or even killed and relaunched
  (cf button "Restart Coq", ex-"Go to Start"). For allowing such
  interrupts, the Windows version of coqide now requires Windows >= XP
  SP1.
- The communication between CoqIDE and Coqtop is now done via a dialect
  of XML (DOC TODO).
- The backtrack engine of CoqIDE has been reworked, it now used the
  "Backtrack" command similarly to ProofGeneral.
- The Coqide parsing of sentences has be reworked and now supports
  tactic delimitation via { }.
- Coqide now accepts the Abort command (wish #2357).
- Coqide can read coq_makefile files as "project file" and use it to
  set automatically options to send to coqtop.
- Preference files have moved to $XDG_CONFIG_HOME/coq and accelerators
  are not stored as a list anymore.

Tools

- Coq now searches directories specified in COQPATH, $XDG_DATA_HOME/coq,
  $XDG_DATA_DIRS/coq, and user-contribs before the standard library.
- Coq rc file has moved to $XDG_CONFIG_HOME/coq.
- coq_makefile major cleanup.
  * mli/mlpack/mllib taken into account, ml not preproccessed anymore, ml4 work
  * mlihtml generates doc of mli, install-doc install the html doc in DOCDIR
    with the same policy as vo in COQLIB
  * More variables are given by coqtop -config, others are defined only if the
    users doesn't have defined them elsewhere. Consequently, generated makefile
    should work directly on any architecture.
  * Packagers can take advantage of $(DSTROOT) introduction. Installation can
    be made in $XDG_DATA_HOME/coq.
  * -arg option allows to send option as argument to coqc.

Changes from V8.2 to V8.3
=========================

Rewriting tactics

- Tactic "rewrite" now supports rewriting on ad hoc equalities such as eq_true.
- "Hint Rewrite" now checks that the lemma looks like an equation.
- New tactic "etransitivity".
- Support for heterogeneous equality (JMeq) in "injection" and "discriminate".
- Tactic "subst" now supports heterogeneous equality and equality
  proofs that are dependent (use "simple subst" for preserving compatibility).
- Added support for Leibniz-rewriting of dependent hypotheses.
- Renamed "Morphism" into "Proper" and "respect" into "proper_prf"
  (possible source of incompatibility). A partial fix is to define
  "Notation Morphism R f := (Proper (R%signature) f)."
- New tactic variants "rewrite* by" and "autorewrite*" that rewrite
  respectively the first and all matches whose side-conditions are
  solved.
- "Require Import Setoid" does not export all of "Morphisms" and
  "RelationClasses" anymore (possible source of incompatibility, fixed
  by importing "Morphisms" too).
- Support added for using Chung-Kil Hur's Heq library for rewriting over
  heterogeneous equality (courtesy of the library's author).
- Tactic "replace" supports matching terms with holes.

Automation tactics

- Tactic "intuition" now preserves inner "iff" and "not" (exceptional
  source of incompatibilities solvable by redefining "intuition" as
  "unfold iff, not in *; intuition", or, for iff only, by using
  "Set Intuition Iff Unfolding".)
- Tactic "tauto" now proves classical tautologies as soon as classical logic
  (i.e. library Classical_Prop or Classical) is loaded.
- Tactic "gappa" has been removed from the Dp plugin.
- Tactic "firstorder" now supports the combination of its "using" and
  "with" options.
- New "Hint Resolve ->" (or "<-") for declaring iff's as oriented
  hints (wish #2104).
- An inductive type as argument of the "using" option of "auto/eauto/firstorder"
  is interpreted as using the collection of its constructors.
- New decision tactic "nsatz" to prove polynomial equations
  by computation of Groebner bases.

Other tactics

- Tactic "discriminate" now performs intros before trying to discriminate an
  hypothesis of the goal (previously it applied intro only if the goal
  had the form t1<>t2) (exceptional source of incompatibilities - former
  behavior can be obtained by "Unset Discriminate Introduction").
- Tactic "quote" now supports quotation of arbitrary terms (not just the
  goal).
- Tactic "idtac" now displays its "list" arguments.
- New introduction patterns "*" for introducing the next block of dependent
  variables and "**" for introducing all quantified variables and hypotheses.
- Pattern Unification for existential variables activated in tactics and
  new option "Unset Tactic Evars Pattern Unification" to deactivate it.
- Resolution of canonical structure is now part of the tactic's unification
  algorithm.
- New tactic "decide lemma with hyp" for rewriting decidability lemmas
  when one knows which side is true.
- Improved support of dependent goals over objects in dependent types for
  "destruct" (rare source of incompatibility that can be avoided by unsetting
  option "Dependent Propositions Elimination").
- Tactic "exists", "eexists", "destruct" and "edestruct" supports iteration
  using comma-separated arguments.
- Tactic names "case" and "elim" now support clauses "as" and "in" and become
  then synonymous of "destruct" and "induction" respectively.
- A new tactic name "exfalso" for the use of 'ex-falso quodlibet' principle.
  This tactic is simply a shortcut for "elimtype False".
- Made quantified hypotheses get the name they would have if introduced in
  the context (possible but rare source of incompatibilities).
- When applying a component of a conjunctive lemma, "apply in" (and
  sequences of "apply in") now leave the side conditions of the lemmas
  uniformly after the main goal (possible source of rare incompatibilities).
- In "simpl c" and "change c with d", c can be a pattern.
- Tactic "revert" now preserves let-in's making it the exact inverse of
  "intro".
- New tactics "clear dependent H" and "revert dependent H" that
  clears (resp. reverts) H and all the hypotheses that depend on H.
- Ltac's pattern-matching now supports matching metavariables that
  depend on variables bound upwards in the pattern.

Tactic definitions

- Ltac definitions support Local option for non-export outside modules.
- Support for parsing non-empty lists with separators in tactic notations.
- New command "Locate Ltac" to get the full name of an Ltac definition.

Notations

- Record syntax "{|x=...; y=...|}" now works inside patterns too.
- Abbreviations from non-imported module now invisible at printing time.
- Abbreviations now use implicit arguments and arguments scopes for printing.
- Abbreviations to pure names now strictly behave like the name they refer to
  (make redirections of qualified names easier).
- Abbreviations for applied constant now propagate the implicit arguments
  and arguments scope of the underlying reference (possible source of
  incompatibilities generally solvable by changing such abbreviations from
  e.g. "Notation foo' := (foo x)" to "Notation foo' y := (foo x (y:=y))").
- The "where" clause now supports multiple notations per defined object.
- Recursive notations automatically expand one step on the left for better
  factorization; recursion notations inner separators now ensured being tokens.
- Added "Reserved Infix" as a specific shortcut of the corresponding
  "Reserved Notation".
- Open/Close Scope command supports Global option in sections.

Specification language

- New support for local binders in the syntax of Record/Structure fields.
- Fixpoint/CoFixpoint now support building part or all of bodies using tactics.
- Binders given before ":" in lemmas and in definitions built by tactics are
  now automatically introduced (possible source of incompatibility that can
  be resolved by invoking "Unset Automatic Introduction").
- New support for multiple implicit arguments signatures per reference.

Module system

- Include Type is now deprecated since Include now accept both modules and
  module types.
- Declare ML Module supports Local option.
- The sharing between non-logical object and the management of the
  name-space has been improved by the new "Delta-equivalence" on
  qualified name.
- The include operator has been extended to high-order structures
- Sequences of Include can be abbreviated via new syntax "<+".
- A module (or module type) can be given several "<:" signatures.
- Interactive proofs are now permitted in module type. Functors can hence
  be declared as Module Type and be used later to type themselves.
- A functor application can be prefixed by a "!" to make it ignore any
  "Inline" annotation in the type of its argument(s) (for examples of
  use of the new features, see libraries Structures and Numbers).
- Coercions are now active only when modules are imported (use "Set Automatic
  Coercions Import" to get the behavior of the previous versions of Coq).

Extraction

- When using (Recursive) Extraction Library, the filenames are directly the
  Coq ones with new appropriate extensions : we do not force anymore
  uncapital first letters for Ocaml and capital ones for Haskell.
- The extraction now tries harder to avoid code transformations that can be
  dangerous for the complexity. In particular many eta-expansions at the top
  of functions body are now avoided, clever partial applications will likely
  be preserved, let-ins are almost always kept, etc.
- In the same spirit, auto-inlining is now disabled by default, except for
  induction principles, since this feature was producing more frequently
  weird code than clear gain. The previous behavior can be restored via
  "Set Extraction AutoInline".
- Unicode characters in identifiers are now transformed into ascii strings
  that are legal in Ocaml and other languages.
- Harsh support of module extraction to Haskell and Scheme: module hierarchy
  is flattened, module abbreviations and functor applications are expanded,
  module types and unapplied functors are discarded.
- Less unsupported situations when extracting modules to Ocaml. In particular
  module parameters might be alpha-renamed if a name clash is detected.
- Extract Inductive is now possible toward non-inductive types (e.g. nat => int)
- Extraction Implicit: this new experimental command allows to mark
  some arguments of a function or constructor for removed during
  extraction, even if these arguments don't fit the usual elimination
  principles of extraction, for instance the length n of a vector.
- Files ExtrOcaml*.v in plugins/extraction try to provide a library of common
  extraction commands: mapping of basics types toward Ocaml's counterparts,
  conversions from/to int and big_int, or even complete mapping of nat,Z,N
  to int or big_int, or mapping of ascii to char and string to char list
  (in this case recognition of ascii constants is hard-wired in the extraction).

Program

- Streamlined definitions using well-founded recursion and measures so
  that they can work on any subset of the arguments directly (uses currying).
- Try to automatically clear structural fixpoint prototypes in
  obligations to avoid issues with opacity.
- Use return type clause inference in pattern-matching as in the standard
  typing algorithm.
- Support [Local Obligation Tactic] and [Next Obligation with tactic].
- Use [Show Obligation Tactic] to print the current default tactic.
- [fst] and [snd] have maximal implicit arguments in Program now (possible
  source of incompatibility).

Type classes

- Declaring axiomatic type class instances in Module Type should be now
  done via new command "Declare Instance", while the syntax "Instance"
  now always provides a concrete instance, both in and out of Module Type.
- Use [Existing Class foo] to declare foo as a class a posteriori.
  [foo] can be an inductive type or a constant definition. No
  projections or instances are defined.
- Various bug fixes and improvements: support for defined fields,
  anonymous instances, declarations giving terms, better handling of
  sections and [Context].

Vernacular commands

- New command "Timeout <n> <command>." interprets a command and a timeout
  interrupts the interpretation after <n> seconds.
- New command "Compute <expr>." is a shortcut for "Eval vm_compute in <expr>".
- New command "Fail <command>." interprets a command and is successful iff
  the command fails on an error (but not an anomaly). Handy for tests and
  illustration of wrong commands.
- Most commands referring to constant (e.g. Print or About) now support
  referring to the constant by a notation string.
- New option "Boolean Equality Schemes" to make generation of boolean
  equality automatic for datatypes (together with option "Decidable
  Equality Schemes", this replaces deprecated option "Equality Scheme").
- Made support for automatic generation of case analysis schemes available
  to user (governed by option "Set Case Analysis Schemes").
- New command "(Global?) Generalizable [All|No] Variable(s)? ident(s)?" to
  declare which identifiers are generalizable in `{} and `() binders.
- New command "Print Opaque Dependencies" to display opaque constants in
  addition to all variables, parameters or axioms a theorem or
  definition relies on.
- New command "Declare Reduction <id> := <conv_expr>", allowing to write
  later "Eval <id> in ...". This command accepts a Local variant.
- Syntax of Implicit Type now supports more than one block of variables of
  a given type.
- Command "Canonical Structure" now warns when it has no effects.
- Commands of the form "Set X" or "Unset X" now support "Local" and "Global"
  prefixes.

