\[\begin{split}\newcommand{\alors}{\textsf{then}} \newcommand{\alter}{\textsf{alter}} \newcommand{\as}{\kw{as}} \newcommand{\Assum}[3]{\kw{Assum}(#1)(#2:#3)} \newcommand{\bool}{\textsf{bool}} \newcommand{\case}{\kw{case}} \newcommand{\conc}{\textsf{conc}} \newcommand{\cons}{\textsf{cons}} \newcommand{\consf}{\textsf{consf}} \newcommand{\conshl}{\textsf{cons\_hl}} \newcommand{\Def}[4]{\kw{Def}(#1)(#2:=#3:#4)} \newcommand{\emptyf}{\textsf{emptyf}} \newcommand{\End}{\kw{End}} \newcommand{\kwend}{\kw{end}} \newcommand{\EqSt}{\textsf{EqSt}} \newcommand{\even}{\textsf{even}} \newcommand{\evenO}{\textsf{even}_\textsf{O}} \newcommand{\evenS}{\textsf{even}_\textsf{S}} \newcommand{\false}{\textsf{false}} \newcommand{\filter}{\textsf{filter}} \newcommand{\Fix}{\kw{Fix}} \newcommand{\fix}{\kw{fix}} \newcommand{\for}{\textsf{for}} \newcommand{\forest}{\textsf{forest}} \newcommand{\from}{\textsf{from}} \newcommand{\Functor}{\kw{Functor}} \newcommand{\haslength}{\textsf{has\_length}} \newcommand{\hd}{\textsf{hd}} \newcommand{\ident}{\textsf{ident}} \newcommand{\In}{\kw{in}} \newcommand{\Ind}[4]{\kw{Ind}[#2](#3:=#4)} \newcommand{\ind}[3]{\kw{Ind}~[#1]\left(#2\mathrm{~:=~}#3\right)} \newcommand{\Indp}[5]{\kw{Ind}_{#5}(#1)[#2](#3:=#4)} \newcommand{\Indpstr}[6]{\kw{Ind}_{#5}(#1)[#2](#3:=#4)/{#6}} \newcommand{\injective}{\kw{injective}} \newcommand{\kw}[1]{\textsf{#1}} \newcommand{\lb}{\lambda} \newcommand{\length}{\textsf{length}} \newcommand{\letin}[3]{\kw{let}~#1:=#2~\kw{in}~#3} \newcommand{\List}{\textsf{list}} \newcommand{\lra}{\longrightarrow} \newcommand{\Match}{\kw{match}} \newcommand{\Mod}[3]{{\kw{Mod}}({#1}:{#2}\,\zeroone{:={#3}})} \newcommand{\ModA}[2]{{\kw{ModA}}({#1}=={#2})} \newcommand{\ModS}[2]{{\kw{Mod}}({#1}:{#2})} \newcommand{\ModType}[2]{{\kw{ModType}}({#1}:={#2})} \newcommand{\mto}{.\;} \newcommand{\Nat}{\mathbb{N}} \newcommand{\nat}{\textsf{nat}} \newcommand{\Nil}{\textsf{nil}} \newcommand{\nilhl}{\textsf{nil\_hl}} \newcommand{\nO}{\textsf{O}} \newcommand{\node}{\textsf{node}} \newcommand{\nS}{\textsf{S}} \newcommand{\odd}{\textsf{odd}} \newcommand{\oddS}{\textsf{odd}_\textsf{S}} \newcommand{\ovl}[1]{\overline{#1}} \newcommand{\Pair}{\textsf{pair}} \newcommand{\plus}{\mathsf{plus}} \newcommand{\Prod}{\textsf{prod}} \newcommand{\SProp}{\textsf{SProp}} \newcommand{\Prop}{\textsf{Prop}} \newcommand{\return}{\kw{return}} \newcommand{\Set}{\textsf{Set}} \newcommand{\si}{\textsf{if}} \newcommand{\sinon}{\textsf{else}} \newcommand{\Sort}{\mathcal{S}} \newcommand{\Str}{\textsf{Stream}} \newcommand{\Struct}{\kw{Struct}} \newcommand{\subst}[3]{#1\{#2/#3\}} \newcommand{\tl}{\textsf{tl}} \newcommand{\tree}{\textsf{tree}} \newcommand{\trii}{\triangleright_\iota} \newcommand{\true}{\textsf{true}} \newcommand{\Type}{\textsf{Type}} \newcommand{\unfold}{\textsf{unfold}} \newcommand{\WEV}[3]{\mbox{$#1[] \vdash #2 \lra #3$}} \newcommand{\WEVT}[3]{\mbox{$#1[] \vdash #2 \lra$}\\ \mbox{$ #3$}} \newcommand{\WF}[2]{{\mathcal{W\!F}}(#1)[#2]} \newcommand{\WFE}[1]{\WF{E}{#1}} \newcommand{\WFT}[2]{#1[] \vdash {\mathcal{W\!F}}(#2)} \newcommand{\WFTWOLINES}[2]{{\mathcal{W\!F}}\begin{array}{l}(#1)\\\mbox{}[{#2}]\end{array}} \newcommand{\with}{\kw{with}} \newcommand{\WS}[3]{#1[] \vdash #2 <: #3} \newcommand{\WSE}[2]{\WS{E}{#1}{#2}} \newcommand{\WT}[4]{#1[#2] \vdash #3 : #4} \newcommand{\WTE}[3]{\WT{E}{#1}{#2}{#3}} \newcommand{\WTEG}[2]{\WTE{\Gamma}{#1}{#2}} \newcommand{\WTM}[3]{\WT{#1}{}{#2}{#3}} \newcommand{\zeroone}[1]{[{#1}]} \newcommand{\zeros}{\textsf{zeros}} \end{split}\]

Recent changes

Unreleased changes


Specification language, type inference



Tactic language


Commands and options



Standard library

Infrastructure and dependencies


Version 8.10

Summary of changes

Coq version 8.10 contains two major new features: support for a native fixed-precision integer type and a new sort \(\SProp\) of strict propositions. It is also the result of refinements and stabilization of previous features, deprecations or removals of deprecated features, cleanups of the internals of the system and API, and many documentation improvements. This release includes many user-visible changes, including deprecations that are documented in the next subsection, and new features that are documented in the reference manual. Here are the most important user-visible changes:

  • Kernel:

    • A notion of primitive object was added to the calculus. Its first instance is primitive cyclic unsigned integers, axiomatized in module UInt63. See Section Primitive Integers. The Coq.Numbers.Cyclic.Int31 library is deprecated (#6914, by Maxime Dénès, Benjamin Grégoire and Vincent Laporte, with help and reviews from many others).
    • The \(\SProp\) sort of definitionally proof-irrelevant propositions was introduced. \(\SProp\) allows to mark proof terms as irrelevant for conversion, and is treated like \(\Prop\) during extraction. It is enabled using the -allow-sprop command-line flag or the Allow StrictProp flag. See Chapter SProp (proof irrelevant propositions) (#8817, by Gaëtan Gilbert).
    • The unfolding heuristic in termination checking was made more complete, allowing more constants to be unfolded to discover valid recursive calls. Performance regression may occur in Fixpoint declarations without an explicit {struct} annotation, since guessing the decreasing argument can now be more expensive (#9602, by Enrico Tassi).
  • Universes:

  • Notations:

    • New command String Notation to register string syntax for custom inductive types (#8965, by Jason Gross).
    • Experimental: Numeral Notations now parse decimal constants such as 1.02e+01 or 10.2. Parsers added for Q and R. In the rare case when such numeral notations were used in a development along with Q or R, they may have to be removed or disambiguated through explicit scope annotations (#8764, by Pierre Roux).
  • Ltac backtraces can be turned on using the Ltac Backtrace flag, which is off by default (#9142, fixes #7769 and #7385, by Pierre-Marie Pédrot).

  • The tactics lia, nia, lra, nra are now using a novel Simplex-based proof engine. In case of regression, unset Simplex to get the venerable Fourier-based engine (#8457, by Fréderic Besson).

