From 3e96002677226c0cdaa8f355938a76cfb37a722a Mon Sep 17 00:00:00 2001 From: Stephane Glondu Date: Thu, 14 Oct 2010 17:51:11 +0200 Subject: Imported Upstream version 8.3 --- doc/refman/RefMan-pre.tex | 783 ++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 783 insertions(+) create mode 100644 doc/refman/RefMan-pre.tex (limited to 'doc/refman/RefMan-pre.tex') diff --git a/doc/refman/RefMan-pre.tex b/doc/refman/RefMan-pre.tex new file mode 100644 index 00000000..a2cdb5ec --- /dev/null +++ b/doc/refman/RefMan-pre.tex @@ -0,0 +1,783 @@ +%BEGIN LATEX +\setheaders{Credits} +%END LATEX +\chapter*{Credits} +%\addcontentsline{toc}{section}{Credits} + +\Coq{}~ is a proof assistant for higher-order logic, allowing the +development of computer programs consistent with their formal +specification. It is the result of about ten years of research of the +Coq project. We shall briefly survey here three main aspects: the +\emph{logical language} in which we write our axiomatizations and +specifications, the \emph{proof assistant} which allows the development +of verified mathematical proofs, and the \emph{program extractor} which +synthesizes computer programs obeying their formal specifications, +written as logical assertions in the language. + +The logical language used by {\Coq} is a variety of type theory, +called the \emph{Calculus of Inductive Constructions}. Without going +back to Leibniz and Boole, we can date the creation of what is now +called mathematical logic to the work of Frege and Peano at the turn +of the century. The discovery of antinomies in the free use of +predicates or comprehension principles prompted Russell to restrict +predicate calculus with a stratification of \emph{types}. This effort +culminated with \emph{Principia Mathematica}, the first systematic +attempt at a formal foundation of mathematics. A simplification of +this system along the lines of simply typed $\lambda$-calculus +occurred with Church's \emph{Simple Theory of Types}. The +$\lambda$-calculus notation, originally used for expressing +functionality, could also be used as an encoding of natural deduction +proofs. This Curry-Howard isomorphism was used by N. de Bruijn in the +\emph{Automath} project, the first full-scale attempt to develop and +mechanically verify mathematical proofs. This effort culminated with +Jutting's verification of Landau's \emph{Grundlagen} in the 1970's. +Exploiting this Curry-Howard isomorphism, notable achievements in +proof theory saw the emergence of two type-theoretic frameworks; the +first one, Martin-L\"of's \emph{Intuitionistic Theory of Types}, +attempts a new foundation of mathematics on constructive principles. +The second one, Girard's polymorphic $\lambda$-calculus $F_\omega$, is +a very strong functional system in which we may represent higher-order +logic proof structures. Combining both systems in a higher-order +extension of the Automath languages, T. Coquand presented in 1985 the +first version of the \emph{Calculus of Constructions}, CoC. This strong +logical system allowed powerful axiomatizations, but direct inductive +definitions were not possible, and inductive notions had to be defined +indirectly through functional encodings, which introduced +inefficiencies and awkwardness. The formalism was extended in 1989 by +T. Coquand and C. Paulin with primitive inductive definitions, leading +to the current \emph{Calculus of Inductive Constructions}. This +extended formalism is not rigorously defined here. Rather, numerous +concrete examples are discussed. We refer the interested reader to +relevant research papers for more information about the formalism, its +meta-theoretic properties, and semantics. However, it should not be +necessary to understand this theoretical material in order to write +specifications. It is possible to understand the Calculus of Inductive +Constructions at a higher level, as a mixture of predicate calculus, +inductive predicate definitions presented as typed PROLOG, and +recursive function definitions close to the language ML. + +Automated theorem-proving was pioneered in the 1960's by Davis and +Putnam in propositional calculus. A complete mechanization (in the +sense of a semi-decision procedure) of classical first-order logic was +proposed in 1965 by J.A. Robinson, with a single uniform inference +rule called \emph{resolution}. Resolution relies on solving equations +in free algebras (i.e. term structures), using the \emph{unification + algorithm}. Many refinements of resolution were studied in the +1970's, but few convincing implementations were realized, except of +course that PROLOG is in some sense issued from this effort. A less +ambitious approach to proof development is computer-aided +proof-checking. The most notable proof-checkers developed in the +1970's were LCF, designed by R. Milner and his colleagues at U. +Edinburgh, specialized