Library

- Use "standard" Coq names for the properties of eq and identity
  (e.g. refl_equal is now eq_refl). Support for compatibility is provided.
- The function Compare_dec.nat_compare is now defined directly,
  instead of relying on lt_eq_lt_dec. The earlier version is still
  available under the name nat_compare_alt.
- Lemmas in library Relations and Reals have been homogenized a bit.
- The implicit argument of Logic.eq is now maximally inserted, allowing
  to simply write "eq" instead of "@eq _" in morphism signatures.
- Wrongly named lemmas (Zlt_gt_succ and Zlt_succ_gt) fixed (potential source
  of incompatibilities)
- List library:
  - Definitions of list, length and app are now in Init/Datatypes.
    Support for compatibility is provided.
  - Definition of Permutation is now in Sorting/Permtation.v
  - Some other light revisions and extensions (possible source
    of incompatibilities solvable by qualifying names accordingly).
- In ListSet, set_map has been fixed (source of incompatibilities if used).
- Sorting library:
  - new mergesort of worst-case complexity O(n*ln(n)) made available in
    Mergesort.v;
  - former notion of permutation up to setoid from Permutation.v is
    deprecated and moved to PermutSetoid.v;
  - heapsort from Heap.v of worst-case complexity O(n*n) is deprecated;
  - new file Sorted.v for some definitions of being sorted.
- Structure library. This new library is meant to contain generic
  structures such as types with equalities or orders, either
  in Module version (for now) or Type Classes (still to do):
  - DecidableType.v and OrderedType.v: initial notions for FSets/FMaps,
    left for compatibility but considered as deprecated.
  - Equalities.v and Orders.v: evolutions of the previous files,
    with fine-grain Module architecture, many variants, use of
    Equivalence and other relevant Type Classes notions.
  - OrdersTac.v: a generic tactic for solving chains of (in)equalities
    over variables. See {Nat,N,Z,P}OrderedType.v for concrete instances.
  - GenericMinMax.v: any ordered type can be equipped with min and max.
    We derived here all the generic properties of these functions.
- MSets library: an important evolution of the FSets library.
  "MSets" stands for Modular (Finite) Sets, by contrast with a forthcoming
  library of Class (Finite) Sets contributed by S. Lescuyer which will be
  integrated with the next release of Coq. The main features of MSets are:
  - The use of Equivalence, Proper and other Type Classes features
    easing the handling of setoid equalities.
  - The interfaces are now stated in iff-style. Old specifications
    are now derived properties.
  - The compare functions are now pure, and return a "comparison" value.
    Thanks to the CompSpec inductive type, reasoning on them remains easy.
  - Sets structures requiring invariants (i.e. sorted lists) are
    built first as "Raw" sets (pure objects and separate proofs) and
    attached with their proofs thanks to a generic functor. "Raw" sets
    have now a proper interface and can be manipulated directly.
  Note: No Maps yet in MSets. The FSets library is still provided
  for compatibility, but will probably be considered as deprecated in the
  next release of Coq.
- Numbers library:
  - The abstract layer (NatInt, Natural/Abstract, Integer/Abstract) has
    been simplified and enhance thanks to new features of the module
    system such as Include (see above). It has been extended to Euclidean
    division (three flavors for integers: Trunc, Floor and Math).
  - The arbitrary-large efficient numbers (BigN, BigZ, BigQ) has also
    been reworked. They benefit from the abstract layer improvements
    (especially for div and mod). Note that some specifications have
    slightly changed (compare, div, mod, shift{r,l}). Ring/Field should
    work better (true recognition of constants).

Tools

- Option -R now supports binding Coq root read-only.
- New coqtop/coqc option -beautify to reformat .v files (usable
  e.g. to globally update notations).
- New tool beautify-archive to beautify a full archive of developments.
- New coqtop/coqc option -compat X.Y to simulate the general behavior
  of previous versions of Coq (provides e.g. support for 8.2 compatibility).

Coqdoc

- List have been revamped.  List depth and scope is now determined by
  an "offside" whitespace rule.
- Text may be italicized by placing it in _underscores_.
- The "--index <string>" flag changes the filename of the index.
- The "--toc-depth <int>" flag limits the depth of headers which are
  included in the table of contents.
- The "--lib-name <string>" flag prints "<string> Foo" instead of
  "Library Foo" where library titles are called for.  The
  "--no-lib-name" flag eliminates the extra title.
- New option "--parse-comments" to allow parsing of regular "(* *)"
  comments.
- New option "--plain-comments" to disable interpretation inside comments.
- New option "--interpolate" to try and typeset identifiers in Coq escapings
  using the available globalization information.
- New option "--external url root" to refer to external libraries.
- Links to section variables and notations now supported.

Internal infrastructure

- To avoid confusion with the repository of user's contributions,
  the subdirectory "contrib" has been renamed into "plugins".
  On platforms supporting ocaml native dynlink, code located there
  is built as loadable plugins for coqtop.
- An experimental build mechanism via ocamlbuild is provided.
  From the top of the archive, run ./configure as usual, and
  then ./build. Feedback about this build mechanism is most welcome.
  Compiling Coq on platforms such as Windows might be simpler
  this way, but this remains to be tested.
- The Makefile system has been simplified and factorized with
  the ocamlbuild system. In particular "make" takes advantage
  of .mllib files for building .cma/.cmxa. The .vo files to
  compile are now listed in several vo.itarget files.

Changes from V8.1 to V8.2
=========================

Language

- If a fixpoint is not written with an explicit { struct ... }, then
  all arguments are tried successively (from left to right) until one is
  found that satisfies the structural decreasing condition.
- New experimental typeclass system giving ad-hoc polymorphism and
  overloading based on dependent records and implicit arguments.
- New syntax "let 'pat := b in c" for let-binding using irrefutable patterns.
- New syntax "forall {A}, T" for specifying maximally inserted implicit
  arguments in terms.
- Sort of Record/Structure, Inductive and CoInductive defaults to Type
  if omitted.
- (Co)Inductive types can be defined as records
  (e.g. "CoInductive stream := { hd : nat; tl : stream }.")
- New syntax "Theorem id1:t1 ... with idn:tn" for proving mutually dependent
  statements.
- Support for sort-polymorphism on constants denoting inductive types.
- Several evolutions of the module system (handling of module aliases,
  functorial module types, an Include feature, etc).
- Prop now a subtype of Set (predicative and impredicative forms).
- Recursive inductive types in Prop with a single constructor of which
  all arguments are in Prop is now considered to be a singleton
  type. It consequently supports all eliminations to Prop, Set and Type.
  As a consequence, Acc_rect has now a more direct proof [possible source
  of easily fixed incompatibility in case of manual definition of a recursor
  in a recursive singleton inductive type].

Vernacular commands

- Added option Global to "Arguments Scope" for section surviving.
- Added option "Unset Elimination Schemes" to deactivate the automatic
  generation of elimination schemes.
- Modification of the Scheme command so you can ask for the name to be
  automatically computed (e.g. Scheme Induction for nat Sort Set).
- New command "Combined Scheme" to build combined mutual induction
  principles from existing mutual induction principles.
- New command "Scheme Equality" to build a decidable (boolean) equality
  for simple inductive datatypes and a decision property over this equality
  (e.g.  Scheme Equality for nat).
- Added option "Set Equality Scheme" to make automatic the declaration
  of the boolean equality when possible.
- Source of universe inconsistencies now printed when option
  "Set Printing Universes" is activated.
- New option "Set Printing Existential Instances" for making the display of
  existential variable instances explicit.
- Support for option "[id1 ... idn]", and "-[id1 ... idn]", for the
  "compute"/"cbv" reduction strategy, respectively meaning reduce only, or
  everything but, the constants id1 ... idn. "lazy" alone or followed by
  "[id1 ... idn]", and "-[id1 ... idn]" also supported, meaning apply
  all of beta-iota-zeta-delta, possibly restricting delta.
- New command "Strategy" to control the expansion of constants during
  conversion tests. It generalizes commands Opaque and Transparent by
  introducing a range of levels. Lower levels are assigned to constants
  that should be expanded first.
- New options Global and Local to Opaque and Transparent.
- New command "Print Assumptions" to display all variables, parameters
  or axioms a theorem or definition relies on.
- "Add Rec LoadPath" now provides references to libraries using partially
  qualified names (this holds also for coqtop/coqc option -R).
- SearchAbout supports negated search criteria, reference to logical objects
  by their notation, and more generally search of subterms.
- "Declare ML Module" now allows to import .cmxs files when Coq is
  compiled in native code with a version of OCaml that supports native
  Dynlink (>= 3.11).
- Specific sort constraints on Record now taken into account.
- "Print LoadPath" supports a path argument to filter the display.