  • SSReflect:

    • New intro patterns:

      • temporary introduction: => +

      • block introduction: => [^ prefix ] [^~ suffix ]

      • fast introduction: => >

      • tactics as views: => /ltac:mytac

      • replace hypothesis: => {}H

        See Section Introduction in the context (#6705, by Enrico Tassi, with help from Maxime Dénès, ideas coming from various users).

    • New tactic under to rewrite under binders, given an extensionality lemma:

      • interactive mode: under term, associated terminator: over
      • one-liner mode: under @term do [@tactic | ...]

      It can take occurrence switches, contextual patterns, and intro patterns: under {2}[in RHS]eq_big => [i|i ?] do ... (#9651, by Erik Martin-Dorel and Enrico Tassi).

  • Combined Scheme now works when inductive schemes are generated in sort \(\Type\). It used to be limited to sort Prop (#7634, by Théo Winterhalter).

  • A new registration mechanism for reference from ML code to Coq constructs has been added (#186, by Emilio Jesús Gallego Arias, Maxime Dénès and Vincent Laporte).

  • CoqIDE:

    • CoqIDE now depends on gtk+3 and lablgtk3 instead of gtk+2 and lablgtk2. The INSTALL file available in the Coq sources has been updated to list the new dependencies (#9279, by Hugo Herbelin, with help from Jacques Garrigue, Emilio Jesús Gallego Arias, Michael Sogetrop and Vincent Laporte).
    • Smart input for Unicode characters. For example, typing \alpha then Shift+Space will insert the greek letter alpha. A larger number of default bindings are provided, following the latex naming convention. Bindings can be customized, either globally, or on a per-project basis. See Section Bindings for input of Unicode symbols for details (#8560, by Arthur Charguéraud).
  • Infrastructure and dependencies:

    • Coq 8.10 requires OCaml >= 4.05.0, bumped from 4.02.3 See the INSTALL file for more information on dependencies (#7522, by Emilio Jesús Gallego Arías).

    • Coq 8.10 doesn't need Camlp5 to build anymore. It now includes a fork of the core parsing library that Coq uses, which is a small subset of the whole Camlp5 distribution. In particular, this subset doesn't depend on the OCaml AST, allowing easier compilation and testing on experimental OCaml versions. Coq also ships a new parser coqpp that plugin authors must switch to (#7902, #7979, #8161, #8667, and #8945, by Pierre-Marie Pédrot and Emilio Jesús Gallego Arias).

      The Coq developers would like to thank Daniel de Rauglaudre for many years of continued support.

    • Coq now supports building with Dune, in addition to the traditional Makefile which is scheduled for deprecation (#6857, by Emilio Jesús Gallego Arias, with help from Rudi Grinberg).

      Experimental support for building Coq projects has been integrated in Dune at the same time, providing an improved experience for plugin developers. We thank the Dune team for their work supporting Coq.

Version 8.10 also comes with a bunch of smaller-scale changes and improvements regarding the different components of the system, including many additions to the standard library (see the next subsection for details).

On the implementation side, the dev/doc/changes.md file documents the numerous changes to the implementation and improvements of interfaces. The file provides guidelines on porting a plugin to the new version and a plugin development tutorial originally made by Yves Bertot is now in doc/plugin_tutorial. The dev/doc/critical-bugs file documents the known critical bugs of Coq and affected releases.

The efficiency of the whole system has seen improvements thanks to contributions from Gaëtan Gilbert, Pierre-Marie Pédrot, and Maxime Dénès.

Maxime Dénès, Emilio Jesús Gallego Arias, Gaëtan Gilbert, Michael Soegtrop, Théo Zimmermann worked on maintaining and improving the continuous integration system and package building infrastructure. Coq is now continuously tested against OCaml trunk, in addition to the oldest supported and latest OCaml releases.

Coq's documentation for the development branch is now deployed continuously at https://coq.github.io/doc/master/api (documentation of the ML API), https://coq.github.io/doc/master/refman (reference manual), and https://coq.github.io/doc/master/stdlib (documentation of the standard library). Similar links exist for the v8.10 branch.

The OPAM repository for Coq packages has been maintained by Guillaume Melquiond, Matthieu Sozeau, Enrico Tassi (who migrated it to opam 2) with contributions from many users. A list of packages is available at https://coq.inria.fr/opam/www/.

The 61 contributors to this version are David A. Dalrymple, Tanaka Akira, Benjamin Barenblat, Yves Bertot, Frédéric Besson, Lasse Blaauwbroek, Martin Bodin, Joachim Breitner, Tej Chajed, Frédéric Chapoton, Arthur Charguéraud, Cyril Cohen, Lukasz Czajka, Christian Doczkal, Maxime Dénès, Andres Erbsen, Jim Fehrle, Gaëtan Gilbert, Matěj Grabovský, Simon Gregersen, Jason Gross, Samuel Gruetter, Hugo Herbelin, Jasper Hugunin, Mirai Ikebuchi, Emilio Jesus Gallego Arias, Chantal Keller, Matej Košík, Vincent Laporte, Olivier Laurent, Larry Darryl Lee Jr, Pierre Letouzey, Nick Lewycky, Yao Li, Yishuai Li, Xia Li-yao, Assia Mahboubi, Simon Marechal, Erik Martin-Dorel, Thierry Martinez, Guillaume Melquiond, Kayla Ngan, Sam Pablo Kuper, Karl Palmskog, Clément Pit-Claudel, Pierre-Marie Pédrot, Pierre Roux, Kazuhiko Sakaguchi, Ryan Scott, Vincent Semeria, Gan Shen, Michael Soegtrop, Matthieu Sozeau, Enrico Tassi, Laurent Théry, Kamil Trzciński, whitequark, Théo Winterhalter, Beta Ziliani and Théo Zimmermann.

Many power users helped to improve the design of the new features via the issue and pull request system, the Coq development mailing list, the coq-club@inria.fr mailing list or the new Discourse forum. It would be impossible to mention exhaustively the names of everybody who to some extent influenced the development.

Version 8.10 is the fifth release of Coq developed on a time-based development cycle. Its development spanned 6 months from the release of Coq 8.9. Vincent Laporte is the release manager and maintainer of this release. This release is the result of ~2500 commits and ~650 PRs merged, closing 150+ issues.

Santiago de Chile, April 2019,
Matthieu Sozeau for the Coq development team

Other changes in 8.10+beta1

  • Command-line tools and options:

    • The use of coqtop as a compiler has been deprecated, in favor of coqc. Consequently option -compile will stop to be accepted in the next release. coqtop is now reserved to interactive use (#9095, by Emilio Jesús Gallego Arias).

    • New option -topfile filename, which will set the current module name (à la -top) based on the filename passed, taking into account the proper -R/-Q options. For example, given -R Foo foolib using -topfile foolib/bar.v will set the module name to Foo.Bar. CoqIDE now properly sets the module name for a given file based on its path (#8991, closes #8989, by Gaëtan Gilbert).

    • Experimental: Coq flags and options can now be set on the command-line, e.g. -set "Universe Polymorphism=true" (#9876, by Gaëtan Gilbert).

    • The -native-compiler flag of coqc and coqtop now takes an argument which can have three values:

      • no disables native_compute
      • yes enables native_compute and precompiles .v files to native code
      • ondemand enables native_compute but compiles code only when native_compute is called

      The default value is ondemand. Note that this flag now has priority over the configure flag of the same name.

      A new -bytecode-compiler flag for coqc and coqtop controls whether conversion can use the VM. The default value is yes.

      (#8870, by Maxime Dénès)

    • The pretty timing diff scripts (flag TIMING=1 to a coq_makefile-made Makefile, also tools/make-both-single-timing-files.py, tools/make-both-time-files.py, and tools/make-one-time-file.py) now correctly support non-UTF-8 characters in the output of coqc / make as well as printing to stdout, on both python2 and python3 (#9872, closes #9767 and #9705, by Jason Gross)

    • coq_makefile's install target now errors if any file to install is missing (#9906, by Gaëtan Gilbert).