in proving properties about denotational +semantics recursion equations, and the Boyer and Moore theorem-prover, +an automation of primitive recursion over inductive data types. While +the Boyer-Moore theorem-prover attempted to synthesize proofs by a +combination of automated methods, LCF constructed its proofs through +the programming of \emph{tactics}, written in a high-level functional +meta-language, ML. + +The salient feature which clearly distinguishes our proof assistant +from say LCF or Boyer and Moore's, is its possibility to extract +programs from the constructive contents of proofs. This computational +interpretation of proof objects, in the tradition of Bishop's +constructive mathematics, is based on a realizability interpretation, +in the sense of Kleene, due to C. Paulin. The user must just mark his +intention by separating in the logical statements the assertions +stating the existence of a computational object from the logical +assertions which specify its properties, but which may be considered +as just comments in the corresponding program. Given this information, +the system automatically extracts a functional term from a consistency +proof of its specifications. This functional term may be in turn +compiled into an actual computer program. This methodology of +extracting programs from proofs is a revolutionary paradigm for +software engineering. Program synthesis has long been a theme of +research in artificial intelligence, pioneered by R. Waldinger. The +Tablog system of Z. Manna and R. Waldinger allows the deductive +synthesis of functional programs from proofs in tableau form of their +specifications, written in a variety of first-order logic. Development +of a systematic \emph{programming logic}, based on extensions of +Martin-L\"of's type theory, was undertaken at Cornell U. by the Nuprl +team, headed by R. Constable. The first actual program extractor, PX, +was designed and implemented around 1985 by S. Hayashi from Kyoto +University. It allows the extraction of a LISP program from a proof +in a logical system inspired by the logical formalisms of S. Feferman. +Interest in this methodology is growing in the theoretical computer +science community. We can foresee the day when actual computer systems +used in applications will contain certified modules, automatically +generated from a consistency proof of their formal specifications. We +are however still far from being able to use this methodology in a +smooth interaction with the standard tools from software engineering, +i.e. compilers, linkers, run-time systems taking advantage of special +hardware, debuggers, and the like. We hope that {\Coq} can be of use +to researchers interested in experimenting with this new methodology. + +A first implementation of CoC was started in 1984 by G. Huet and T. +Coquand. Its implementation language was CAML, a functional +programming language from the ML family designed at INRIA in +Rocquencourt. The core of this system was a proof-checker for CoC seen +as a typed $\lambda$-calculus, called the \emph{Constructive Engine}. +This engine was operated through a high-level notation permitting the +declaration of axioms and parameters, the definition of mathematical +types and objects, and the explicit construction of proof objects +encoded as $\lambda$-terms. A section mechanism, designed and +implemented by G. Dowek, allowed hierarchical developments of +mathematical theories. This high-level language was called the +\emph{Mathematical Vernacular}. Furthermore, an interactive +\emph{Theorem Prover} permitted the incremental construction of proof +trees in a top-down manner, subgoaling recursively and backtracking +from dead-alleys. The theorem prover executed tactics written in CAML, +in the LCF fashion. A basic set of tactics was predefined, which the +user could extend by his own specific tactics. This system (Version +4.10) was released in 1989. Then, the system was extended to deal +with the new calculus with inductive types by C. Paulin, with +corresponding new tactics for proofs by induction. A new standard set +of tactics was streamlined, and the vernacular extended for tactics +execution. A package to compile programs extracted from proofs to +actual computer programs in CAML or some other functional language was +designed and implemented by B. Werner. A new user-interface, relying +on a CAML-X interface by D. de Rauglaudre, was designed and +implemented by A. Felty. It allowed operation of the theorem-prover +through the manipulation of windows, menus, mouse-sensitive buttons, +and other widgets. This system (Version 5.6) was released in 1991. + +\Coq{} was ported to the new implementation Caml-light of X. Leroy and +D. Doligez by D. de Rauglaudre (Version 5.7) in 1992. A new version +of \Coq{} was then coordinated by C. Murthy, with new tools designed +by