Libraries

- Several parts of the libraries are now in Type, in particular FSets,
  SetoidList, ListSet, Sorting, Zmisc. This may induce a few
  incompatibilities. In case of trouble while fixing existing development,
  it may help to simply declare Set as an alias for Type (see file
  SetIsType).
- New arithmetical library in theories/Numbers. It contains:
  * an abstract modular development of natural and integer arithmetics
    in Numbers/Natural/Abstract and Numbers/Integer/Abstract
  * an implementation of efficient computational bounded and unbounded
    integers that can be mapped to processor native arithmetics.
    See Numbers/Cyclic/Int31 for 31-bit integers and Numbers/Natural/BigN
    for unbounded natural numbers and Numbers/Integer/BigZ for unbounded
    integers.
  * some proofs that both older libraries Arith, ZArith and NArith and
    newer BigN and BigZ implement the abstract modular development.
    This allows in particular BigN and BigZ to already come with a
    large database of basic lemmas and some generic tactics (ring),
  This library has still an experimental status, as well as the
  processor-acceleration mechanism, but both its abstract and its
  concrete parts are already quite usable and could challenge the use
  of nat, N and Z in actual developments. Moreover, an extension of
  this framework to rational numbers is ongoing, and an efficient
  Q structure is already provided (see Numbers/Rational/BigQ), but
  this part is currently incomplete (no abstract layer and generic
  lemmas).
- Many changes in FSets/FMaps. In practice, compatibility with earlier
  version should be fairly good, but some adaptations may be required.
  * Interfaces of unordered ("weak") and ordered sets have been factorized
    thanks to new features of Coq modules (in particular Include), see
    FSetInterface. Same for maps. Hints in these interfaces have been
    reworked (they are now placed in a "set" database).
  * To allow full subtyping between weak and ordered sets, a field
    "eq_dec" has been added to OrderedType. The old version of OrderedType
    is now called MiniOrderedType and functor MOT_to_OT allow to
    convert to the new version. The interfaces and implementations
    of sets now contain also such a "eq_dec" field.
  * FSetDecide, contributed by Aaron Bohannon, contains a decision
    procedure allowing to solve basic set-related goals (for instance,
    is a point in a particular set ?). See FSetProperties for examples.
  * Functors of properties have been improved, especially the ones about
    maps, that now propose some induction principles. Some properties
    of fold need less hypothesis.
  * More uniformity in implementations of sets and maps: they all use
    implicit arguments, and no longer export unnecessary scopes (see
    bug #1347)
  * Internal parts of the implementations based on AVL have evolved a
    lot. The main files FSetAVL and FMapAVL are now much more
    lightweight now. In particular, minor changes in some functions
    has allowed to fully separate the proofs of operational
    correctness from the proofs of well-balancing: well-balancing is
    critical for efficiency, but not anymore for proving that these
    trees implement our interfaces, hence we have moved these proofs
    into appendix files FSetFullAVL and FMapFullAVL. Moreover, a few
    functions like union and compare have been modified in order to be
    structural yet efficient. The appendix files also contains
    alternative versions of these few functions, much closer to the
    initial Ocaml code and written via the Function framework.
- Library IntMap, subsumed by FSets/FMaps, has been removed from
  Coq Standard Library and moved into a user contribution Cachan/IntMap
- Better computational behavior of some constants (eq_nat_dec and
  le_lt_dec more efficient, Z_lt_le_dec and Positive_as_OT.compare
  transparent, ...) (exceptional source of incompatibilities).
- Boolean operators moved from module Bool to module Datatypes (may need
  to rename qualified references in script and force notations || and &&
  to be at levels 50 and 40 respectively).
- The constructors xI and xO of type positive now have postfix notations
  "~1" and "~0", allowing to write numbers in binary form easily, for instance
  6 is 1~1~0 and 4*p is p~0~0 (see BinPos.v).
- Improvements to NArith (Nminus, Nmin, Nmax), and to QArith (in particular
  a better power function).
- Changes in ZArith: several additional lemmas (used in theories/Numbers),
  especially in Zdiv, Znumtheory, Zpower. Moreover, many results in
  Zdiv have been generalized: the divisor may simply be non-null
  instead of strictly positive (see lemmas with name ending by
  "_full"). An alternative file ZOdiv proposes a different behavior
  (the one of Ocaml) when dividing by negative numbers.
- Changes in Arith: EqNat and Wf_nat now exported from Arith, some
  constructions on nat that were outside Arith are now in (e.g. iter_nat).
- In SetoidList, eqlistA now expresses that two lists have similar elements
  at the same position, while the predicate previously called eqlistA
  is now equivlistA (this one only states that the lists contain the same
  elements, nothing more).
- Changes in Reals:
  * Most statement in "sigT" (including the
    completeness axiom) are now in "sig" (in case of incompatibility,
    use proj1_sig instead of projT1, sig instead of sigT, etc).
  * More uniform naming scheme (identifiers in French moved to English,
    consistent use of 0 -- zero -- instead of O -- letter O --, etc).
  * Lemma on prod_f_SO is now on prod_f_R0.
  * Useless hypothesis of ln_exists1 dropped.
  * New Rlogic.v states a few logical properties about R axioms.
  * RIneq.v extended and made cleaner.
- Slight restructuration of the Logic library regarding choice and classical
  logic. Addition of files providing intuitionistic axiomatizations of
  descriptions: Epsilon.v, Description.v and IndefiniteDescription.v.
- Definition of pred and minus made compatible with the structural
  decreasing criterion for use in fixpoints.
- Files Relations/Rstar.v and Relations/Newman.v moved out to the user
  contribution repository (contribution CoC_History). New lemmas about
  transitive closure added and some bound variables renamed (exceptional
  risk of incompatibilities).
- Syntax for binders in terms (e.g. for "exists") supports anonymous names.

Notations, coercions, implicit arguments and type inference

- More automation in the inference of the return clause of dependent
  pattern-matching problems.
- Experimental allowance for omission of the clauses easily detectable as
  impossible in pattern-matching problems.
- Improved inference of implicit arguments.
- New options "Set Maximal Implicit Insertion", "Set Reversible Pattern
  Implicit", "Set Strongly Strict Implicit" and "Set Printing Implicit
  Defensive" for controlling inference and use of implicit arguments.
- New modifier in "Implicit Arguments" to force an implicit argument to
  be maximally inserted.
- New modifier of "Implicit Arguments" to enrich the set of implicit arguments.
- New options Global and Local to "Implicit Arguments" for section
  surviving or non export outside module.
- Level "constr" moved from 9 to 8.
- Structure/Record now printed as Record (unless option Printing All is set).
- Support for parametric notations defining constants.
- Insertion of coercions below product types refrains to unfold
  constants (possible source of incompatibility).
- New support for fix/cofix in notations.

Tactic Language

- Second-order pattern-matching now working in Ltac "match" clauses
  (syntax for second-order unification variable is "@?X").
- Support for matching on let bindings in match context using syntax
  "H := body" or "H := body : type".
- Ltac accepts integer arguments (syntax is "ltac:nnn" for nnn an integer).
- The general sequence tactical "expr_0 ; [ expr_1 | ... | expr_n ]"
  is extended so that at most one expr_i may have the form "expr .."
  or just "..". Also, n can be different from the number of subgoals
  generated by expr_0. In this case, the value of expr (or idtac in
  case of just "..") is applied to the intermediate subgoals to make
  the number of tactics equal to the number of subgoals.
- A name used as the name of the parameter of a lemma (like f in
  "apply f_equal with (f:=t)") is now interpreted as a ltac variable
  if such a variable exists (this is a possible source of
  incompatibility and it can be fixed by renaming the variables of a
  ltac function into names that do not clash with the lemmas
  parameter names used in the tactic).
- New syntax "Ltac tac ::= ..." to rebind a tactic to a new expression.
- "let rec ... in ... " now supported for expressions without explicit
  parameters; interpretation is lazy to the contrary of "let ... in ...";
  hence, the "rec" keyword can be used to turn the argument of a
  "let ... in ..." into a lazy one.
- Patterns for hypotheses types in "match goal" are now interpreted in
  type_scope.
- A bound variable whose name is not used elsewhere now serves as
  metavariable in "match" and it gets instantiated by an identifier
  (allow e.g. to extract the name of a statement like "exists x, P x").
- New printing of Ltac call trace for better debugging.

Tactics

- New tactics "apply -> term", "apply <- term", "apply -> term in
  ident", "apply <- term in ident" for applying equivalences (iff).
- Slight improvement of the hnf and simpl tactics when applied on
  expressions with explicit occurrences of match or fix.
- New tactics "eapply in", "erewrite", "erewrite in".
- New tactics "ediscriminate", "einjection", "esimplify_eq".
- Tactics "discriminate", "injection", "simplify_eq" now support any
  term as argument. Clause "with" is also supported.
- Unfoldable references can be given by notation's string rather than by name
  in unfold.
- The "with" arguments are now typed using informations from the current goal:
  allows support for coercions and more inference of implicit arguments.
- Application of "f_equal"-style lemmas works better.
- Tactics elim, case, destruct and induction now support variants eelim,
  ecase, edestruct and einduction.
- Tactics destruct and induction now support the "with" option and the
  "in" clause option. If the option "in" is used, an equality is added
  to remember the term to which the induction or case analysis applied
  (possible source of parsing incompatibilities when destruct or induction is
   part of a let-in expression in Ltac; extra parentheses are then required).
- New support for "as" clause in tactics "apply in" and "eapply in".
- Some new intro patterns:
  * intro pattern "?A" genererates a fresh name based on A.
    Caveat about a slight loss of compatibility:
    Some intro patterns don't need space between them. In particular
    intros ?a?b used to be legal and equivalent to intros ? a ? b. Now it
    is still legal but equivalent to intros ?a ?b.
  * intro pattern "(A & ... & Y & Z)" synonym to "(A,....,(Y,Z)))))"
    for right-associative constructs like /\ or exists.
- Several syntax extensions concerning "rewrite":
  * "rewrite A,B,C" can be used to rewrite A, then B, then C. These rewrites
    occur only on the first subgoal: in particular, side-conditions of the
    "rewrite A" are not concerned by the "rewrite B,C".
  * "rewrite A by tac" allows to apply tac on all side-conditions generated by
    the "rewrite A".
  * "rewrite A at n" allows to select occurrences to rewrite: rewrite only
    happen at the n-th exact occurrence of the first successful matching of
    A in the goal.
  * "rewrite 3 A" or "rewrite 3!A" is equivalent to "rewrite A,A,A".
  * "rewrite !A" means rewriting A as long as possible (and at least once).
  * "rewrite 3?A" means rewriting A at most three times.
  * "rewrite ?A" means rewriting A as long as possible (possibly never).
  * many of the above extensions can be combined with each other.
- Introduction patterns better respect the structure of context in presence of
  missing or extra names in nested disjunction-conjunction patterns [possible
  source of rare incompatibilities].
- New syntax "rename a into b, c into d" for "rename a into b; rename c into d"
- New tactics "dependent induction/destruction H [ generalizing id_1 .. id_n ]"
  to do induction-inversion on instantiated inductive families à la BasicElim.
- Tactics "apply" and "apply in" now able to reason modulo unfolding of
  constants (possible source of incompatibility in situations where apply
  may fail, e.g. as argument of a try or a repeat and in a ltac function);
  versions that do not unfold are renamed into "simple apply" and
  "simple apply in" (usable for compatibility or for automation).
- Tactics "apply" and "apply in" now able to traverse conjunctions and to
  select the first matching lemma among the components of the conjunction;
  tactic "apply" also able to apply lemmas of conclusion an empty type.
- Tactic "apply" now supports application of several lemmas in a row.
- Tactics "set" and "pose" can set functions using notation "(f x1..xn := c)".
- New tactic "instantiate" (without argument).
- Tactic firstorder "with" and "using" options have their meaning swapped for
  consistency with auto/eauto (source of incompatibility).
- Tactic "generalize" now supports "at" options to specify occurrences
  and "as" options to name the quantified hypotheses.
- New tactic "specialize H with a" or "specialize (H a)" allows to transform
  in-place a universally-quantified hypothesis (H : forall x, T x) into its
  instantiated form (H : T a). Nota: "specialize" was in fact there in earlier
  versions of Coq, but was undocumented, and had a slightly different behavior.
- New tactic "contradict H" can be used to solve any kind of goal as long as
  the user can provide afterwards a proof of the negation of the hypothesis H.
  If H is already a negation, say ~T, then a proof of T is asked.
  If the current goal is a negation, say ~U, then U is saved in H afterwards,
  hence this new tactic "contradict" extends earlier tactic "swap", which is
  now obsolete.
- Tactics f_equal is now done in ML instead of Ltac: it now works on any
  equality of functions, regardless of the arity of the function.
- New options "before id", "at top", "at bottom" for tactics "move"/"intro".
- Some more debug of reflexive omega (romega), and internal clarifications.
  Moreover, romega now has a variant "romega with *" that can be also used
  on non-Z goals (nat, N, positive) via a call to a translation tactic named
  zify (its purpose is to Z-ify your goal...). This zify may also be used
  independantly of romega.
- Tactic "remember" now supports an "in" clause to remember only selected
  occurrences of a term.
- Tactic "pose proof" supports name overwriting in case of specialization of an
  hypothesis.
- Semi-decision tactic "jp" for first-order intuitionistic logic moved to user
  contributions (subsumed by "firstorder").