    • Preferences from coqide.keys are no longer overridden by modifiers preferences in coqiderc (#10014, by Hugo Herbelin).

  • Specification language, type inference:

    • Fixing a missing check in interpreting instances of existential variables that are bound to local definitions. Might exceptionally induce an overhead if the cost of checking the conversion of the corresponding definitions is additionally high (#8217, closes #8215, by Hugo Herbelin).

    • A few improvements in inference of the return clause of match that can exceptionally introduce incompatibilities. This can be solved by writing an explicit return clause, sometimes even simply an explicit return _ clause (#262, by Hugo Herbelin).

    • Using non-projection values with the projection syntax is not allowed. For instance 0.(S) is not a valid way to write S 0. Projections from non-primitive (emulated) records are allowed with warning "nonprimitive-projection-syntax" (#8829, by Gaëtan Gilbert).

    • An option and attributes to control the automatic decision to declare an inductive type as template polymorphic were added. Warning "auto-template" (off by default) can trigger when an inductive is automatically declared template polymorphic without the attribute.

      Inductive types declared by Funind will never be template polymorphic.

      (#8488, by Gaëtan Gilbert)

  • Notations:

    • New command Declare Scope to explicitly declare a scope name before any use of it. Implicit declaration of a scope at the time of Bind Scope, Delimit Scope, Undelimit Scope, or Notation is deprecated (#7135, by Hugo Herbelin).
    • Various bugs have been fixed (e.g. #9214 on removing spurious parentheses on abbreviations shortening a strict prefix of an application, by Hugo Herbelin).
    • Numeral Notation now support inductive types in the input to printing functions (e.g., numeral notations can be defined for terms containing things like @cons nat O O), and parsing functions now fully normalize terms including parameters of constructors (so that, e.g., a numeral notation whose parsing function outputs a proof of Nat.gcd x y = 1 will no longer fail to parse due to containing the constant Nat.gcd in the parameter-argument of eq_refl) (#9874, closes #9840 and #9844, by Jason Gross).
    • Deprecated compatibility notations have actually been removed. Uses of these notations are generally easy to fix thanks to the hint contained in the deprecation warning emitted by Coq 8.8 and 8.9. For projects that require more than a handful of such fixes, there is a script that will do it automatically, using the output of coqc (#8638, by Jason Gross).
    • Allow inspecting custom grammar entries by Print Custom Grammar (#10061, fixes #9681, by Jasper Hugunin, review by Pierre-Marie Pédrot and Hugo Herbelin).
  • The quote plugin was removed. If some users are interested in maintaining this plugin externally, the Coq development team can provide assistance for extracting the plugin and setting up a new repository (#7894, by Maxime Dénès).

  • Ltac:

    • Tactic names are no longer allowed to clash, even if they are not defined in the same section. For example, the following is no longer accepted: Ltac foo := idtac. Section S. Ltac foo := fail. End S. (#8555, by Maxime Dénès).
    • Names of existential variables occurring in Ltac functions (e.g. ?[n] or ?n in terms - not in patterns) are now interpreted the same way as other variable names occurring in Ltac functions (#7309, by Hugo Herbelin).
  • Tactics:

    • Removed the deprecated romega tactic (#8419, by Maxime Dénès and Vincent Laporte).
    • Hint declaration and removal should now specify a database (e.g. Hint Resolve foo : database). When the database name is omitted, the hint is added to the core database (as previously), but a deprecation warning is emitted (#8987, by Maxime Dénès).
    • There are now tactics in PreOmega.v called Z.div_mod_to_equations, Z.quot_rem_to_equations, and Z.to_euclidean_division_equations (which combines the div_mod and quot_rem variants) which allow lia, nia, etc to support Z.div and Z.modulo (Z.quot and Z.rem, respectively), by posing the specifying equation for Z.div and Z.modulo before replacing them with atoms (#8062, by Jason Gross).
    • The syntax of the autoapply tactic was fixed to conform with preexisting documentation: it now takes a with clause instead of a using clause (#9524, closes #7632, by Théo Zimmermann).
    • Modes are now taken into account by typeclasses eauto for local hypotheses (#9996, fixes #5752, by Maxime Dénès, review by Pierre-Marie Pédrot).
    • New variant change_no_check of change, usable as a documented replacement of convert_concl_no_check (#10012, #10017, #10053, and #10059, by Hugo Herbelin and Paolo G. Giarrusso).
    • The simplified value returned by field_simplify is not always a fraction anymore. When the denominator is 1, it returns x while previously it was returning x/1. This change could break codes that were post-processing application of field_simplify to get rid of these x/1 (#9854, by Laurent Théry, with help from Michael Soegtrop, Maxime Dénès, and Vincent Laporte).
  • SSReflect:

    • Clear discipline made consistent across the entire proof language. Whenever a clear switch {x..} comes immediately before an existing proof context entry (used as a view, as a rewrite rule or as name for a new context entry) then such entry is cleared too.

      E.g. The following sentences are elaborated as follows (when H is an existing proof context entry):

      • => {x..} H -> => {x..H} H
      • => {x..} /H -> => /v {x..H}
      • rewrite {x..} H -> rewrite E {x..H}

      (#9341, by Enrico Tassi).

    • inE now expands y in r x when r is a simpl_rel. New {pred T} notation for a pred T alias in the pred_sort coercion class, simplified predType interface: pred_class and mkPredType deprecated, {pred T} and PredType should be used instead. if c return t then ... now expects c to be a variable bound in t. New nonPropType interface matching types that do _not_ have sort Prop. New relpre R f definition for the preimage of a relation R under f (#9995, by Georges Gonthier).

  • Vernacular commands:

    • Binders for an Instance now act more like binders for a Theorem. Names may not be repeated, and may not overlap with section variable names (#8820, closes #8791, by Jasper Hugunin).

    • Removed the deprecated Implicit Tactic family of commands (#8779, by Pierre-Marie Pédrot).

    • The Automatic Introduction option has been removed and is now the default (#9001, by Emilio Jesús Gallego Arias).

    • Arguments now accepts names for arguments provided with extra_scopes (#9117, by Maxime Dénès).

    • The naming scheme for anonymous binders in a Theorem has changed to avoid conflicts with explicitly named binders (#9160, closes #8819, by Jasper Hugunin).

    • Computation of implicit arguments now properly handles local definitions in the binders for an Instance, and can be mixed with implicit binders {x : T} (#9307, closes #9300, by Jasper Hugunin).

    • Declare Instance now requires an instance name.

      The flag Refine Instance Mode has been turned off by default, meaning that Instance no longer opens a proof when a body is provided. The flag has been deprecated and will be removed in the next version.

      (#9270, and #9825, by Maxime Dénès)

    • Command Instance, when no body is provided, now always opens a proof. This is a breaking change, as instance of Instance ident1 : ident2. where ident2 is a trivial class will have to be changed into Instance ident1 : ident2 := {}. or Instance ident1 : ident2. Proof. Qed. (#9274, by Maxime Dénès).

    • The flag Program Mode now means that the Program attribute is enabled for all commands that support it. In particular, it does not have any effect on tactics anymore. May cause some incompatibilities (#9410, by Maxime Dénès).

    • The algorithm computing implicit arguments now behaves uniformly for primitive projection and application nodes (#9509, closes #9508, by Pierre-Marie Pédrot).

    • Hypotheses and Variables can now take implicit binders inside sections (#9364, closes #9363, by Jasper Hugunin).

    • Removed deprecated option Automatic Coercions Import (#8094, by Maxime Dénès).

    • The Show Script command has been deprecated (#9829, by Vincent Laporte).