C. Parent to prove properties of ML programs (this methodology is +dual to program extraction) and a new user-interaction loop. This +system (Version 5.8) was released in May 1993. A Centaur interface +\textsc{CTCoq} was then developed by Y. Bertot from the Croap project +from INRIA-Sophia-Antipolis. + +In parallel, G. Dowek and H. Herbelin developed a new proof engine, +allowing the general manipulation of existential variables +consistently with dependent types in an experimental version of \Coq{} +(V5.9). + +The version V5.10 of \Coq{} is based on a generic system for +manipulating terms with binding operators due to Chet Murthy. A new +proof engine allows the parallel development of partial proofs for +independent subgoals. The structure of these proof trees is a mixed +representation of derivation trees for the Calculus of Inductive +Constructions with abstract syntax trees for the tactics scripts, +allowing the navigation in a proof at various levels of details. The +proof engine allows generic environment items managed in an +object-oriented way. This new architecture, due to C. Murthy, +supports several new facilities which make the system easier to extend +and to scale up: + +\begin{itemize} +\item User-programmable tactics are allowed +\item It is possible to separately verify development modules, and to + load their compiled images without verifying them again - a quick + relocation process allows their fast loading +\item A generic parsing scheme allows user-definable notations, with a + symmetric table-driven pretty-printer +\item Syntactic definitions allow convenient abbreviations +\item A limited facility of meta-variables allows the automatic + synthesis of certain type expressions, allowing generic notations + for e.g. equality, pairing, and existential quantification. +\end{itemize} + +In the Fall of 1994, C. Paulin-Mohring replaced the structure of +inductively defined types and families by a new structure, allowing +the mutually recursive definitions. P. Manoury implemented a +translation of recursive definitions into the primitive recursive +style imposed by the internal recursion operators, in the style of the +ProPre system. C. Mu{\~n}oz implemented a decision procedure for +intuitionistic propositional logic, based on results of R. Dyckhoff. +J.C. Filli{\^a}tre implemented a decision procedure for first-order +logic without contraction, based on results of J. Ketonen and R. +Weyhrauch. Finally C. Murthy implemented a library of inversion +tactics, relieving the user from tedious definitions of ``inversion +predicates''. + +\begin{flushright} +Rocquencourt, Feb. 1st 1995\\ +Gérard Huet +\end{flushright} + +\section*{Credits: addendum for version 6.1} +%\addcontentsline{toc}{section}{Credits: addendum for version V6.1} + +The present version 6.1 of \Coq{} is based on the V5.10 architecture. It +was ported to the new language Objective Caml by Bruno Barras. The +underlying framework has slightly changed and allows more conversions +between sorts. + +The new version provides powerful tools for easier developments. + +Cristina Cornes designed an extension of the \Coq{} syntax to allow +definition of terms using a powerful pattern-matching analysis in the +style of ML programs. + +Amokrane Saïbi wrote a mechanism to simulate +inheritance between types families extending a proposal by Peter +Aczel. He also developed a mechanism to automatically compute which +arguments of a constant may be inferred by the system and consequently +do not need to be explicitly written. + +Yann Coscoy designed a command which explains a proof term using +natural language. Pierre Cr{\'e}gut built a new tactic which solves +problems in quantifier-free Presburger Arithmetic. Both +functionalities have been integrated to the \Coq{} system by Hugo +Herbelin. + +Samuel Boutin designed a tactic for simplification of commutative +rings using a canonical set of rewriting rules and equality modulo +associativity and commutativity. + +Finally the organisation of the \Coq{} distribution has been supervised +by Jean-Christophe Filliâtre with the help of Judicaël Courant +and Bruno Barras. + +\begin{flushright} +Lyon, Nov. 18th 1996\\ +Christine Paulin +\end{flushright} + +\section*{Credits: addendum for version 6.2} +%\addcontentsline{toc}{section}{Credits: addendum for version V6.2} + +In version 6.2 of \Coq{}, the parsing is done using camlp4, a +preprocessor and pretty-printer for CAML designed by Daniel de +Rauglaudre at INRIA. Daniel de Rauglaudre made the first adaptation +of \Coq{} for camlp4, this work was continued by Bruno Barras who also +changed the structure of \Coq{} abstract syntax trees and the primitives +to manipulate them. The result of +these changes is a faster parsing procedure with greatly improved +syntax-error messages. The user-interface to introduce grammar or +pretty-printing