Program

- Moved useful tactics in theories/Program and documented them.
- Add Program.Basics which contains standard definitions for functional
  programming (id, apply, flip...)
- More robust obligation handling, dependent pattern-matching and
  well-founded definitions.
- New syntax " dest term as pat in term " for destructing objects using
  an irrefutable pattern while keeping equalities (use this instead of
  "let" in Programs).
- Program CoFixpoint is accepted, Program Fixpoint uses the new way to infer
  which argument decreases structurally.
- Program Lemma, Axiom etc... now permit to have obligations in the statement
  iff they can be automatically solved by the default tactic.
- Renamed "Obligations Tactic" command to "Obligation Tactic".
- New command "Preterm [ of id ]" to see the actual term fed to Coq for
  debugging purposes.
- New option "Transparent Obligations" to control the declaration of
  obligations as transparent or opaque. All obligations are now transparent
  by default, otherwise the system declares them opaque if possible.
- Changed the notations "left" and "right" to "in_left" and "in_right" to hide
  the proofs in standard disjunctions, to avoid breaking existing scripts when
  importing Program. Also, put them in program_scope.

Type Classes

- New "Class", "Instance" and "Program Instance" commands to define
  classes and instances documented in the reference manual.
- New binding construct " [ Class_1 param_1 .. param_n, Class_2 ... ] "
  for binding type classes, usable everywhere.
- New command " Print Classes " and " Print Instances some_class " to
  print tables for typeclasses.
- New default eauto hint database "typeclass_instances" used by the default
  typeclass instance search tactic.
- New theories directory "theories/Classes" for standard typeclasses
  declarations. Module Classes.RelationClasses is a typeclass port of
  Relation_Definitions plus a generic development of algebra on
  n-ary heterogeneous predicates.

Setoid rewriting

- Complete (and still experimental) rewrite of the tactic
  based on typeclasses. The old interface and semantics are
  almost entirely respected, except:

  - Import Setoid is now mandatory to be able to call setoid_replace
  and declare morphisms.

  - "-->", "++>" and "==>" are now right associative notations
  declared at level 55 in scope signature_scope.
  Their introduction may break existing scripts that defined
  them as notations with different levels.

  - One needs to use [Typeclasses unfold [cst]] if [cst] is used
  as an abbreviation hiding products in types of morphisms,
  e.g. if ones redefines [relation] and declares morphisms
  whose type mentions [relation].

  - The [setoid_rewrite]'s semantics change when rewriting with
  a lemma: it can rewrite two different instantiations of the lemma
  at once. Use [setoid_rewrite H at 1] for (almost) the usual semantics.
  [setoid_rewrite] will also try to rewrite under binders now, and can
  succeed on different terms than before. In particular, it will unify under
  let-bound variables. When called through [rewrite], the semantics are
  unchanged though.

  - [Add Morphism term : id] has different semantics when used with
  parametric morphism: it will try to find a relation on the parameters
  too. The behavior has also changed with respect to default relations:
  the most recently declared Setoid/Relation will be used, the documentation
  explains how to customize this behavior.

  - Parametric Relation and Morphism are declared differently, using the
  new [Add Parametric] commands, documented in the manual.

  - Setoid_Theory is now an alias to Equivalence, scripts building objects
  of type Setoid_Theory need to unfold (or "red") the definitions
  of Reflexive, Symmetric and Transitive in order to get the same goals
  as before. Scripts which introduced variables explicitely will not break.

  - The order of subgoals when doing [setoid_rewrite] with side-conditions
  is always the same: first the new goal, then the conditions.

- New standard library modules Classes.Morphisms declares
  standard morphisms on refl/sym/trans relations.
  Classes.Morphisms_Prop declares morphisms on propositional
  connectives and Classes.Morphisms_Relations on generalized predicate
  connectives. Classes.Equivalence declares notations and tactics
  related to equivalences and Classes.SetoidTactics defines the
  setoid_replace tactics and some support for the "Add *" interface,
  notably the tactic applied automatically before each "Add Morphism"
  proof.

- User-defined subrelations are supported, as well as higher-order morphisms
  and rewriting under binders. The tactic is also extensible entirely in Ltac.
  The documentation has been updated to cover these features.

- [setoid_rewrite] and [rewrite] now support the [at] modifier to select
  occurrences to rewrite, and both use the [setoid_rewrite] code, even when
  rewriting with leibniz equality if occurrences are specified.

Extraction

- Improved behavior of the Caml extraction of modules: name clashes should
  not happen anymore.
- The command Extract Inductive has now a syntax for infix notations. This
  allows in particular to map Coq lists and pairs onto Caml ones:
    Extract Inductive list => list [ "[]" "(::)" ].
    Extract Inductive prod => "(*)" [ "(,)" ].
- In pattern matchings, a default pattern "| _ -> ..." is now used whenever
  possible if several branches are identical. For instance, functions
  corresponding to decidability of equalities are now linear instead of
  quadratic.
- A new instruction Extraction Blacklist id1 .. idn allows to prevent filename
  conflits with existing code, for instance when extracting module List
  to Ocaml.

CoqIDE

- CoqIDE font defaults to monospace so as indentation to be meaningful.
- CoqIDE supports nested goals and any other kind of declaration in the middle
  of a proof.
- Undoing non-tactic commands in CoqIDE works faster.
- New CoqIDE menu for activating display of various implicit informations.
- Added the possibility to choose the location of tabs in coqide:
  (in Edit->Preferences->Misc)
- New Open and Save As dialogs in CoqIDE which filter *.v files.

Tools

- New stand-alone .vo files verifier "coqchk".
- Extended -I coqtop/coqc option to specify a logical dir: "-I dir -as coqdir".
- New coqtop/coqc option -exclude-dir to exclude subdirs for option -R.
- The binary "parser" has been renamed to "coq-parser".
- Improved coqdoc and dump of globalization information to give more
  meta-information on identifiers. All categories of Coq definitions are
  supported, which makes typesetting trivial in the generated documentation.
  Support for hyperlinking and indexing developments in the tex output
  has been implemented as well.

Miscellaneous

- Coq installation provides enough files so that Ocaml's extensions need not
  the Coq sources to be compiled (this assumes O'Caml 3.10 and Camlp5).
- New commands "Set Whelp Server" and "Set Whelp Getter" to customize the
  Whelp search tool.
- Syntax of "Test Printing Let ref" and "Test Printing If ref" changed into
  "Test Printing Let for ref" and "Test Printing If for ref".
- An overhauled build system (new Makefiles); see dev/doc/build-system.txt.
- Add -browser option to configure script.
- Build a shared library for the C part of Coq, and use it by default on
  non-(Windows or MacOS) systems. Bytecode executables are now pure. The
  behaviour is configurable with -coqrunbyteflags, -coqtoolsbyteflags and
  -custom configure options.
- Complexity tests can be skipped by setting the environment variable
  COQTEST_SKIPCOMPLEXITY.

Changes from V8.1gamma to V8.1
==============================

Bug fixes

- Many bugs have been fixed (cf coq-bugs web page)

Tactics

- New tactics ring, ring_simplify and new tactic field now able to manage
  power to a positive integer constant. Tactic ring on Z and R, and
  field on R manage power (may lead to incompatibilities with V8.1gamma).
- Tactic field_simplify now applicable in hypotheses.
- New field_simplify_eq for simplifying field equations into ring equations.
- Tactics ring, ring_simplify, field, field_simplify and field_simplify_eq
  all able to apply user-given equations to rewrite monoms on the fly
  (see documentation).

Libraries

- New file ConstructiveEpsilon.v defining an epsilon operator and
  proving the axiom of choice constructively for a countable domain
  and a decidable predicate.

Changes from V8.1beta to V8.1gamma
==================================

Syntax

- changed parsing precedence of let/in and fun constructions of Ltac:
  let x := t in e1; e2 is now parsed as let x := t in (e1;e2).

Language and commands

- Added sort-polymorphism for definitions in Type (but finally abandonned).
- Support for implicit arguments in the types of parameters in
  (co-)fixpoints and (co-)inductive declarations.
- Improved type inference: use as much of possible general information.
  before applying irreversible unification heuristics (allow e.g. to
  infer the predicate in "(exist _ 0 (refl_equal 0) : {n:nat | n=0 })").
- Support for Miller-Pfenning's patterns unification in type synthesis
  (e.g. can infer P such that P x y = phi(x,y)).
- Support for "where" clause in cofixpoint definitions.
- New option "Set Printing Universes" for making Type levels explicit.

Tactics

- Improved implementation of the ring and field tactics. For compatibility
  reasons, the previous tactics are renamed as legacy ring and legacy field,
  but should be considered as deprecated.
- New declarative mathematical proof language.
- Support for argument lists of arbitrary length in Tactic Notation.
- [rewrite ... in H] now fails if [H] is used either in an hypothesis
  or in the goal.
- The semantics of [rewrite ... in *] has been slightly modified (see doc).
- Support for "as" clause in tactic injection.
- New forward-reasoning tactic "apply in".
- Ltac fresh operator now builds names from a concatenation of its arguments.
- New ltac tactic "remember" to abstract over a subterm and keep an equality
- Support for Miller-Pfenning's patterns unification in apply/rewrite/...
  (may lead to few incompatibilities - generally now useless tactic calls).

Bug fixes

- Fix for notations involving basic "match" expressions.
- Numerous other bugs solved (a few fixes may lead to incompatibilities).


Changes from V8.0 to V8.1beta
=============================

Logic

- Added sort-polymorphism on inductive families
- Allowance for recursively non uniform parameters in inductive types

Syntax

- No more support for version 7 syntax and for translation to version 8 syntax.
- In fixpoints, the { struct ... } annotation is not mandatory any more when
  only one of the arguments has an inductive type
- Added disjunctive patterns in match-with patterns
- Support for primitive interpretation of string literals
- Extended support for Unicode ranges

Vernacular commands

- Added "Print Ltac qualid" to print a user defined tactic.
- Added "Print Rewrite HintDb" to print the content of a DB used by
  autorewrite.
- Added "Print Canonical Projections".
- Added "Example" as synonym of "Definition".
- Added "Proposition" and "Corollary" as extra synonyms of "Lemma".
- New command "Whelp" to send requests to the Helm database of proofs
  formalized in the Calculus of Inductive Constructions.
- Command "functional induction" has been re-implemented from the new
  "Function" command.

Ltac and tactic syntactic extensions

- New primitive "external" for communication with tool external to Coq
- New semantics for "match t with": if a clause returns a
  tactic, it is now applied to the current goal. If it fails, the next
  clause or next matching subterm is tried (i.e. it behaves as "match
  goal with" does). The keyword "lazymatch" can be used to delay the
  evaluation of tactics occurring in matching clauses.
- Hint base names can be parametric in auto and trivial.
- Occurrence values can be parametric in unfold, pattern, etc.
- Added entry constr_may_eval for tactic extensions.
- Low-priority term printer made available in ML-written tactic extensions.
- "Tactic Notation" extended to allow notations of tacticals.