    • Coercion does not warn ambiguous paths which are obviously convertible with existing ones. The ambiguous paths messages have been turned to warnings, thus now they could appear in the output of coqc. The convertibility checking procedure for coercion paths is complete for paths consisting of coercions satisfying the uniform inheritance condition, but some coercion paths could be reported as ambiguous even if they are convertible with existing ones when they have coercions that don't satisfy the uniform inheritance condition (#9743, closes #3219, by Kazuhiko Sakaguchi).

    • A new flag Fast Name Printing has been introduced. It changes the algorithm used for allocating bound variable names for a faster but less clever one (#9078, by Pierre-Marie Pédrot).

    • Option Typeclasses Axioms Are Instances (compatibility option introduced in the previous version) is deprecated. Use Declare Instance for axioms which should be instances (#8920, by Gaëtan Gilbert).

    • Removed option Printing Primitive Projection Compatibility (#9306, by Gaëtan Gilbert).

  • Standard Library:

    • Added Bvector.BVeq that decides whether two Bvectors are equal. Added notations for BVxor, BVand, BVor, BVeq and BVneg (#8171, by Yishuai Li).
    • Added ByteVector type that can convert to and from string (#8365, by Yishuai Li).
    • Added lemmas about monotonicity of N.double and N.succ_double, and about the upper bound of number represented by a vector. Allowed implicit vector length argument in Ndigits.Bv2N (#8815, by Yishuai Li).
    • The prelude used to be automatically Exported and is now only Imported. This should be relevant only when importing files which don't use -noinit into files which do (#9013, by Gaëtan Gilert).
    • Added Coq.Structures.OrderedTypeEx.String_as_OT to make strings an ordered type, using lexical order (#7221, by Li Yao).
    • Added lemmas about Z.testbit, Z.ones, and Z.modulo (#9425, by Andres Erbsen).
    • Moved the auto hints of the FSet library into a new fset database (#9725, by Frédéric Besson).
    • Added Coq.Structures.EqualitiesFacts.PairUsualDecidableTypeFull (#9984, by Jean-Christophe Léchenet and Oliver Nash).
  • Some error messages that show problems with a pair of non-matching values will now highlight the differences (#8669, by Jim Fehrle).

  • Changelog has been moved from a specific file CHANGES.md to the reference manual; former Credits chapter of the reference manual has been split in two parts: a History chapter which was enriched with additional historical information about Coq versions 1 to 5, and a Changes chapter which was enriched with the content formerly in CHANGES.md and COMPATIBILITY (#9133, #9668, #9939, #9964, and #10085, by Théo Zimmermann, with help and ideas from Emilio Jesús Gallego Arias, Gaëtan Gilbert, Clément Pit-Claudel, Matthieu Sozeau, and Enrico Tassi).

Changes in 8.10+beta2

Many bug fixes and documentation improvements, in particular:




  • Fix CoqIDE instability on Windows after the update to gtk3 (#10360, by Michael Soegtrop, closes #9885).


  • Proof General can now display Coq-generated diffs between proof steps in color (#10019 and (in Proof General) #421, by Jim Fehrle).

Version 8.9

Summary of changes

Coq version 8.9 contains the result of refinements and stabilization of features and deprecations or removals of deprecated features, cleanups of the internals of the system and API along with a few new features. This release includes many user-visible changes, including deprecations that are documented in the next subsection and new features that are documented in the reference manual. Here are the most important changes:

  • Kernel: mutually recursive records are now supported, by Pierre-Marie Pédrot.
  • Notations:
    • Support for autonomous grammars of terms called “custom entries”, by Hugo Herbelin (see Section Custom entries of the reference manual).
    • Deprecated notations of the standard library will be removed in the next version of Coq, see the next subsection for a script to ease porting, by Jason Gross and Jean-Christophe Léchenet.
    • Added the Numeral Notation command for registering decimal numeral notations for custom types, by Daniel de Rauglaudre, Pierre Letouzey and Jason Gross.
  • Tactics: Introduction tactics intro/intros on a goal that is an existential variable now force a refinement of the goal into a dependent product rather than failing, by Hugo Herbelin.
  • Decision procedures: deprecation of tactic romega in favor of lia and removal of fourier, replaced by lra which subsumes it, by Frédéric Besson, Maxime Dénès, Vincent Laporte and Laurent Théry.
  • Proof language: focusing bracket { now supports named goals, e.g. [x]:{ will focus on a goal (existential variable) named x, by Théo Zimmermann.
  • SSReflect: the implementation of delayed clear was simplified by Enrico Tassi: the variables are always renamed using inaccessible names when the clear switch is processed and finally cleared at the end of the intro pattern. In addition to that, the use-and-discard flag {} typical of rewrite rules can now be also applied to views, e.g. => {}/v applies v and then clears v. See Section Introduction in the context.
  • Vernacular:
    • Experimental support for attributes on commands, by Vincent Laporte, as in #[local] Lemma foo : bar. Tactics and tactic notations now support the deprecated attribute.
    • Removed deprecated commands Arguments Scope and Implicit Arguments in favor of Arguments (scopes) and Arguments (implicits), with the help of Jasper Hugunin.
    • New flag Uniform Inductive Parameters by Jasper Hugunin to avoid repeating uniform parameters in constructor declarations.
    • New commands Hint Variables and Hint Constants, by Matthieu Sozeau, for controlling the opacity status of variables and constants in hint databases. It is recommended to always use these commands after creating a hint database with Create HintDb.
    • Multiple sections with the same name are now allowed, by Jasper Hugunin.
  • Library: additions and changes in the VectorDef, Ascii, and String libraries. Syntax notations are now available only when using Import of libraries and not merely Require, by various contributors (source of incompatibility, see the next subsection for details).
  • Toplevels: coqtop and coqide can now display diffs between proof steps in color, using the Diffs option, by Jim Fehrle.
  • Documentation: we integrated a large number of fixes to the new Sphinx documentation by various contributors, coordinated by Clément Pit-Claudel and Théo Zimmermann.
  • Tools: removed the gallina utility and the homebrewed Emacs mode.
  • Packaging: as in Coq 8.8.2, the Windows installer now includes many more external packages that can be individually selected for installation, by Michael Soegtrop.

Version 8.9 also comes with a bunch of smaller-scale changes and improvements regarding the different components of the system. Most important ones are documented in the next subsection file.

On the implementation side, the dev/doc/changes.md file documents the numerous changes to the implementation and improvements of interfaces. The file provides guidelines on porting a plugin to the new version and a plugin development tutorial kept in sync with Coq was introduced by Yves Bertot http://github.com/ybertot/plugin_tutorials. The new dev/doc/critical-bugs file documents the known critical bugs of Coq and affected releases.

The efficiency of the whole system has seen improvements thanks to contributions from Gaëtan Gilbert, Pierre-Marie Pédrot, and Maxime Dénès.

Maxime Dénès, Emilio Jesús Gallego Arias, Gaëtan Gilbert, Michael Soegtrop, Théo Zimmermann worked on maintaining and improving the continuous integration system.

The OPAM repository for Coq packages has been maintained by Guillaume Melquiond, Matthieu Sozeau, Enrico Tassi with contributions from many users. A list of packages is available at https://coq.inria.fr/opam/www/.

The 54 contributors for this version are Léo Andrès, Rin Arakaki, Benjamin Barenblat, Langston Barrett, Siddharth Bhat, Martin Bodin, Simon Boulier, Timothy Bourke, Joachim Breitner, Tej Chajed, Arthur Charguéraud, Pierre Courtieu, Maxime Dénès, Andres Erbsen, Jim Fehrle, Julien Forest, Emilio Jesus Gallego Arias, Gaëtan Gilbert, Matěj Grabovský, Jason Gross, Samuel Gruetter, Armaël Guéneau, Hugo Herbelin, Jasper Hugunin, Ralf Jung, Sam Pablo Kuper, Ambroise Lafont, Leonidas Lampropoulos, Vincent Laporte, Peter LeFanu Lumsdaine, Pierre Letouzey, Jean-Christophe Léchenet, Nick Lewycky, Yishuai Li, Sven M. Hallberg, Assia Mahboubi, Cyprien Mangin, Guillaume Melquiond, Perry E. Metzger, Clément Pit-Claudel, Pierre-Marie Pédrot, Daniel R. Grayson, Kazuhiko Sakaguchi, Michael Soegtrop, Matthieu Sozeau, Paul Steckler, Enrico Tassi, Laurent Théry, Anton Trunov, whitequark, Théo Winterhalter, Zeimer, Beta Ziliani, Théo Zimmermann.