rules has also changed. + +Eduardo Giménez redesigned the internal +tactic libraries, giving uniform names +to Caml functions corresponding to \Coq{} tactic names. + +Bruno Barras wrote new more efficient reductions functions. + +Hugo Herbelin introduced more uniform notations in the \Coq{} +specification language: the definitions by fixpoints and +pattern-matching have a more readable syntax. Patrick Loiseleur +introduced user-friendly notations for arithmetic expressions. + +New tactics were introduced: Eduardo Giménez improved a mechanism to +introduce macros for tactics, and designed special tactics for +(co)inductive definitions; Patrick Loiseleur designed a tactic to +simplify polynomial expressions in an arbitrary commutative ring which +generalizes the previous tactic implemented by Samuel Boutin. +Jean-Christophe Filli\^atre introduced a tactic for refining a goal, +using a proof term with holes as a proof scheme. + +David Delahaye designed the \textsf{SearchIsos} tool to search an +object in the library given its type (up to isomorphism). + +Henri Laulhère produced the \Coq{} distribution for the Windows environment. + +Finally, Hugo Herbelin was the main coordinator of the \Coq{} +documentation with principal contributions by Bruno Barras, David Delahaye, +Jean-Christophe Filli\^atre, Eduardo +Giménez, Hugo Herbelin and Patrick Loiseleur. + +\begin{flushright} +Orsay, May 4th 1998\\ +Christine Paulin +\end{flushright} + +\section*{Credits: addendum for version 6.3} +The main changes in version V6.3 was the introduction of a few new tactics +and the extension of the guard condition for fixpoint definitions. + + +B. Barras extended the unification algorithm to complete partial terms +and solved various tricky bugs related to universes.\\ +D. Delahaye developed the \texttt{AutoRewrite} tactic. He also designed the new +behavior of \texttt{Intro} and provided the tacticals \texttt{First} and +\texttt{Solve}.\\ +J.-C. Filli\^atre developed the \texttt{Correctness} tactic.\\ +E. Gim\'enez extended the guard condition in fixpoints.\\ +H. Herbelin designed the new syntax for definitions and extended the +\texttt{Induction} tactic.\\ +P. Loiseleur developed the \texttt{Quote} tactic and +the new design of the \texttt{Auto} +tactic, he also introduced the index of +errors in the documentation.\\ +C. Paulin wrote the \texttt{Focus} command and introduced +the reduction functions in definitions, this last feature +was proposed by J.-F. Monin from CNET Lannion. + +\begin{flushright} +Orsay, Dec. 1999\\ +Christine Paulin +\end{flushright} + +%\newpage + +\section*{Credits: versions 7} + +The version V7 is a new implementation started in September 1999 by +Jean-Christophe Filliâtre. This is a major revision with respect to +the internal architecture of the system. The \Coq{} version 7.0 was +distributed in March 2001, version 7.1 in September 2001, version +7.2 in January 2002, version 7.3 in May 2002 and version 7.4 in +February 2003. + +Jean-Christophe Filliâtre designed the architecture of the new system, he +introduced a new representation for environments and wrote a new kernel +for type-checking terms. His approach was to use functional +data-structures in order to get more sharing, to prepare the addition +of modules and also to get closer to a certified kernel. + +Hugo Herbelin introduced a new structure of terms with local +definitions. He introduced ``qualified'' names, wrote a new +pattern-matching compilation algorithm and designed a more compact +algorithm for checking the logical consistency of universes. He +contributed to the simplification of {\Coq} internal structures and the +optimisation of the system. He added basic tactics for forward +reasoning and coercions in patterns. + +David Delahaye introduced a new language for tactics. General tactics +using pattern-matching on goals and context can directly be written +from the {\Coq} toplevel. He also provided primitives for the design +of user-defined tactics in \textsc{Caml}. + +Micaela Mayero contributed the library on real numbers. +Olivier Desmettre extended this library with axiomatic +trigonometric functions, square, square roots, finite sums, Chasles +property and basic plane geometry. + +Jean-Christophe Filliâtre and Pierre Letouzey redesigned a new +extraction procedure from \Coq{} terms to \textsc{Caml} or +\textsc{Haskell} programs. This new +extraction procedure, unlike the one implemented in previous version +of \Coq{} is able to handle all terms in the Calculus of Inductive +Constructions, even involving universes and strong elimination. P. +Letouzey adapted user contributions to extract ML programs when it was +sensible. +Jean-Christophe Filliâtre wrote \verb=coqdoc=, a documentation +tool for {\Coq} libraries usable from version 7.2. + +Bruno Barras improved the reduction algorithms efficiency and +the