Tactics

- New implementation and generalization of [setoid_]* (setoid_rewrite,
  setoid_symmetry, setoid_transitivity, setoid_reflexivity and autorewite).
  New syntax for declaring relations and morphisms (old syntax still working
  with minor modifications, but deprecated).
- New implementation (still experimental) of the ring tactic with a built-in
  notion of coefficients and a better usage of setoids.
- New conversion tactic "vm_compute": evaluates the goal (or an hypothesis)
  with a call-by-value strategy, using the compiled version of terms.
- When rewriting H where H is not directly a Coq equality, search first H for
  a registered setoid equality before starting to reduce in H. This is unlikely
  to break any script. Should this happen nonetheless, one can insert manually
  some "unfold ... in H" before rewriting.
- Fixed various bugs about (setoid) rewrite ... in ... (in particular #1101)
- "rewrite ... in" now accepts a clause as place where to rewrite instead of
  juste a simple hypothesis name. For instance:
   rewrite H in H1,H2 |- * means rewrite H in H1; rewrite H in H2; rewrite H
   rewrite H in * |-  will do try rewrite H in Hi for all hypothesis Hi <> H.
- Added "dependent rewrite term" and "dependent rewrite term in hyp".
- Added "autorewrite with ... in hyp [using ...]".
- Tactic "replace" now accepts a "by" tactic clause.
- Added "clear - id" to clear all hypotheses except the ones depending in id.
- The argument of Declare Left Step and Declare Right Step is now a term
  (it used to be a reference).
- Omega now handles arbitrary precision integers.
- Several bug fixes in Reflexive Omega (romega).
- Idtac can now be left implicit in a [...|...] construct: for instance,
  [ foo | | bar ] stands for [ foo | idtac | bar ].
- Fixed a "fold" bug (non critical but possible source of incompatibilities).
- Added classical_left and classical_right which transforms |- A \/ B into
  ~B |- A and ~A |- B respectively.
- Added command "Declare Implicit Tactic" to set up a default tactic to be
  used to solve unresolved subterms of term arguments of tactics.
- Better support for coercions to Sortclass in tactics expecting type
  arguments.
- Tactic "assert" now accepts "as" intro patterns and "by" tactic clauses.
- New tactic "pose proof" that generalizes "assert (id:=p)" with intro patterns.
- New introduction pattern "?" for letting Coq choose a name.
- Introduction patterns now support side hypotheses (e.g. intros [|] on
  "(nat -> nat) -> nat" works).
- New introduction patterns "->" and "<-" for immediate rewriting of
  introduced hypotheses.
- Introduction patterns coming after non trivial introduction patterns now
  force full introduction of the first pattern (e.g. "intros [[|] p]" on
  "nat->nat->nat" now behaves like "intros [[|?] p]")
- Added "eassumption".
- Added option 'using lemmas' to auto, trivial and eauto.
- Tactic "congruence" is now complete for its intended scope (ground
  equalities and inequalities with constructors). Furthermore, it
  tries to equates goal and hypotheses.
- New tactic "rtauto" solves pure propositional logic and gives a
  reflective version of the available proof.
- Numbering of "pattern", "unfold", "simpl", ... occurrences in "match
  with" made consistent with the printing of the return clause after
  the term to match in the "match-with" construct (use "Set Printing All"
  to see hidden occurrences).
- Generalization of induction "induction x1...xn using scheme" where
  scheme is an induction principle with complex predicates (like the
  ones generated by function induction).
- Some small Ltac tactics has been added to the standard library
  (file Tactics.v):
  * f_equal : instead of using the different f_equalX lemmas
  * case_eq : a "case" without loss of information. An equality
     stating the current situation is generated in every sub-cases.
  * swap : for a negated goal ~B and a negated hypothesis H:~A,
     swap H asks you to prove A from hypothesis B
  * revert : revert H is generalize H; clear H.

Extraction

- All type parts should now disappear instead of sometimes producing _
  (for instance in Map.empty).
- Haskell extraction: types of functions are now printed, better
  unsafeCoerce mechanism, both for hugs and ghc.
- Scheme extraction improved, see http://www.pps.jussieu.fr/~letouzey/scheme.
- Many bug fixes.

Modules

- Added "Locate Module qualid" to get the full path of a module.
- Module/Declare Module syntax made more uniform.
- Added syntactic sugar "Declare Module Export/Import" and
  "Module Export/Import".
- Added syntactic sugar "Module M(Export/Import X Y: T)" and
  "Module Type M(Export/Import X Y: T)"
  (only for interactive definitions)
- Construct "with" generalized to module paths:
   T with (Definition|Module) M1.M2....Mn.l := l'.

Notations

- Option "format" aware of recursive notations.
- Added insertion of spaces by default in recursive notations w/o separators.
- No more automatic printing box in case of user-provided printing "format".
- New notation "exists! x:A, P" for unique existence.
- Notations for specific numerals now compatible with generic notations of
  numerals (e.g. "1" can be used to denote the unit of a group without
  hiding 1%nat)

Libraries

- New library on String and Ascii characters (contributed by L. Thery).
- New library FSets+FMaps of finite sets and maps.
- New library QArith on rational numbers.
- Small extension of Zmin.V, new Zmax.v, new Zminmax.v.
- Reworking and extension of the files on classical logic and
  description principles (possible incompatibilities)
- Few other improvements in ZArith potentially exceptionally breaking the
  compatibility (useless hypothesys of Zgt_square_simpl and
  Zlt_square_simpl removed; fixed names mentioning letter O instead of
  digit 0; weaken premises in Z_lt_induction).
- Restructuration of Eqdep_dec.v and Eqdep.v: more lemmas in Type.
- Znumtheory now contains a gcd function that can compute within Coq.
- More lemmas stated on Type in Wf.v, removal of redundant Acc_iter and
  Acc_iter2.
- Change of the internal names of lemmas in OmegaLemmas.
- Acc in Wf.v and clos_refl_trans in Relation_Operators.v now rely on
  the allowance for recursively non uniform parameters (possible
  source of incompatibilities: explicit pattern-matching on these
  types may require to remove the occurrence associated to their
  recursively non uniform parameter).
- Coq.List.In_dec has been set transparent (this may exceptionally break
  proof scripts, set it locally opaque for compatibility).
- More on permutations of lists in List.v and Permutation.v.
- List.v has been much expanded.
- New file SetoidList.v now contains results about lists seen with
  respect to a setoid equality.
- Library NArith has been expanded, mostly with results coming from
  Intmap (for instance a bitwise xor), plus also a bridge between N and
  Bitvector.
- Intmap has been reorganized. In particular its address type "addr" is
  now N. User contributions known to use Intmap have been adapted
  accordingly. If you're using this library please contact us.
  A wrapper FMapIntMap now presents Intmap as a particular implementation
  of FMaps. New developments are strongly encouraged to use either this
  wrapper or any other implementations of FMap instead of using directly
  this obsolete Intmap.

Tools

- New semantics for coqtop options ("-batch" expects option "-top dir"
  for loading vernac file that contains definitions).
- Tool coq_makefile now removes custom targets that are file names in
  "make clean"
- New environment variable COQREMOTEBROWSER to set the command invoked
  to start the remote browser both in Coq and coqide. Standard syntax:
  "%s" is the placeholder for the URL.


Changes from V8.0beta to V8.0
=============================

Vernacular commands

- New option "Set Printing All" to deactivate all high-level forms of
  printing (implicit arguments, coercions, destructing let,
  if-then-else, notations, projections)
- "Functional Scheme" and "Functional Induction" extended to polymorphic
  types and dependent types
- Notation now allows recursive patterns, hence recovering parts of the
  fonctionalities of pre-V8 Grammar/Syntax commands
- Command "Print." discontinued.
- Redundant syntax "Implicit Arguments On/Off" discontinued

New syntax

- Semantics change of the if-then-else construction in new syntax:
  "if c then t1 else t2" now stands for
  "match c with c1 _ ... _ => t1 | c2 _ ... _ => t2 end"
  with no dependency of t1 and t2 in the arguments of the constructors;
  this may cause incompatibilities for files translated using coq 8.0beta

Interpretation scopes

- Delimiting key %bool for bool_scope added
- Import no more needed to activate argument scopes from a module

Tactics and the tactic Language

- Semantics of "assert" is now consistent with the reference manual
- New tactics stepl and stepr for chaining transitivity steps
- Tactic "replace ... with ... in" added
- Intro patterns now supported in Ltac (parsed with prefix "ipattern:")

Executables and tools

- Added option -top to change the name of the toplevel module "Top"
- Coqdoc updated to new syntax and now part of Coq sources
- XML exportation tool now exports the structure of vernacular files
  (cf chapter 13 in the reference manual)

User contributions

- User contributions have been updated to the new syntax

Bug fixes

- Many bugs have been fixed (cf coq-bugs web page)

Changes from V8.0beta old syntax to V8.0beta
============================================

New concrete syntax

- A completely new syntax for terms
- A more uniform syntax for tactics and the tactic language
- A few syntactic changes for vernacular commands
- A smart automatic translator translating V8.0 files in old syntax to
  files valid for V8.0

Syntax extensions

- "Grammar" for terms disappears
- "Grammar" for tactics becomes "Tactic Notation"
- "Syntax" disappears
- Introduction of a notion of interpretation scope allowing to use the
  same notations in various contexts without using specific delimiters
  (e.g the same expression "4<=3+x" is interpreted either in "nat",
  "positive", "N" (previously "entier"), "Z", "R", depending on which
  interpretation scope is currently open) [see documentation for details]
- Notation now mandatorily requires a precedence and associativity
  (default was to set precedence to 1 and associativity to none)

Revision of the standard library

- Many lemmas and definitions names have been made more uniform mostly
  in Arith, NArith, ZArith and Reals (e.g : "times" -> "Pmult",
  "times_sym" -> "Pmult_comm", "Zle_Zmult_pos_right" ->
  "Zmult_le_compat_r", "SUPERIEUR" -> "Gt", "ZERO" -> "Z0")
- Order and names of arguments of basic lemmas on nat, Z, positive and R
  have been made uniform.
- Notions of Coq initial state are declared with (strict) implicit arguments
- eq merged with eqT: old eq disappear, new eq (written =) is old eqT
  and new eqT is syntactic sugar for new eq (notation == is an alias
  for = and is written as it, exceptional source of incompatibilities)
- Similarly, ex, ex2, all, identity are merged with exT, exT2, allT, identityT
- Arithmetical notations for nat, positive, N, Z, R, without needing
  any backquote or double-backquotes delimiters.
- In Lists: new concrete notations; argument of nil is now implicit
- All changes in the library are taken in charge by the translator

Semantical changes during translation

- Recursive keyword set by default (and no longer needed) in Tactic Definition
- Set Implicit Arguments is strict by default in new syntax
- reductions in hypotheses of the form "... in H" now apply to the type
  also if H is a local definition
- etc

Gallina

- New syntax of the form "Inductive bool : Set := true, false : bool." for
  enumerated types
- Experimental syntax of the form p.(fst) for record projections
  (activable with option "Set Printing Projections" which is
   recognized by the translator)

Known problems of the automatic translation

- iso-latin-1 characters are no longer supported: move your files to
  7-bits ASCII or unicode before translation (swith to unicode is
  automatically done if a file is loaded and saved again by coqide)
- Renaming in ZArith: incompatibilities in Coq user contribs due to
  merging names INZ, from Reals, and inject_nat.
- Renaming and new lemmas in ZArith: may clash with names used by users
- Restructuration of ZArith: replace requirement of specific modules
  in ZArith by "Require Import ZArith_base" or "Require Import ZArith"
- Some implicit arguments must be made explicit before translation: typically
  for "length nil", the implicit argument of length must be made explicit
- Grammar rules, Infix notations and V7.4 Notations must be updated wrt the
  new scheme for syntactic extensions (see translator documentation)
- Unsafe for annotation Cases when constructors coercions are used or when
  annotations are eta-reduced predicates


Changes from V7.4 to V8.0beta old syntax
========================================

Logic

- Set now predicative by default
- New option -impredicative-set to set Set impredicative
- The standard library doesn't need impredicativity of Set and is
  compatible with the classical axioms which contradict Set impredicativity

Syntax for arithmetic

- Notation "=" and "<>" in Z and R are no longer implicitly in Z or R
  (with possible introduction of a coercion), use <Z>...=... or
  <Z>...<>... instead
- Locate applied to a simple string (e.g. "+") searches for all
  notations containing this string

Vernacular commands

- "Declare ML Module" now allows to import .cma files. This avoids to use a
   bunch of "Declare ML Module" statements when using several ML files.
- "Set Printing Width n" added, allows to change the size of width printing.
- "Implicit Variables Type x,y:t" (new syntax: "Implicit Types x y:t")
  assigns default types for binding variables.
- Declarations of Hints and Notation now accept a "Local" flag not to
  be exported outside the current file even if not in section
- "Print Scopes" prints all notations
- New command "About name" for light printing of type, implicit arguments, etc.
- New command "Admitted" to declare incompletely proven statement as axioms
- New keyword "Conjecture" to declare an axiom intended to be provable
- SearchAbout can now search for lemmas referring to more than one constant
  and on substrings of the name of the lemma
- "Print Implicit" displays the implicit arguments of a constant
- Locate now searches for all names having a given suffix
- New command "Functional Scheme" for building an induction principle
  from a function defined by case analysis and fix.