Many power users helped to improve the design of the new features via the issue and pull request system, the Coq development mailing list or the coq-club@inria.fr mailing list. It would be impossible to mention exhaustively the names of everybody who to some extent influenced the development.

Version 8.9 is the fourth release of Coq developed on a time-based development cycle. Its development spanned 7 months from the release of Coq 8.8. The development moved to a decentralized merging process during this cycle. Guillaume Melquiond was in charge of the release process and is the maintainer of this release. This release is the result of ~2,000 commits and ~500 PRs merged, closing 75+ issues.

The Coq development team welcomed Vincent Laporte, a new Coq engineer working with Maxime Dénès in the Coq consortium.

Paris, November 2018,
Matthieu Sozeau for the Coq development team

Details of changes in 8.9+beta1


  • Mutually defined records are now supported.


  • New support for autonomous grammars of terms, called "custom entries" (see chapter "Syntax extensions" of the reference manual).
  • Deprecated compatibility notations will actually be removed in the next version of Coq. Uses of these notations are generally easy to fix thanks to the hint contained in the deprecation warnings. For projects that require more than a handful of such fixes, there is a script that will do it automatically, using the output of coqc. The script contains documentation on its usage in a comment at the top.


  • Added toplevel goal selector ! which expects a single focused goal. Use with Set Default Goal Selector to force focusing before tactics are called.
  • The undocumented "nameless" forms fix N, cofix that were deprecated in 8.8 have been removed from Ltac's syntax; please use fix ident N/cofix ident to explicitly name the (co)fixpoint hypothesis to be introduced.
  • Introduction tactics intro/intros on a goal that is an existential variable now force a refinement of the goal into a dependent product rather than failing.
  • Support for fix/cofix added in Ltac match and lazymatch.
  • Ltac backtraces now include trace information about tactics called by OCaml-defined tactics.
  • Option Ltac Debug now applies also to terms built using Ltac functions.
  • Deprecated the Implicit Tactic family of commands.
  • The default program obligation tactic uses a bounded proof search instead of an unbounded and potentially non-terminating one now (source of incompatibility).
  • The simple apply tactic now respects the Opaque flag when called from Ltac (auto still does not respect it).
  • Tactic constr_eq now adds universe constraints needed for the identity to the context (it used to ignore them). New tactic constr_eq_strict checks that the required constraints already hold without adding new ones. Preexisting tactic constr_eq_nounivs can still be used if you really want to ignore universe constraints.
  • Tactics and tactic notations now understand the deprecated attribute.
  • The fourier tactic has been removed. Please now use lra instead. You may need to add Require Import Lra to your developments. For compatibility, we now define fourier as a deprecated alias of lra.
  • The romega tactics have been deprecated; please use lia instead.


  • Focusing bracket { now supports named goal selectors, e.g. [x]: { will focus on a goal (existential variable) named x. As usual, unfocus with } once the sub-goal is fully solved.

Specification language

  • A fix to unification (which was sensitive to the ascii name of variables) may occasionally change type inference in incompatible ways, especially regarding the inference of the return clause of match.

Standard Library

  • Added Ascii.eqb and String.eqb and the =? notation for them, and proved some lemmas about them. Note that this might cause incompatibilities if you have, e.g., string_scope and Z_scope both open with string_scope on top, and expect =? to refer to Z.eqb. Solution: wrap _ =? _ in (_ =? _)%Z (or whichever scope you want).
  • Added Ndigits.N2Bv_sized, and proved some lemmas about it. Deprecated Ndigits.N2Bv_gen.
  • The scopes int_scope and uint_scope have been renamed to dec_int_scope and dec_uint_scope, to clash less with ssreflect and other packages. They are still delimited by %int and %uint.
  • Syntax notations for string, ascii, Z, positive, N, R, and int31 are no longer available merely by Require`ing the files that define the inductives.  You must `Import Coq.Strings.String.StringSyntax (after Require Coq.Strings.String), Coq.Strings.Ascii.AsciiSyntax (after Require Coq.Strings.Ascii), Coq.ZArith.BinIntDef, Coq.PArith.BinPosDef, Coq.NArith.BinNatDef, Coq.Reals.Rdefinitions, and Coq.Numbers.Cyclic.Int31.Int31, respectively, to be able to use these notations. Note that passing -compat 8.8 or issuing Require Import Coq.Compat.Coq88 will make these notations available. Users wishing to port their developments automatically may download fix.py from https://gist.github.com/JasonGross/5d4558edf8f5c2c548a3d96c17820169 and run a command like while true; do make -Okj 2>&1 | /path/to/fix.py; done and get a cup of coffee. (This command must be manually interrupted once the build finishes all the way though. Note also that this method is not fail-proof; you may have to adjust some scopes if you were relying on string notations not being available even when string_scope was open.)
  • Numeral syntax for nat is no longer available without loading the entire prelude (Require Import Coq.Init.Prelude). This only impacts users running Coq without the init library (-nois or -noinit) and also issuing Require Import Coq.Init.Datatypes.


  • Coq_makefile lets one override or extend the following variables from the command line: COQFLAGS, COQCHKFLAGS, COQDOCFLAGS. COQFLAGS is now entirely separate from COQLIBS, so in custom Makefiles $(COQFLAGS) should be replaced by $(COQFLAGS) $(COQLIBS).
  • Removed the gallina utility (extracts specification from Coq vernacular files). If you would like to maintain this tool externally, please contact us.
  • Removed the Emacs modes distributed with Coq. You are advised to use Proof-General (and optionally Company-Coq) instead. If your use case is not covered by these alternative Emacs modes, please open an issue. We can help set up external maintenance as part of Proof-General, or independently as part of coq-community.

Vernacular Commands

  • Removed deprecated commands Arguments Scope and Implicit Arguments (not the option). Use the Arguments command instead.
  • Nested proofs may be enabled through the option Nested Proofs Allowed. By default, they are disabled and produce an error. The deprecation warning which used to occur when using nested proofs has been removed.
  • Added option Uniform Inductive Parameters which abstracts over parameters before typechecking constructors, allowing to write for example Inductive list (A : Type) := nil : list | cons : A -> list -> list.
  • New Set Hint Variables/Constants Opaque/Transparent commands for setting globally the opacity flag of variables and constants in hint databases, overwriting the opacity set of the hint database.
  • Added generic syntax for "attributes", as in: #[local] Lemma foo : bar.
  • Added the Numeral Notation command for registering decimal numeral notations for custom types
  • The Set SsrHave NoTCResolution command no longer has special global scope. If you want the previous behavior, use Global Set SsrHave NoTCResolution.
  • Multiple sections with the same name are allowed.

Coq binaries and process model

  • Before 8.9, Coq distributed a single coqtop binary and a set of dynamically loadable plugins that used to take over the main loop for tasks such as IDE language server or parallel proof checking.

    These plugins have been turned into full-fledged binaries so each different process has associated a particular binary now, in particular coqidetop is the CoqIDE language server, and coq{proof,tactic,query}worker are in charge of task-specific and parallel proof checking.


  • The implementation of delayed clear switches in intro patterns is now simpler to explain:

    1. The immediate effect of a clear switch like {x} is to rename the variable x to _x_ (i.e. a reserved identifier that cannot be mentioned explicitly)
    2. The delayed effect of {x} is that _x_ is cleared at the end of the intro pattern
    3. A clear switch immediately before a view application like {x}/v is translated to /v{x}.

    In particular, the third rule lets one write {x}/v even if v uses the variable x: indeed the view is executed before the renaming.

