Changes from V8.1pl2 to V8.1pl3
===============================

Bug fixes 

- A critical bug and a few other bugs have been fixed.

Changes from V8.1pl1 to V8.1pl2
===============================

Installation

- Support for compilation with ocaml 3.10 and (transitional) camlp5.

Bug fixes 

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

Changes from V8.1 to V8.1pl1
============================

Bug fixes 

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

Tactics
 
- All known failures of ROmega have been fixed. It should now be a 
  faithful and quicker replacement for Omega (except when nat parts
  are involved). ROmega and Omega now handle <->. 

Libraries

- 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) [exceptionally source of incompatibilities].
- Loading FSets/FMap used to open unwanted scopes of integer datatypes 
  (see bug #1347). These scopes may need to be manually opened now.

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.
- 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" (doc TODO)
- 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.
- 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' (doc TODO).

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 Fix_F.
- 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
   (TODO : doc).
- "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 contrib/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 contrib/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 contrib/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 contrib/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 contrib/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  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. Crgut]

- 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. Fillitre 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 Thry, 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 Gimnez, Emmanuel Ledinot, Suresnes) 

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

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

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