Commands

- new coqtop/coqc option -dont-load-proofs not to load opaque proofs in memory

Implicit arguments

- Inductive in sections declared with implicits now "discharged" with
  implicits (like constants and variables)
- Implicit Arguments flags are now synchronous with reset
- New switch "Unset/Set Printing Implicits" (new syntax: "Unset/Set Printing
  Implicit") to globally control printing of implicits

Grammar extensions

- Many newly supported UTF-8 encoded unicode blocks
  - Greek letters (0380-03FF), Hebrew letters (U05D0-05EF), letter-like
  symbols (2100-214F, that includes double N,Z,Q,R), prime
  signs (from 2080-2089) and characters from many written languages
  are valid in identifiers
  - mathematical operators (2200-22FF), supplemental mathematical
  operators (2A00-2AFF), miscellaneous technical (2300-23FF that
  includes sqrt symbol), miscellaneous symbols (2600-26FF), arrows
  (2190-21FF and 2900-297F), invisible mathematical operators (from
  2080-2089), ... are valid symbols

Library

- New file about the factorial function in Arith
- An additional elimination Acc_iter for Acc, simplier than Acc_rect.
  This new elimination principle is used for definition well_founded_induction.
- New library NArith on binary natural numbers
- R is now of type Set
- Restructuration in ZArith library
  - "true_sub" used in Zplus now a definition, not a local one (source
  of incompatibilities in proof referring to true_sub, may need extra Unfold)
  - Some lemmas about minus moved from fast_integer to Arith/Minus.v
  (le_minus, lt_mult_left) (theoretical source of incompatibilities)
  - Several lemmas moved from auxiliary.v and zarith_aux.v to
  fast_integer.v (theoretical source of incompatibilities)
  - Variables names of iff_trans changed (source of incompatibilities)
  - ZArith lemmas named OMEGA something or fast_ something, and lemma new_var
    are now out of ZArith (except OMEGA2)
  - Redundant ZArith lemmas have been renamed: for the following pairs,
  use the second name (Zle_Zmult_right2, Zle_mult_simpl), (OMEGA2,
  Zle_0_plus), (Zplus_assoc_l, Zplus_assoc), (Zmult_one, Zmult_1_n),
  (Zmult_assoc_l, Zmult_assoc), (Zmult_minus_distr, Zmult_Zminus_distr_l)
  (add_un_double_moins_un_xO, is_double_moins_un),
  (Rlt_monotony_rev,Rlt_monotony_contra) (source of incompatibilities)
- Few minor changes (no more implicit arguments in
  Zmult_Zminus_distr_l and Zmult_Zminus_distr_r, lemmas moved from
  Zcomplements to other files) (rare source of incompatibilities)
- New lemmas provided by users added

Tactic language

- Fail tactic now accepts a failure message
- Idtac tactic now accepts a message
- New primitive tactic "FreshId" (new syntax: "fresh") to generate new names
- Debugger prints levels of calls

Tactics

- Replace can now replace proofs also
- Fail levels are now decremented at "Match Context" blocks only and
  if the right-hand-side of "Match term With" are tactics, these
  tactics are never evaluated immediately and do not induce
  backtracking (in contrast with "Match Context")
- Quantified names now avoid global names of the current module (like
  Intro names did) [source of rare incompatibilities: 2 changes in the set of
  user contribs]
- NewDestruct/NewInduction accepts intro patterns as introduction names
- NewDestruct/NewInduction now work for non-inductive type using option "using"
- A NewInduction naming bug for inductive types with functional
  arguments (e.g. the accessibility predicate) has been fixed (source
  of incompatibilities)
- Symmetry now applies to hypotheses too
- Inversion now accept option "as [ ... ]" to name the hypotheses
- Contradiction now looks also for contradictory hypotheses stating ~A and A
  (source of incompatibility)
- "Contradiction c" try to find an hypothesis in context which
  contradicts the type of c
- Ring applies to new library NArith (require file NArithRing)
- Field now works on types in Set
- Auto with reals now try to replace le by ge (Rge_le is no longer an
  immediate hint), resulting in shorter proofs
- Instantiate now works in hyps (syntax : Instantiate in ...)
- Some new tactics : EConstructor, ELeft, Eright, ESplit, EExists
- New tactic "functional induction" to perform case analysis and
  induction following the definition of a function.
- Clear now fails when trying to remove a local definition used by
  a constant appearing in the current goal

Extraction (See details in plugins/extraction/CHANGES)

- The old commands: 	(Recursive) Extraction Module M.
  are now:              (Recursive) Extraction Library M.
  To use these commands, M should come from a library M.v
- The other syntax Extraction & Recursive Extraction now accept
  module names as arguments.

Bugs

- see coq-bugs server for the complete list of fixed bugs

Miscellaneous

- Implicit parameters of inductive types definition now taken into
  account for infering other implicit arguments

Incompatibilities

- Persistence of true_sub (4 incompatibilities in Coq user contributions)
- Variable names of some constants changed for a better uniformity (2 changes
  in Coq user contributions)
- Naming of quantified names in goal now avoid global names (2 occurrences)
- NewInduction naming for inductive types with functional arguments
  (no incompatibility in Coq user contributions)
- Contradiction now solve more goals (source of 2 incompatibilities)
- Merge of eq and eqT may exceptionally result in subgoals now
  solved automatically
- Redundant pairs of ZArith lemmas may have different names: it may
  cause "Apply/Rewrite with" to fail if using the first name of a pair
  of redundant lemmas (this is solved by renaming the variables bound by
  "with"; 3 incompatibilities in Coq user contribs)
- ML programs referring to constants from fast_integer.v must use
  "Coqlib.gen_constant_modules Coqlib.zarith_base_modules" instead

Changes from V7.3.1 to V7.4
===========================

Symbolic notations

- Introduction of a notion of scope gathering notations in a consistent set;
  a notation sets has been developped for nat, Z and R (undocumented)
- New command "Notation" for declaring notations simultaneously for
  parsing and printing (see chap 10 of the reference manual)
- Declarations with only implicit arguments now handled (e.g. the
  argument of nil can be set implicit; use !nil to refer to nil
  without arguments)
- "Print Scope sc" and "Locate ntn" allows to know to what expression a
  notation is bound
- New defensive strategy for printing or not implicit arguments to ensure
  re-type-checkability of the printed term
- In Grammar command, the only predefined non-terminal entries are ident,
  global, constr and pattern (e.g. nvar, numarg disappears); the only
  allowed grammar types are constr and pattern; ast and ast list are no
  longer supported; some incompatibilities in Grammar: when a syntax is a
  initial segment of an other one,  Grammar does not work, use Notation

Library

- Lemmas in Set from Compare_dec.v (le_lt_dec, ...) and Wf_nat.v
  (lt_wf_rec, ...) are now transparent. This may be source of
  incompatibilities.
- Syntactic Definitions Fst, Snd, Ex, All, Ex2, AllT, ExT, ExT2,
  ProjS1, ProjS2, Error, Value and Except are turned to
  notations. They now must be applied (incompatibilities only in
  unrealistic cases).
- More efficient versions of Zmult and times (30% faster)
- Reals: the library is now divided in 6 parts (Rbase, Rfunctions,
  SeqSeries, Rtrigo, Ranalysis, Integration). New tactics: Sup and
  RCompute. See Reals.v for details.

Modules

- Beta version, see doc chap 2.5 for commands and chap 5 for theory

Language

- Inductive definitions now accept ">" in constructor types to declare
  the corresponding constructor as a coercion.
- Idem for assumptions declarations and constants when the type is mentionned.
- The "Coercion" and "Canonical Structure" keywords now accept the
  same syntax as "Definition", i.e. "hyps :=c (:t)?" or "hyps :t".
- Theorem-like declaration now accepts the syntax "Theorem thm [x:t;...] : u".
- Remark's and Fact's now definitively behave as Theorem and Lemma: when
  sections are closed, the full name of a Remark or a Fact has no longer a
  section part (source of incompatibilities)
- Opaque Local's (i.e. built by tactics and ended by Qed), do not
  survive section closing any longer; as a side-effect, Opaque Local's
  now appear in the local context of proofs; their body is hidden
  though (source of incompatibilities); use one of Remark/Fact/Lemma/Theorem
  instead to simulate the old behaviour of Local (the section part of
  the name is not kept though)

ML tactic and vernacular commands

- "Grammar tactic" and "Grammar vernac" of type "ast" are no longer
  supported (only "Grammar tactic simple_tactic" of type "tactic"
  remains available).
- Concrete syntax for ML written vernacular commands and tactics is
  now declared at ML level using camlp4 macros TACTIC EXTEND et VERNAC
  COMMAND EXTEND.
- "Check n c" now "n:Check c", "Eval n ..." now "n:Eval ..."
- "Proof with T" (* no documentation *)
-  SearchAbout id - prints all theorems which contain id in their type

Tactic definitions

- Static globalisation of identifiers and global references (source of
  incompatibilities, especially, Recursive keyword is required for
  mutually recursive definitions).
- New evaluation semantics: no more partial evaluation at definition time;
  evaluation of all Tactic/Meta Definition, even producing terms, expect
  a proof context to be evaluated (especially "()" is no longer needed).
- Debugger now shows the nesting level and the reasons of failure

Tactics

- Equality tactics (Rewrite, Reflexivity, Symmetry, Transitivity) now
  understand JM equality
- Simpl and Change now apply to subterms also
- "Simpl f" reduces subterms whose head constant is f
- Double Induction now referring to hypotheses like "Intros until"
- "Inversion" now applies also on quantified hypotheses (naming as
  for Intros until)
- NewDestruct now accepts terms with missing hypotheses
- NewDestruct and NewInduction now accept user-provided elimination scheme
- NewDestruct and NewInduction now accept user-provided introduction names
- Omega could solve goals such as ~`x<y` |- `x>=y` but failed when the
  hypothesis was unfolded to `x < y` -> False. This is fixed. In addition,
  it can also recognize 'False' in the hypothesis and use it to solve the
  goal.
- Coercions now handled in "with" bindings
- "Subst x" replaces all ocurrences of x by t in the goal and hypotheses
   when an hypothesis x=t or x:=t or t=x exists
- Fresh names for Assert and Pose now based on collision-avoiding
  Intro naming strategy (exceptional source of incompatibilities)
- LinearIntuition (* no documentation *)
- Unfold expects a correct evaluable argument
- Clear expects existing hypotheses

Extraction (See details in plugins/extraction/CHANGES and README):

- An experimental Scheme extraction is provided.
- Concerning Ocaml, extracted code is now ensured to always type-check,
  thanks to automatic inserting of Obj.magic.
- Experimental extraction of Coq new modules to Ocaml modules.