  • An empty clear switch is now accepted in intro patterns before a view application whenever the view is a variable. One can now write {}/v to mean {v}/v. Remark that {}/x is very similar to the idiom {}e for the rewrite tactic (the equation e is used for rewriting and then discarded).

Standard Library

  • There are now conversions between string and positive, Z, nat, and N in binary, octal, and hex.

Display diffs between proof steps

  • coqtop and coqide can now highlight the differences between proof steps in color. This can be enabled from the command line or the Set Diffs "on"/"off"/"removed" command. Please see the documentation for details. Showing diffs in Proof General requires small changes to PG (under discussion).


  • Added ++ infix for VectorDef.append. Note that this might cause incompatibilities if you have, e.g., list_scope and vector_scope both open with vector_scope on top, and expect ++ to refer to app. Solution: wrap _ ++ _ in (_ ++ _)%list (or whichever scope you want).

Changes in 8.8.0

Various bug fixes.

Changes in 8.8.1

  • Some quality-of-life fixes.
  • Numerous improvements to the documentation.
  • Fix a critical bug related to primitive projections and native_compute.
  • Ship several additional Coq libraries with the Windows installer.

Version 8.8

Summary of changes

Coq version 8.8 contains the result of refinements and stabilization of features and deprecations, cleanups of the internals of the system along with a few new features. The main user visible changes are:

  • Kernel: fix a subject reduction failure due to allowing fixpoints on non-recursive values, by Matthieu Sozeau. Handling of evars in the VM (the kernel still does not accept evars) by Pierre-Marie Pédrot.
  • Notations: many improvements on recursive notations and support for destructuring patterns in the syntax of notations by Hugo Herbelin.
  • Proof language: tacticals for profiling, timing and checking success or failure of tactics by Jason Gross. The focusing bracket { supports single-numbered goal selectors, e.g. 2:{, by Théo Zimmermann.
  • Vernacular: deprecation of commands and more uniform handling of the Local flag, by Vincent Laporte and Maxime Dénès, part of a larger attribute system overhaul. Experimental Show Extraction command by Pierre Letouzey. Coercion now accepts Prop or Type as a source by Arthur Charguéraud. Export modifier for options allowing to export the option to modules that Import and not only Require a module, by Pierre-Marie Pédrot.
  • Universes: many user-level and API level enhancements: qualified naming and printing, variance annotations for cumulative inductive types, more general constraints and enhancements of the minimization heuristics, interaction with modules by Gaëtan Gilbert, Pierre-Marie Pédrot and Matthieu Sozeau.
  • Library: Decimal Numbers library by Pierre Letouzey and various small improvements.
  • Documentation: a large community effort resulted in the migration of the reference manual to the Sphinx documentation tool. The result is this manual. The new documentation infrastructure (based on Sphinx) is by Clément Pit-Claudel. The migration was coordinated by Maxime Dénès and Paul Steckler, with some help of Théo Zimmermann during the final integration phase. The 14 people who ported the manual are Calvin Beck, Heiko Becker, Yves Bertot, Maxime Dénès, Richard Ford, Pierre Letouzey, Assia Mahboubi, Clément Pit-Claudel, Laurence Rideau, Matthieu Sozeau, Paul Steckler, Enrico Tassi, Laurent Théry, Nikita Zyuzin.
  • Tools: experimental -mangle-names option to coqtop/coqc for linting proof scripts, by Jasper Hugunin.

On the implementation side, the dev/doc/changes.md file documents the numerous changes to the implementation and improvements of interfaces. The file provides guidelines on porting a plugin to the new version.

Version 8.8 also comes with a bunch of smaller-scale changes and improvements regarding the different components of the system. Most important ones are documented in the next subsection file.

The efficiency of the whole system has seen improvements thanks to contributions from Gaëtan Gilbert, Pierre-Marie Pédrot, Maxime Dénès and Matthieu Sozeau and performance issue tracking by Jason Gross and Paul Steckler.

The official wiki and the bugtracker of Coq migrated to the GitHub platform, thanks to the work of Pierre Letouzey and Théo Zimmermann. Gaëtan Gilbert, Emilio Jesús Gallego Arias worked on maintaining and improving the continuous integration system.

The OPAM repository for Coq packages has been maintained by Guillaume Melquiond, Matthieu Sozeau, Enrico Tassi with contributions from many users. A list of packages is available at https://coq.inria.fr/opam/www/.

The 44 contributors for this version are Yves Bertot, Joachim Breitner, Tej Chajed, Arthur Charguéraud, Jacques-Pascal Deplaix, Maxime Dénès, Jim Fehrle, Julien Forest, Yannick Forster, Gaëtan Gilbert, Jason Gross, Samuel Gruetter, Thomas Hebb, Hugo Herbelin, Jasper Hugunin, Emilio Jesus Gallego Arias, Ralf Jung, Johannes Kloos, Matej Košík, Robbert Krebbers, Tony Beta Lambda, Vincent Laporte, Peter LeFanu Lumsdaine, Pierre Letouzey, Farzon Lotfi, Cyprien Mangin, Guillaume Melquiond, Raphaël Monat, Carl Patenaude Poulin, Pierre-Marie Pédrot, Clément Pit-Claudel, Matthew Ryan, Matt Quinn, Sigurd Schneider, Bernhard Schommer, Michael Soegtrop, Matthieu Sozeau, Arnaud Spiwack, Paul Steckler, Enrico Tassi, Anton Trunov, Martin Vassor, Vadim Zaliva and Théo Zimmermann.

Version 8.8 is the third release of Coq developed on a time-based development cycle. Its development spanned 6 months from the release of Coq 8.7 and was based on a public roadmap. The development process was coordinated by Matthieu Sozeau. Maxime Dénès was in charge of the release process. Théo Zimmermann is the maintainer of this release.

Many power users helped to improve the design of the new features via the bug tracker, the pull request system, the Coq development mailing list or the coq-club@inria.fr mailing list. Special thanks to the users who contributed patches and intensive brain-storming and code reviews, starting with Jason Gross, Ralf Jung, Robbert Krebbers and Amin Timany. It would however be impossible to mention exhaustively the names of everybody who to some extent influenced the development.

The Coq consortium, an organization directed towards users and supporters of the system, is now running and employs Maxime Dénès. The contacts of the Coq Consortium are Yves Bertot and Maxime Dénès.

Santiago de Chile, March 2018,
Matthieu Sozeau for the Coq development team

Details of changes in 8.8+beta1


  • Support for template polymorphism for definitions was removed. May trigger more "universe inconsistency" errors in rare occasions.
  • Fixpoints are no longer allowed on non-recursive inductive types.


  • Recursive notations with the recursive pattern repeating on the right (e.g. "( x ; .. ; y ; z )") now supported.
  • Notations with a specific level for the leftmost nonterminal, when printing-only, are supported.
  • Notations can now refer to the syntactic category of patterns (as in "fun 'pat =>" or "match p with pat => ... end"). Two variants are available, depending on whether a single variable is considered as a pattern or not.
  • Recursive notations now support ".." patterns with several occurrences of the recursive term or binder, possibly mixing terms and binders, possibly in reverse left-to-right order.
  • "Locate" now working also on notations of the form "x + y" (rather than "_ + _").

Specification language

  • When printing clauses of a "match", clauses with same right-hand side are factorized and the last most factorized clause with no variables, if it exists, is turned into a default clause. Use "Unset Printing Allow Default Clause" do deactivate printing of a default clause. Use "Unset Printing Factorizable Match Patterns" to deactivate factorization of clauses with same right-hand side.