confidence level in the correctness of {\Coq} critical type-checking +algorithm. + +Yves Bertot designed the \texttt{SearchPattern} and +\texttt{SearchRewrite} tools and the support for the \textsc{pcoq} interface +(\url{http://www-sop.inria.fr/lemme/pcoq/}). + +Micaela Mayero and David Delahaye introduced {\tt Field}, a decision tactic for commutative fields. + +Christine Paulin changed the elimination rules for empty and singleton +propositional inductive types. + +Loïc Pottier developed {\tt Fourier}, a tactic solving linear inequalities on real numbers. + +Pierre Crégut developed a new version based on reflexion of the {\tt Omega} +decision tactic. + +Claudio Sacerdoti Coen designed an XML output for the {\Coq} +modules to be used in the Hypertextual Electronic Library of +Mathematics (HELM cf \url{http://www.cs.unibo.it/helm}). + +A library for efficient representation of finite maps using binary trees +contributed by Jean Goubault was integrated in the basic theories. + +Pierre Courtieu developed a command and a tactic to reason on the +inductive structure of recursively defined functions. + +Jacek Chrz\k{a}szcz designed and implemented the module system of +{\Coq} whose foundations are in Judicaël Courant's PhD thesis. + +\bigskip + +The development was coordinated by C. Paulin. + +Many discussions within the Démons team and the LogiCal project +influenced significantly the design of {\Coq} especially with +%J. Chrz\k{a}szcz, P. Courtieu, +J. Courant, J. Duprat, J. Goubault, A. Miquel, +C. Marché, B. Monate and B. Werner. + +Intensive users suggested improvements of the system : +Y. Bertot, L. Pottier, L. Théry, P. Zimmerman from INRIA, +C. Alvarado, P. Crégut, J.-F. Monin from France Telecom R \& D. +\begin{flushright} +Orsay, May. 2002\\ +Hugo Herbelin \& Christine Paulin +\end{flushright} + +\section*{Credits: version 8.0} + +{\Coq} version 8 is a major revision of the {\Coq} proof assistant. +First, the underlying logic is slightly different. The so-called {\em +impredicativity} of the sort {\tt Set} has been dropped. The main +reason is that it is inconsistent with the principle of description +which is quite a useful principle for formalizing %classical +mathematics within classical logic. Moreover, even in an constructive +setting, the impredicativity of {\tt Set} does not add so much in +practice and is even subject of criticism from a large part of the +intuitionistic mathematician community. Nevertheless, the +impredicativity of {\tt Set} remains optional for users interested in +investigating mathematical developments which rely on it. + +Secondly, the concrete syntax of terms has been completely +revised. The main motivations were + +\begin{itemize} +\item a more uniform, purified style: all constructions are now lowercase, + with a functional programming perfume (e.g. abstraction is now + written {\tt fun}), and more directly accessible to the novice + (e.g. dependent product is now written {\tt forall} and allows + omission of types). Also, parentheses and are no longer mandatory + for function application. +\item extensibility: some standard notations (e.g. ``<'' and ``>'') were + incompatible with the previous syntax. Now all standard arithmetic + notations (=, +, *, /, <, <=, ... and more) are directly part of the + syntax. +\end{itemize} + +Together with the revision of the concrete syntax, a new mechanism of +{\em interpretation scopes} permits to reuse the same symbols +(typically +, -, *, /, <, <=) in various mathematical theories without +any ambiguities for {\Coq}, leading to a largely improved readability of +{\Coq} scripts. New commands to easily add new symbols are also +provided. + +Coming with the new syntax of terms, a slight reform of the tactic +language and of the language of commands has been carried out. The +purpose here is a better uniformity making the tactics and commands +easier to use and to remember. + +Thirdly, a restructuration and uniformisation of the standard library +of {\Coq} has been performed. There is now just one Leibniz' equality +usable for all the different kinds of {\Coq} objects. Also, the set of +real numbers now lies at the same level as the sets of natural and +integer numbers. Finally, the names of the standard properties of +numbers now follow a standard pattern and the symbolic +notations for the standard definitions as well. + +The fourth point is the release of \CoqIDE{}, a new graphical +gtk2-based interface fully integrated to {\Coq}. Close in style from +the Proof General Emacs interface, it is faster and its integration +with {\Coq} makes interactive developments more friendly. All +mathematical Unicode symbols are usable within \CoqIDE{}. + +Finally, the module system of {\Coq} completes the picture of {\Coq} +version 8.0. Though released with an experimental status in the previous +version 7.4, it should be considered