Proof rendering in natural language

- Export of theories to XML for publishing and rendering purposes now
  includes proof-trees (see http://www.cs.unibo.it/helm)

Miscellaneous

- Printing Coercion now used through the standard keywords Set/Add, Test, Print
- "Print Term id" is an alias for "Print id"
- New switch "Unset/Set Printing Symbols" to control printing of
  symbolic notations
- Two new variants of implicit arguments are available
   - "Unset/Set Contextual Implicits" tells to consider implicit also the
     arguments inferable from the context (e.g. for nil or refl_eq)
   - "Unset/Set Strict Implicits" tells to consider implicit only the
     arguments that are inferable in any case (i.e. arguments that occurs
     as argument of rigid constants in the type of the remaining arguments;
     e.g. the witness of an existential is not strict since it can vanish when
     applied to a predicate which does not use its argument)

Incompatibilities

- "Grammar tactic ... : ast" and "Grammar vernac ... : ast" are no
  longer supported, use TACTIC EXTEND and VERNAC COMMAND EXTEND on the
  ML-side instead
- Transparency of le_lt_dec and co (leads to some simplification in
  proofs; in some cases, incompatibilites is solved by declaring locally
  opaque the relevant constant)
- Opaque Local do not now survive section closing (rename them into
  Remark/Lemma/... to get them still surviving the sections; this
  renaming allows also to solve incompatibilites related to now
  forbidden calls to the tactic Clear)
- Remark and Fact have no longer (very) long names (use Local instead in case
  of name conflict)

Bugs

- Improved localisation of errors in Syntactic Definitions
- Induction principle creation failure in presence of let-in fixed (#238)
- Inversion bugs fixed (#212 and #220)
- Omega bug related to Set fixed (#180)
- Type-checking inefficiency of nested destructuring let-in fixed (#216)
- Improved handling of let-in during holes resolution phase (#239)

Efficiency

- Implementation of a memory sharing strategy reducing memory
  requirements by an average ratio of 3.

Changes from V7.3 to V7.3.1
===========================

Bug fixes

  - Corrupted Field tactic and Match Context tactic construction fixed
  - Checking of names already existing in Assert added (PR#182)
  - Invalid argument bug in Exact tactic solved (PR#183)
  - Colliding bound names bug fixed (PR#202)
  - Wrong non-recursivity test for Record fixed (PR#189)
  - Out of memory/seg fault bug related to parametric inductive fixed (PR#195)
  - Setoid_replace/Setoid_rewrite bug wrt "==" fixed

Misc

  - Ocaml version >= 3.06 is needed to compile Coq from sources
  - Simplification of fresh names creation strategy for Assert, Pose and
    LetTac (PR#192)

Changes from V7.2 to V7.3
=========================

Language

- Slightly improved compilation of pattern-matching (slight source of
  incompatibilities)
- Record's now accept anonymous fields "_" which does not build projections
- Changes in the allowed elimination sorts for certain class of inductive
  definitions : an inductive definition without constructors
  of Sort Prop can be eliminated on sorts Set and Type A "singleton"
  inductive definition (one constructor with arguments in the sort Prop
  like conjunction of two propositions or equality) can be eliminated
  directly on sort Type (In V7.2, only the sorts Prop and Set were allowed)

Tactics

- New tactic "Rename x into y" for renaming hypotheses
- New tactics "Pose x:=u" and "Pose u" to add definitions to local context
- Pattern now working on partially applied subterms
- Ring no longer applies irreversible congruence laws of mult but
  better applies congruence laws of plus (slight source of incompatibilities).
- Field now accepts terms to be simplified as arguments (as for Ring). This
  extension has been also implemented using the toplevel tactic language.
- Intuition does no longer unfold constants except "<->" and "~". It
  can be parameterized by a tactic. It also can introduce dependent
  product if needed (source of incompatibilities)
- "Match Context" now matching more recent hypotheses first and failing only
  on user errors and Fail tactic (possible source of incompatibilities)
- Tactic Definition's without arguments now allowed in Coq states
- Better simplification and discrimination made by Inversion (source
  of incompatibilities)

Bugs

- "Intros H" now working like "Intro H" trying first to reduce if not a product
- Forward dependencies in Cases now taken into account
- Known bugs related to Inversion and let-in's fixed
- Bug unexpected Delta with let-in now fixed

Extraction (details in plugins/extraction/CHANGES or documentation)

- Signatures of extracted terms are now mostly expunged from dummy arguments.
- Haskell extraction is now operational (tested & debugged).

Standard library

- Some additions in [ZArith]: three files (Zcomplements.v, Zpower.v
  and Zlogarithms.v) moved from plugins/omega in order to be more
  visible, one Zsgn function, more induction principles (Wf_Z.v and
  tail of Zcomplements.v), one more general Euclid theorem
- Peano_dec.v and Compare_dec.v now part of Arith.v

Tools

- new option -dump-glob to coqtop to dump globalizations (to be used by the
  new documentation tool coqdoc; see http://www.lri.fr/~filliatr/coqdoc)

User Contributions

- CongruenceClosure (congruence closure decision procedure)
  [Pierre Corbineau, ENS Cachan]
- MapleMode (an interface to embed Maple simplification procedures over
  rational fractions in Coq)
  [David Delahaye, Micaela Mayero, Chalmers University]
- Presburger: A formalization of Presburger's algorithm
  [Laurent Thery, INRIA Sophia Antipolis]
- Chinese has been rewritten using Z from ZArith as datatype
  ZChinese is the new version, Chinese the obsolete one
  [Pierre Letouzey, LRI Orsay]

Incompatibilities

- Ring: exceptional incompatibilities (1 above 650 in submitted user
  contribs, leading to a simplification)
- Intuition: does not unfold any definition except "<->" and "~"
- Cases: removal of some extra Cases in configurations of the form
  "Cases ... of C _ => ... | _ D => ..."  (effects on 2 definitions of
  submitted user contributions necessitating the removal of now superfluous
  proof steps in 3 different proofs)
- Match Context, in case of incompatibilities because of a now non
  trapped error (e.g. Not_found or Failure), use instead tactic Fail
  to force Match Context trying the next clause
- Inversion: better simplification and discrimination may occasionally
  lead to less subgoals and/or hypotheses and different naming of hypotheses
- Unification done by Apply/Elim has been changed and may exceptionally lead
  to incompatible instantiations
- Peano_dec.v and Compare_dec.v parts of Arith.v make Auto more
  powerful if these files were not already required (1 occurrence of
  this in submitted user contribs)

Changes from V7.1 to V7.2
=========================

Language

- Automatic insertion of patterns for local definitions in the type of
  the constructors of an inductive types (for compatibility with V6.3
  let-in style)
- Coercions allowed in Cases patterns
- New declaration "Canonical Structure id = t : I" to help resolution of
  equations of the form (proj ?)=a; if proj(e)=a then a is canonically
  equipped with the remaining fields in e, i.e. ? is instantiated by e

Tactics

- New tactic "ClearBody H" to clear the body of definitions in local context
- New tactic "Assert H := c" for forward reasoning
- Slight improvement in naming strategy for NewInduction/NewDestruct
- Intuition/Tauto do not perform useless unfolding and work up to conversion

Extraction (details in plugins/extraction/CHANGES or documentation)

- Syntax changes: there are no more options inside the extraction commands.
  New commands for customization and options have been introduced instead.
- More optimizations on extracted code.
- Extraction tests are now embedded in 14 user contributions.

Standard library

- In [Relations], Rstar.v and Newman.v now axiom-free.
- In [Sets], Integers.v now based on nat
- In [Arith], more lemmas in Min.v, new file Max.v, tail-recursive
  plus and mult added to Plus.v and Mult.v respectively
- New directory [Sorting] with a proof of heapsort (dragged from 6.3.1 lib)
- In [Reals], more lemmas in Rbase.v, new lemmas on square, square root and
  trigonometric functions (R_sqr.v - Rtrigo.v); a complementary approach
  and new theorems about continuity and derivability in Ranalysis.v;  some
  properties in plane geometry such as translation, rotation or similarity
  in Rgeom.v; finite sums and Chasles property in Rsigma.v

Bugs

- Confusion between implicit args of locals and globals of same base name fixed
- Various incompatibilities wrt inference of "?" in V6.3.1 fixed
- Implicits in infix section variables bug fixed
- Known coercions bugs fixed

- Apply "universe anomaly" bug fixed
- NatRing now working
- "Discriminate 1", "Injection 1", "Simplify_eq 1" now working
- NewInduction bugs with let-in and recursively dependent hypotheses fixed
- Syntax [x:=t:T]u now allowed as mentioned in documentation

- Bug with recursive inductive types involving let-in fixed
- Known pattern-matching bugs fixed
- Known Cases elimination predicate bugs fixed
- Improved errors messages for pattern-matching and projections
- Better error messages for ill-typed Cases expressions

Incompatibilities

- New naming strategy for NewInduction/NewDestruct may affect 7.1 compatibility
- Extra parentheses may exceptionally be needed in tactic definitions.
- Coq extensions written in Ocaml need to be updated (see dev/changements.txt
  for a description of the main changes in the interface files of V7.2)
- New behaviour of Intuition/Tauto may exceptionally lead to incompatibilities

----------------------------------------------------------------------------
Changes from V6.3.1 and V7.0 to V7.1
====================================

Notes:

- items followed by (**) are important sources of incompatibilities
- items followed by (*) may exceptionally be sources of incompatibilities
- items followed by (+) have been introduced in version 7.0


Main novelties
==============

References are to Coq V7.1 reference manual

- New primitive let-in construct (see sections 1.2.8 and )
- Long names (see sections 2.6 and 2.7)
- New high-level tactic language (see chapter 10)
- Improved search facilities (see section 5.2)
- New extraction algorithm managing the Type level (see chapter 17)
- New rewriting tactic for arbitrary equalities (see chapter 19)
- New tactic Field to decide equalities on commutative fields (see 7.11)
- New tactic Fourier to solve linear inequalities on reals numbers (see 7.11)
- New tactics for induction/case analysis in "natural" style (see 7.7)
- Deep restructuration of the code (safer, simpler and more efficient)
- Export of theories to XML for publishing and rendering purposes
  (see http://www.cs.unibo.it/helm)


Details of changes
==================

Language: new "let-in" construction
-----------------------------------

- New construction for local definitions (let-in) with syntax [x:=u]t (*)(+)

- Local definitions allowed in Record (a.k.a. record à la Randy Pollack)