  • On Linux, "native_compute" calls can be profiled using the "perf" utility. The command "Set NativeCompute Profiling" enables profiling, and "Set NativeCompute Profile Filename" customizes the profile filename.
  • The tactic "omega" is now aware of the bodies of context variables such as "x := 5 : Z" (see #1362). This could be disabled via Unset Omega UseLocalDefs.
  • The tactic "romega" is also aware now of the bodies of context variables.
  • The tactic "zify" resp. "omega with N" is now aware of N.pred.
  • Tactic "decide equality" now able to manage constructors which contain proofs.
  • Added tactics reset ltac profile, show ltac profile (and variants)
  • Added tactics restart_timer, finish_timing, and time_constr as an experimental way of timing Ltac's evaluation phase
  • Added tactic optimize_heap, analogous to the Vernacular Optimize Heap, which performs a major garbage collection and heap compaction in the OCaml run-time system.
  • The tactics "dtauto", "dintuition", "firstorder" now handle inductive types with let bindings in the parameters.
  • The tactic dtauto now handles some inductives such as @sigT A (fun _ => B) as non-dependent conjunctions.
  • A bug fixed in rewrite H in * and rewrite H in * |- may cause a few rare incompatibilities (it was unintendedly recursively rewriting in the side conditions generated by H).
  • Added tactics "assert_succeeds tac" and "assert_fails tac" to ensure properties of the execution of a tactic without keeping the effect of the execution.
  • vm_compute now supports existential variables.
  • Calls to shelve and give_up within calls to tactic refine now working.
  • Deprecated tactic appcontext was removed.


  • Focusing bracket { now supports single-numbered goal selector, e.g. 2: { will focus on the second sub-goal. As usual, unfocus with } once the sub-goal is fully solved. The Focus and Unfocus commands are now deprecated.

Vernacular Commands

  • Proofs ending in "Qed exporting ident, .., ident" are not supported anymore. Constants generated during abstract are kept private to the local environment.
  • The deprecated Coercion Local, Open Local Scope, Notation Local syntax was removed. Use Local as a prefix instead.
  • For the Extraction Language command, "OCaml" is spelled correctly. The older "Ocaml" is still accepted, but deprecated.
  • Using “Require” inside a section is deprecated.
  • An experimental command "Show Extraction" allows to extract the content of the current ongoing proof (grant wish #4129).
  • Coercion now accepts the type of its argument to be "Prop" or "Type".
  • The "Export" modifier can now be used when setting and unsetting options, and will result in performing the same change when the module corresponding the command is imported.
  • The Axiom command does not automatically declare axioms as instances when their type is a class. Previous behavior can be restored using Set Typeclasses Axioms Are Instances.


  • Qualified naming of global universes now works like other namespaced objects (e.g. constants), with a separate namespace, inside and across module and library boundaries. Global universe names introduced in an inductive / constant / Let declaration get qualified with the name of the declaration.
  • Universe cumulativity for inductive types is now specified as a variance for each polymorphic universe. See the reference manual for more information.
  • Inference of universe constraints with cumulative inductive types produces more general constraints. Unsetting new option Cumulativity Weak Constraints produces even more general constraints (but may produce too many universes to be practical).
  • Fix #5726: Notations that start with Type now support universe instances with @{u}.
  • with Definition now understands universe declarations (like @{u| Set < u}).


  • Coq can now be run with the option -mangle-names to change the auto-generated name scheme. This is intended to function as a linter for developments that want to be robust to changes in auto-generated names. This feature is experimental, and may change or disappear without warning.
  • GeoProof support was removed.


  • The checker now accepts filenames in addition to logical paths.


  • Find and Replace All report the number of occurrences found; Find indicates when it wraps.


  • Learned to read -I, -Q, -R and filenames from _CoqProject files. This is used by coq_makefile when generating dependencies for .v files (but not other files).


  • The Coq FAQ, formerly located at https://coq.inria.fr/faq, has been moved to the GitHub wiki section of this repository; the main entry page is https://github.com/coq/coq/wiki/The-Coq-FAQ.
  • Documentation: a large community effort resulted in the migration of the reference manual to the Sphinx documentation tool. The result is partially integrated in this version.

Standard Library

  • New libraries Coq.Init.Decimal, Coq.Numbers.DecimalFacts, Coq.Numbers.DecimalNat, Coq.Numbers.DecimalPos, Coq.Numbers.DecimalN, Coq.Numbers.DecimalZ, Coq.Numbers.DecimalString providing a type of decimal numbers, some facts about them, and conversions between decimal numbers and nat, positive, N, Z, and string.
  • Added [Coq.Strings.String.concat] to concatenate a list of strings inserting a separator between each item
  • Notation ' for Zpos in QArith was removed.
  • Some deprecated aliases are now emitting warnings when used.

Compatibility support

  • Support for compatibility with versions before 8.6 was dropped.


  • The following deprecated options have been removed:
    • Refolding Reduction
    • Standard Proposition Elimination
    • Dependent Propositions Elimination
    • Discriminate Introduction
    • Shrink Abstract
    • Tactic Pattern Unification
    • Intuition Iff Unfolding
    • Injection L2R Pattern Order
    • Record Elimination Schemes
    • Match Strict
    • Tactic Compat Context
    • Typeclasses Legacy Resolution
    • Typeclasses Module Eta
    • Typeclass Resolution After Apply

Details of changes in 8.8.0


  • Asynchronous proof delegation policy was fixed. Since version 8.7 Coq was ignoring previous runs and the -async-proofs-delegation-threshold option did not have the expected behavior.

Tactic language

  • The undocumented "nameless" forms fix N, cofix have been deprecated; please use fix ident N /cofix ident to explicitly name the (co)fixpoint hypothesis to be introduced.


  • The reference manual is now fully ported to Sphinx.

Other small deprecations and bug fixes.

Details of changes in 8.8.1


  • Fix a critical bug with cofixpoints and vm_compute/native_compute (#7333).
  • Fix a critical bug with modules and algebraic universes (#7695)
  • Fix a critical bug with inlining of polymorphic constants (#7615).
  • Fix a critical bug with universe polymorphism and vm_compute (#7723). Was present since 8.5.


  • Fixed unexpected collision between only-parsing and only-printing notations (issue #7462).

Windows installer

  • The Windows installer now includes external packages Ltac2 and Equations (it included the Bignums package since 8.8+beta1).

Many other bug fixes, documentation improvements (including fixes of regressions due to the Sphinx migration), and user message improvements (for details, see the 8.8.1 milestone at https://github.com/coq/coq/milestone/13?closed=1).

Details of changes in 8.8.2


  • A PDF version of the reference manual is available once again.


  • The coq-makefile targets print-pretty-timed, print-pretty-timed-diff, and print-pretty-single-time-diff now correctly label the "before" and "after" columns, rather than swapping them.


  • The kernel does not tolerate capture of global universes by polymorphic universe binders, fixing a soundness break (triggered only through custom plugins)

Windows installer

  • The Windows installer now includes many more external packages that can be individually selected for installation.

Many other bug fixes and lots of documentation improvements (for details, see the 8.8.2 milestone at https://github.com/coq/coq/milestone/15?closed=1).

Version 8.7

Summary of changes

Coq version 8.7 contains the result of refinements, stabilization of features and cleanups of the internals of the system along with a few new features. The main user visible changes are:

  • New tactics: variants of tactics supporting existential variables eassert, eenough, etc... by Hugo Herbelin. Tactics extensionality in H and inversion_sigma by Jason Gross, specialize with ... accepting partial bindings by Pierre Courtieu.
  • Cumulative Polymorphic Inductive types, allowing cumulativity of universes to go through applied inductive types, by Amin Timany and Matthieu Sozeau.
  • Integration of the SSReflect plugin and its documentation in the reference manual, by Enrico Tassi, Assia Mahboubi and Maxime Dénès.
  • The coq_makefile tool was completely redesigned to improve its maintainability and the extensibility of generated Makefiles, and to make _CoqProject files more palatable to IDEs by Enrico Tassi.

Coq 8.7 involved a large amount of work on cleaning and speeding up the code base, notably the work of Pierre-Marie Pédrot on making the tactic-level system insensitive to existential variable expansion, providing a safer API to plugin writers and making the code more robust. The dev/doc/changes.txt file documents the numerous changes to the implementation and improvements of interfaces. An effort to provide an official, streamlined API to plugin writers is in progress, thanks to the work of Matej Košík.