as a salient feature of the new +version. + +Besides, {\Coq} comes with its load of novelties and improvements: new +or improved tactics (including a new tactic for solving first-order +statements), new management commands, extended libraries. + +\bigskip + +Bruno Barras and Hugo Herbelin have been the main contributors of the +reflexion and the implementation of the new syntax. The smart +automatic translator from old to new syntax released with {\Coq} is also +their work with contributions by Olivier Desmettre. + +Hugo Herbelin is the main designer and implementor of the notion of +interpretation scopes and of the commands for easily adding new notations. + +Hugo Herbelin is the main implementor of the restructuration of the +standard library. + +Pierre Corbineau is the main designer and implementor of the new +tactic for solving first-order statements in presence of inductive +types. He is also the maintainer of the non-domain specific automation +tactics. + +Benjamin Monate is the developer of the \CoqIDE{} graphical +interface with contributions by Jean-Christophe Filliâtre, Pierre +Letouzey, Claude Marché and Bruno Barras. + +Claude Marché coordinated the edition of the Reference Manual for + \Coq{} V8.0. + +Pierre Letouzey and Jacek Chrz\k{a}szcz respectively maintained the +extraction tool and module system of {\Coq}. + +Jean-Christophe Filliâtre, Pierre Letouzey, Hugo Herbelin and +contributors from Sophia-Antipolis and Nijmegen participated to the +extension of the library. + +Julien Narboux built a NSIS-based automatic {\Coq} installation tool for +the Windows platform. + +Hugo Herbelin and Christine Paulin coordinated the development which +was under the responsability of Christine Paulin. + +\begin{flushright} +Palaiseau \& Orsay, Apr. 2004\\ +Hugo Herbelin \& Christine Paulin\\ +(updated Apr. 2006) +\end{flushright} + +\section*{Credits: version 8.1} + +{\Coq} version 8.1 adds various new functionalities. + +Benjamin Grégoire implemented an alternative algorithm to check the +convertibility of terms in the {\Coq} type-checker. This alternative +algorithm works by compilation to an efficient bytecode that is +interpreted in an abstract machine similar to Xavier Leroy's ZINC +machine. Convertibility is performed by comparing the normal +forms. This alternative algorithm is specifically interesting for +proofs by reflection. More generally, it is convenient in case of +intensive computations. + +Christine Paulin implemented an extension of inductive types allowing +recursively non uniform parameters. Hugo Herbelin implemented +sort-polymorphism for inductive types. + +Claudio Sacerdoti Coen improved the tactics for rewriting on arbitrary +compatible equivalence relations. He also generalized rewriting to +arbitrary transition systems. + +Claudio Sacerdoti Coen added new features to the module system. + +Benjamin Grégoire, Assia Mahboubi and Bruno Barras developed a new +more efficient and more general simplification algorithm on rings and +semi-rings. + +Laurent Théry and Bruno Barras developed a new significantly more efficient +simplification algorithm on fields. + +Hugo Herbelin, Pierre Letouzey, Julien Forest, Julien Narboux and +Claudio Sacerdoti Coen added new tactic features. + +Hugo Herbelin implemented matching on disjunctive patterns. + +New mechanisms made easier the communication between {\Coq} and external +provers. Nicolas Ayache and Jean-Christophe Filliâtre implemented +connections with the provers {\sc cvcl}, {\sc Simplify} and {\sc +zenon}. Hugo Herbelin implemented an experimental protocol for calling +external tools from the tactic language. + +Matthieu Sozeau developed \textsc{Russell}, an experimental language +to specify the behavior of programs with subtypes. + +A mechanism to automatically use some specific tactic to solve +unresolved implicit has been implemented by Hugo Herbelin. + +Laurent Théry's contribution on strings and Pierre Letouzey and +Jean-Christophe Filliâtre's contribution on finite maps have been +integrated to the {\Coq} standard library. Pierre Letouzey developed a +library about finite sets ``à la Objective Caml''. With Jean-Marc +Notin, he extended the library on lists. Pierre Letouzey's +contribution on rational numbers has been integrated and extended.. + +Pierre Corbineau extended his tactic for solving first-order +statements. He wrote a reflection-based intuitionistic tautology +solver. + +Pierre Courtieu, Julien Forest and Yves Bertot added extra support to +reason on the inductive structure of recursively defined functions. + +Jean-Marc Notin significantly contributed to the general maintenance +of the system. He also took care of {\textsf{coqdoc}}. + +Pierre Castéran contributed to the documentation of (co-)inductive +types and suggested improvements to the libraries. + +Pierre Corbineau implemented a declarative