Language: long names
--------------------

- Each construction has a unique absolute names built from a base
  name, the name of the module in which they are defined (Top if in
  coqtop), and possibly an arbitrary long sequence of directory (e.g.
  "Coq.Lists.PolyList.flat_map" where "Coq" means that "flat_map" is part
  of Coq standard library, "Lists" means it is defined in the Lists
  library and "PolyList" means it is in the file Polylist) (+)

- Constructions can be referred by their base name, or, in case of
  conflict, by a "qualified" name, where the base name is prefixed
  by the module name (and possibly by a directory name, and so
  on). A fully qualified name is an absolute name which always refer
  to the construction it denotes (to preserve the visibility of
  all constructions, no conflict is allowed for an absolute name) (+)

- Long names are available for modules with the possibility of using
  the directory name as a component of the module full name (with
  option -R to coqtop and coqc, or command Add LoadPath) (+)

- Improved conflict resolution strategy (the Unix PATH model),
  allowing more constructions to be referred just by their base name


Language: miscellaneous
-----------------------

- The names of variables for Record projections _and_ for induction principles
  (e.g. sum_ind) is now based on the first letter of their type (main
  source of incompatibility) (**)(+)

- Most typing errors have now a precise location in the source (+)

- Slightly different mechanism to solve "?" (*)(+)

- More arguments may be considered implicit at section closing (*)(+)

- Bug with identifiers ended by a number greater than 2^30 fixed (+)

- New visibility discipline for Remark, Fact and Local: Remark's and
  Fact's now survive at the end of section, but are only accessible using a
  qualified names as soon as their strength expires; Local's disappear and
  are moved into local definitions for each construction persistent at
  section closing


Language: Cases
---------------

- Cases no longer considers aliases inferable from dependencies in types (*)(+)

- A redundant clause in Cases is now an error (*)


Reduction
---------

- New reduction flags "Zeta" and "Evar" in Eval Compute, for inlining of
  local definitions and instantiation of existential variables

- Delta reduction flag does not perform Zeta and Evar reduction any more (*)

- Constants declared as opaque (using Qed) can no longer become
  transparent (a constant intended to be alternatively opaque and
  transparent must be declared as transparent (using Defined)); a risk
  exists (until next Coq version) that Simpl and Hnf reduces opaque
  constants (*)


New tactics
-----------

- New set of tactics to deal with types equipped with specific
  equalities (a.k.a. Setoids, e.g. nat equipped with eq_nat) [by C. Renard]

- New tactic Assert, similar to Cut but expected to be more user-friendly

- New tactic NewDestruct and NewInduction intended to replace Elim
  and Induction, Case and Destruct in a more user-friendly way (see
  restrictions in the reference manual)

- New tactic ROmega: an experimental alternative (based on reflexion) to Omega
  [by P. Crégut]

- New tactic language Ltac (see reference manual) (+)

- New versions of Tauto and Intuition, fully rewritten in the new Ltac
  language; they run faster and produce more compact proofs; Tauto is
  fully compatible but, in exchange of a better uniformity, Intuition
  is slightly weaker (then use Tauto instead) (**)(+)

- New tactic Field to decide equalities on commutative fields (as a
  special case, it works on real numbers) (+)

- New tactic Fourier to solve linear inequalities on reals numbers
  [by L. Pottier] (+)

- New tactics dedicated to real numbers: DiscrR, SplitRmult, SplitAbsolu (+)


Changes in existing tactics
---------------------------

- Reduction tactics in local definitions apply only to the body

- New syntax of the form "Compute in Type of H." to require a reduction on
  the types of local definitions

- Inversion, Injection, Discriminate, ... apply also on the
  quantified premises of a goal (using the "Intros until" syntax)

- Decompose has been fixed but hypotheses may get different names (*)(+)

- Tauto now manages uniformly hypotheses and conclusions of the form
  "t=t" which all are considered equivalent to "True". Especially,
  Tauto now solves goals of the form "H : ~ t = t |- A".

- The "Let" tactic has been renamed "LetTac" and is now based on the
  primitive "let-in" (+)

- Elim can no longer be used with an elimination schema different from
  the one defined at definition time of the inductive type. To overload
  an elimination schema, use "Elim <hyp> using <name of the new schema>"
  (*)(+)

- Simpl no longer unfolds the recursive calls of a mutually defined
  fixpoint (*)(+)

- Intro now fails if the hypothesis name already exists (*)(+)

- "Require Prolog" is no longer needed (i.e. it is available by default) (*)(+)

- Unfold now fails on a non unfoldable identifier (*)(+)

- Unfold also applies on definitions of the local context

- AutoRewrite now deals only with the main goal and it is the purpose of
  Hint Rewrite to deal with generated subgoals (+)

- Redundant or incompatible instantiations in Apply ... with ... are now
  correctly managed (+)


Efficiency
----------

- Excessive memory uses specific to V7.0 fixed

- Sizes of .vo files vary a lot compared to V6.3 (from -30% to +300%
  depending on the developments)

- An improved reduction strategy for lazy evaluation

- A more economical mechanism to ensure logical consistency at the Type level;
  warning: this is experimental and may produce "universes" anomalies
  (please report)


Concrete syntax of constructions
--------------------------------

- Only identifiers starting with "_" or a letter, and followed by letters,
  digits, "_" or "'" are allowed (e.g. "$" and "@" are no longer allowed) (*)

- A multiple binder like (a:A)(a,b:(P a))(Q a) is no longer parsed as
  (a:A)(a0:(P a))(b:(P a))(Q a0) but as (a:A)(a0:(P a))(b:(P a0))(Q a0) (*)(+)

- A dedicated syntax has been introduced for Reals (e.g ``3+1/x``) (+)

- Pretty-printing of Infix notations fixed. (+)


Parsing and grammar extension
-----------------------------

- More constraints when writing ast

  - "{...}" and the macros $LIST, $VAR, etc. now expect a metavariable
    (an identifier starting with $) (*)
  - identifiers should starts with a letter or "_" and be followed
     by letters, digits, "_" or "'" (other characters are still
     supported but it is not advised to use them) (*)(+)

- Entry "command" in "Grammar" and quotations (<<...>> stuff) is
  renamed "constr" as in "Syntax" (+)

- New syntax "[" sentence_1 ... sentence_n"]." to group sentences (useful
  for Time and to write grammar rules abbreviating several commands) (+)

- The default parser for actions in the grammar rules (and for
  patterns in the pretty-printing rules) is now the one associated to
  the grammar (i.e. vernac, tactic or constr); no need then for
  quotations as in <:vernac:<...>>; to return an "ast", the grammar
  must be explicitly typed with tag ": ast" or ": ast list", or if a
  syntax rule, by using <<...>> in the patterns (expression inside
  these angle brackets are parsed as "ast"); for grammars other than
  vernac, tactic or constr, you may explicitly type the action with
  tags ": constr", ": tactic", or ":vernac" (**)(+)

- Interpretation of names in Grammar rule is now based on long names,
  which allows to avoid problems (or sometimes tricks;) related to
  overloaded names (+)


New commands
------------

- New commands "Print XML All", "Show XML Proof", ... to show or
  export theories to XML to be used with Helm's publishing and rendering
  tools (see http://www.cs.unibo.it/helm) (by Claudio Sacerdoti Coen) (+)

- New commands to manually set implicit arguments (+)

  - "Implicits ident." to activate the implicit arguments mode just for ident
  - "Implicits ident [num1 num2 ...]." to explicitly give which
     arguments have to be considered as implicit

- New SearchPattern/SearchRewrite (by Yves Bertot) (+)

- New commands "Debug on"/"Debug off" to activate/deactivate the tactic
  language debugger (+)

- New commands to map physical paths to logical paths (+)
  - Add LoadPath physical_dir as logical_dir
  - Add Rec LoadPath physical_dir as logical_dir


Changes in existing commands
----------------------------

- Generalization of the usage of qualified identifiers in tactics
  and commands about globals, e.g. Decompose, Eval Delta;
  Hints Unfold, Transparent, Require

- Require synchronous with Reset; Require's scope stops at Section ending (*)

- For a module indirectly loaded by a "Require" but not exported,
  the command "Import module" turns the constructions defined in the
  module accessible by their short name, and activates the Grammar,
  Syntax, Hint, ... declared in the module (+)

- The scope of the "Search" command can be restricted to some modules (+)

- Final dot in command (full stop/period) must be followed by a blank
  (newline, tabulation or whitespace) (+)

- Slight restriction of the syntax for Cbv Delta: if present, option [-myconst]
  must immediately follow the Delta keyword (*)(+)

- SearchIsos currently not supported

- Add ML Path is now implied by Add LoadPath (+)

- New names for the following commands (+)

  AddPath -> Add LoadPath
  Print LoadPath -> Print LoadPath
  DelPath -> Remove LoadPath
  AddRecPath -> Add Rec LoadPath
  Print Path -> Print Coercion Paths

  Implicit Arguments On -> Set Implicit Arguments
  Implicit Arguments Off -> Unset Implicit Arguments

  Begin Silent -> Set Silent
  End Silent -> Unset Silent.


Tools
-----

- coqtop (+)

  - Two executables: coqtop.byte and coqtop.opt (if supported by the platform)
  - coqtop is a link to the more efficient executable (coqtop.opt if present)
  - option -full is obsolete (+)

- do_Makefile renamed into coq_makefile (+)

- New option -R to coqtop and coqc to map a physical directory to a logical
  one (+)

- coqc no longer needs to create a temporary file

- No more warning if no initialization file .coqrc exists


Extraction
----------

- New algorithm for extraction able to deal with "Type" (+)
  (by J.-C. Filliâtre and P. Letouzey)


Standard library
----------------

- New library on maps on integers (IntMap, contributed by Jean Goubault)

- New lemmas about integer numbers [ZArith]

- New lemmas and a "natural" syntax for reals [Reals] (+)

- Exc/Error/Value renamed into Option/Some/None (*)


New user contributions
----------------------

- Constructive complex analysis and the Fundamental Theorem of Algebra [FTA]
  (Herman Geuvers, Freek Wiedijk, Jan Zwanenburg, Randy Pollack,
   Henk Barendregt, Nijmegen)

- A new axiomatization of ZFC set theory [Functions_in_ZFC]
  (C. Simpson, Sophia-Antipolis)

- Basic notions of graph theory [GRAPHS-BASICS] (Jean Duprat, Lyon)

- A library for floating-point numbers [Float] (Laurent Théry, Sylvie Boldo,
  Sophia-Antipolis)

- Formalisation of CTL and TCTL temporal logic [CtlTctl] (Carlos
  Daniel Luna,Montevideo)

- Specification and verification of the Railroad Crossing Problem
  in CTL and TCTL [RailroadCrossing] (Carlos Daniel Luna,Montevideo)

- P-automaton and the ABR algorithm [PAutomata]
  (Christine Paulin, Emmanuel Freund, Orsay)

- Semantics of a subset of the C language [MiniC]
  (Eduardo Giménez, Emmanuel Ledinot, Suresnes)

- Correctness proofs of the following imperative algorithms:
  Bresenham line drawing algorithm [Bresenham], Marché's minimal edition
  distance algorithm [Diff] (Jean-Christophe Filliâtre, Orsay)

- Correctness proofs of Buchberger's algorithm [Buchberger] and RSA
  cryptographic algorithm [Rsa] (Laurent Théry, Sophia-Antipolis)

- Correctness proof of Stalmarck tautology checker algorithm
  [Stalmarck] (Laurent Théry, Pierre Letouzey, Sophia-Antipolis)