mathematical proof +language, usable in combination with the tactic-based style of proof. + +Finally, many users suggested improvements of the system through the +Coq-Club mailing list and bug-tracker systems, especially user groups +from INRIA Rocquencourt, Radbout University, University of +Pennsylvania and Yale University. + +\enlargethispage{\baselineskip} +\begin{flushright} +Palaiseau, July 2006\\ +Hugo Herbelin +\end{flushright} + +\section*{Credits: version 8.2} + +{\Coq} version 8.2 adds new features, new libraries and +improves on many various aspects. + +Regarding the language of Coq, the main novelty is the introduction by +Matthieu Sozeau of a package of commands providing Haskell-style +type classes. Type classes, that come with a few convenient features +such as type-based resolution of implicit arguments, plays a new role +of landmark in the architecture of Coq with respect to automatization. +For instance, thanks to type classes support, Matthieu Sozeau could +implement a new resolution-based version of the tactics dedicated to +rewriting on arbitrary transitive relations. + +Another major improvement of Coq 8.2 is the evolution of the +arithmetic libraries and of the tools associated to them. Benjamin +Grégoire and Laurent Théry contributed a modular library for building +arbitrarily large integers from bounded integers while Evgeny Makarov +contributed a modular library of abstract natural and integer +arithmetics together with a few convenient tactics. On his side, +Pierre Letouzey made numerous extensions to the arithmetic libraries on +$\mathbb{Z}$ and $\mathbb{Q}$, including extra support for +automatization in presence of various number-theory concepts. + +Frédéric Besson contributed a reflexive tactic based on +Krivine-Stengle Positivstellensatz (the easy way) for validating +provability of systems of inequalities. The platform is flexible enough +to support the validation of any algorithm able to produce a +``certificate'' for the Positivstellensatz and this covers the case of +Fourier-Motzkin (for linear systems in $\mathbb{Q}$ and $\mathbb{R}$), +Fourier-Motzkin with cutting planes (for linear systems in +$\mathbb{Z}$) and sum-of-squares (for non-linear systems). Evgeny +Makarov made the platform generic over arbitrary ordered rings. + +Arnaud Spiwack developed a library of 31-bits machine integers and, +relying on Benjamin Grégoire and Laurent Théry's library, delivered a +library of unbounded integers in base $2^{31}$. As importantly, he +developed a notion of ``retro-knowledge'' so as to safely extend the +kernel-located bytecode-based efficient evaluation algorithm of Coq +version 8.1 to use 31-bits machine arithmetics for efficiently +computing with the library of integers he developed. + +Beside the libraries, various improvements contributed to provide a +more comfortable end-user language and more expressive tactic +language. Hugo Herbelin and Matthieu Sozeau improved the +pattern-matching compilation algorithm (detection of impossible +clauses in pattern-matching, automatic inference of the return +type). Hugo Herbelin, Pierre Letouzey and Matthieu Sozeau contributed +various new convenient syntactic constructs and new tactics or tactic +features: more inference of redundant information, better unification, +better support for proof or definition by fixpoint, more expressive +rewriting tactics, better support for meta-variables, more convenient +notations, ... + +Élie Soubiran improved the module system, adding new features (such as +an ``include'' command) and making it more flexible and more +general. He and Pierre Letouzey improved the support for modules in +the extraction mechanism. + +Matthieu Sozeau extended the \textsc{Russell} language, ending in an +convenient way to write programs of given specifications, Pierre +Corbineau extended the Mathematical Proof Language and the +automatization tools that accompany it, Pierre Letouzey supervised and +extended various parts the standard library, Stéphane Glondu +contributed a few tactics and improvements, Jean-Marc Notin provided +help in debugging, general maintenance and {\tt coqdoc} support, +Vincent Siles contributed extensions of the {\tt Scheme} command and +of {\tt injection}. + +Bruno Barras implemented the {\tt coqchk} tool: this is a stand-alone +type-checker that can be used to certify {\tt .vo} files. Especially, +as this verifier runs in a separate process, it is granted not to be +``hijacked'' by virtually malicious extensions added to {\Coq}. + +Yves Bertot, Jean-Christophe Filliâtre, Pierre Courtieu and +Julien Forest acted as maintainers of features they implemented in +previous versions of Coq. + +Julien Narboux contributed to CoqIDE. +Nicolas Tabareau made the adaptation of the interface of the old +``setoid rewrite'' tactic to the new version. Lionel Mamane worked on +the interaction between Coq and its external interfaces. With Samuel +Mimram, he also helped making Coq compatible with recent software +tools. Russell O'Connor, Cezary Kaliscyk, Milad Niqui contributed to +improved the libraries of integers, rational, and real numbers. We +also thank many users and partners for suggestions and feedback, in +particular Pierre Castéran and Arthur Charguéraud, the INRIA Marelle +team, Georges Gonthier and the INRIA-Microsoft Mathematical Components team, +the Foundations group at Radbout university in Nijmegen, reporters of bugs +and participants to the Coq-Club mailing list. + +\begin{flushright} +Palaiseau, June 2008\\ +Hugo Herbelin\\ +\end{flushright} + +\section*{Credits: version 8.3} + +{\Coq} version 8.3 is before all a transition version with refinements +or extensions of the existing features and libraries and a new tactic +{\tt nsatz} based on Hilbert's Nullstellensatz for deciding systems of +equations over rings. + +With respect to libraries, the main evolutions are due to Pierre +Letouzey with a rewriting of the library of finite sets {\tt FSets} +and a new round of evolutions in the modular development of arithmetic +(library {\tt Numbers}). The reason for making {\tt FSets} evolve is +that the computational and logical contents were quite intertwined in +the original implementation, leading in some cases to longer +computations than expected and this problem is solved in the new {\tt + MSets} implementation. As for the modular arithmetic library, it was +only dealing with the basic arithmetic operators in the former version +and its current extension adds the standard theory of the division, +min and max functions, all made available for free to any +implementation of $\mathbb{N}$, $\mathbb{Z}$ or +$\mathbb{Z}/n\mathbb{Z}$. + +The main other evolutions of the library are due to Hugo Herbelin who +made a revision of the sorting library (includingh a certified +merge-sort) and to Guillaume Melquiond who slightly revised and +cleaned up the library of reals. + +The module system evolved significantly. Besides the resolution of +some efficiency issues and a more flexible construction of module +types, Élie Soubiran brought a new model of name equivalence, the +$\Delta$-equivalence, which respects as much as possible the names +given by the users. He also designed with Pierre Letouzey a new +convenient operator \verb!<+! for nesting functor application, what +provides a light notation for inheriting the properties of cascading +modules. + +The new tactic {\tt nsatz} is due to Loïc Pottier. It works by +computing Gr\"obner bases. Regarding the existing tactics, various +improvements have been done by Matthieu Sozeau, Hugo Herbelin and +Pierre Letouzey. + +Matthieu Sozeau extended and refined the type classes and {\tt + Program} features (the {\sc Russell} language). Pierre Letouzey +maintained and improved the extraction mechanism. Bruno Barras and +\'Elie Soubiran maintained the Coq checker, Julien Forest maintained +the {\tt Function} mechanism for reasoning over recursively defined +functions. Matthieu Sozeau, Hugo Herbelin and Jean-Marc Notin +maintained {\tt coqdoc}. Frédéric Besson maintained the {\sc + Micromega} plateform for deciding systems of inequalities. Pierre +Courtieu maintained the support for the Proof General Emacs +interface. Claude Marché maintained the plugin for calling external +provers ({\tt dp}). Yves Bertot made some improvements to the +libraries of lists and integers. Matthias Puech improved the search +functions. Guillaume Melquiond usefully contributed here and +there. Yann Régis-Gianas grounded the support for Unicode on a more +standard and more robust basis. + +Though invisible from outside, Arnaud Spiwack improved the general +process of management of existential variables. Pierre Letouzey and +Stéphane Glondu improved the compilation scheme of the Coq archive. +Vincent Gross provided support to CoqIDE. Jean-Marc Notin provided +support for benchmarking and archiving. + +Many users helped by reporting problems, providing patches, suggesting +improvements or making useful comments, either on the bug tracker or +on the Coq-club mailing list. This includes but not exhaustively +Cédric Auger, Arthur Charguéraud, François Garillot, Georges Gonthier, +Robin Green, Stéphane Lescuyer, Eelis van der Weegen,~... + +Though not directly related to the implementation, special thanks are +going to Yves Bertot, Pierre Castéran, Adam Chlipala, and Benjamin +Pierce for the excellent teaching materials they provided. + +\begin{flushright} +Paris, April 2010\\ +Hugo Herbelin\\ +\end{flushright} + +%new Makefile + +%\newpage + +% Integration of ZArith lemmas from Sophia and Nijmegen. + + +% $Id: RefMan-pre.tex 13271 2010-07-08 18:10:54Z herbelin $ + +%%% Local Variables: +%%% mode: latex +%%% TeX-master: "Reference-Manual" +%%% End: -- cgit v1.2.3