Version 8.7 also comes with a bunch of smaller-scale changes and improvements regarding the different components of the system. We shall only list a few of them.

The efficiency of the whole system has been significantly improved thanks to contributions from Pierre-Marie Pédrot, Maxime Dénès and Matthieu Sozeau and performance issue tracking by Jason Gross and Paul Steckler.

Thomas Sibut-Pinote and Hugo Herbelin added support for side effect hooks in cbv, cbn and simpl. The side effects are provided via a plugin available at https://github.com/herbelin/reduction-effects/.

The BigN, BigZ, BigQ libraries are no longer part of the Coq standard library, they are now provided by a separate repository https://github.com/coq/bignums, maintained by Pierre Letouzey.

In the Reals library, IZR has been changed to produce a compact representation of integers and real constants are now represented using IZR (work by Guillaume Melquiond).

Standard library additions and improvements by Jason Gross, Pierre Letouzey and others, documented in the next subsection file.

The mathematical proof language/declarative mode plugin was removed from the archive.

The OPAM repository for Coq packages has been maintained by Guillaume Melquiond, Matthieu Sozeau, Enrico Tassi with contributions from many users. A list of packages is available at https://coq.inria.fr/opam/www/.

Packaging tools and software development kits were prepared by Michael Soegtrop with the help of Maxime Dénès and Enrico Tassi for Windows, and Maxime Dénès for MacOS X. Packages are regularly built on the Travis continuous integration server.

The contributors for this version are Abhishek Anand, C.J. Bell, Yves Bertot, Frédéric Besson, Tej Chajed, Pierre Courtieu, Maxime Dénès, Julien Forest, Gaëtan Gilbert, Jason Gross, Hugo Herbelin, Emilio Jesús Gallego Arias, Ralf Jung, Matej Košík, Xavier Leroy, Pierre Letouzey, Assia Mahboubi, Cyprien Mangin, Erik Martin-Dorel, Olivier Marty, Guillaume Melquiond, Sam Pablo Kuper, Benjamin Pierce, Pierre-Marie Pédrot, Lars Rasmusson, Lionel Rieg, Valentin Robert, Yann Régis-Gianas, Thomas Sibut-Pinote, Michael Soegtrop, Matthieu Sozeau, Arnaud Spiwack, Paul Steckler, George Stelle, Pierre-Yves Strub, Enrico Tassi, Hendrik Tews, Amin Timany, Laurent Théry, Vadim Zaliva and Théo Zimmermann.

The development process was coordinated by Matthieu Sozeau with the help of Maxime Dénès, who was also in charge of the release process. Théo Zimmermann is the maintainer of this release.

Many power users helped to improve the design of the new features via the bug tracker, the pull request system, the Coq development mailing list or the Coq-Club mailing list. Special thanks to the users who contributed patches and intensive brain-storming and code reviews, starting with Jason Gross, Ralf Jung, Robbert Krebbers, Xavier Leroy, Clément Pit–Claudel and Gabriel Scherer. It would however be impossible to mention exhaustively the names of everybody who to some extent influenced the development.

Version 8.7 is the second release of Coq developed on a time-based development cycle. Its development spanned 9 months from the release of Coq 8.6 and was based on a public road-map. It attracted many external contributions. Code reviews and continuous integration testing were systematically used before integration of new features, with an important focus given to compatibility and performance issues, resulting in a hopefully more robust release than Coq 8.6 while maintaining compatibility.

Coq Enhancement Proposals (CEPs for short) and open pull request discussions were used to discuss publicly the new features.

The Coq consortium, an organization directed towards users and supporters of the system, is now upcoming and will rely on Inria’s newly created Foundation.

Paris, August 2017,
Matthieu Sozeau and the Coq development team

Potential compatibility issues

  • Extra superfluous names in introduction patterns may now raise an error rather than a warning when the superfluous name is already in use. The easy fix is to remove the superfluous name.

Details of changes in 8.7+beta1


  • New tactic "extensionality in H" which applies (possibly dependent) functional extensionality in H supposed to be a quantified equality until giving a bare equality.
  • New tactic inversion_sigma which turns equalities of dependent pairs (e.g., existT P x p = existT P y q, frequently left over by inversion on a dependent type family) into pairs of equalities (e.g., a hypothesis H : x = y and a hypothesis of type rew H in p = q); these hypotheses can subsequently be simplified using subst, without ever invoking any kind of axiom asserting uniqueness of identity proofs. If you want to explicitly specify the hypothesis to be inverted, or name the generated hypotheses, you can invoke induction H as [H1 H2] using eq_sigT_rect. The tactic also works for sig, sigT2, and sig2, and there are similar eq_sig*_rect induction lemmas.
  • Tactic "specialize with ..." now accepts any partial bindings. Missing bindings are either solved by unification or left quantified in the hypothesis.
  • New representation of terms that statically ensure stability by evar-expansion. This has several consequences.
    • In terms of performance, this adds a cost to every term destructuration, but at the same time most eager evar normalizations were removed, which couterbalances this drawback and even sometimes outperforms the old implementation. For instance, many operations that would require O(n) normalization of the term are now O(1) in tactics. YMMV.
    • This triggers small changes in unification, which was not evar-insensitive. Most notably, the new implementation recognizes Miller patterns that were missed before because of a missing normalization step. Hopefully this should be fairly uncommon.
  • Tactic "auto with real" can now discharge comparisons of literals.
  • The types of variables in patterns of "match" are now beta-iota-reduced after type-checking. This has an impact on the type of the variables that the tactic "refine" introduces in the context, producing types a priori closer to the expectations.
  • In "Tactic Notation" or "TACTIC EXTEND", entry "constr_with_bindings" now uses type classes and rejects terms with unresolved holes, like entry "constr" does. To get the former behavior use "open_constr_with_bindings" (possible source of incompatibility).
  • New e-variants eassert, eenough, epose proof, eset, eremember, epose which behave like the corresponding variants with no "e" but turn unresolved implicit arguments into existential variables, on the shelf, rather than failing.
  • Tactic injection has become more powerful (closes bug #4890) and its documentation has been updated.
  • New variants of the first and solve tacticals that do not rely on parsing rules, meant to define tactic notations.
  • Added support for side effects hooks in cbv, cbn and simpl. The side effects are provided via a plugin: https://github.com/herbelin/reduction-effects/
  • It is now possible to take hint database names as parameters in a Ltac definition or a Tactic Notation.
  • New option Set Ltac Batch Debug on top of Set Ltac Debug for non-interactive Ltac debug output.


  • Now supporting all kinds of binders, including 'pat, in syntax of record fields.

Vernacular Commands

  • Goals context can be printed in a more compact way when Set Printing Compact Contexts is activated.
  • Unfocused goals can be printed with the Set Printing Unfocused option.
  • Print now shows the types of let-bindings.
  • The compatibility options for printing primitive projections (Set Printing Primitive Projection Parameters and Set Printing Primitive Projection Compatibility) are now off by default.
  • Possibility to unset the printing of notations in a more fine grained fashion than Unset Printing Notations is provided without any user-syntax. The goal is that someone creates a plugin to experiment such a user-syntax, to be later integrated in Coq when stabilized.
  • About now tells if a reference is a coercion.
  • The deprecated Save vernacular and its form Save Theorem id to close proofs have been removed from the syntax. Please use Qed.
  • Search now sorts results by relevance (the relevance metric is a weighted sum of number of distinct symbols and size of the term).

Standard Library

  • New file PropExtensionality.v to explicitly work in the axiomatic context of propositional extensionality.
  • New file SetoidChoice.v axiomatically providing choice over setoids, and, consequently, choice of representatives in equivalence classes. Various proof-theoretic characterizations of choice over setoids in file ChoiceFacts.v.
  • New lemmas about iff and about orders on positive and Z.
  • New lemmas on powerRZ.
  • Strengthened statement of JMeq_eq_dep (closes bug #4912).
  • The BigN, BigZ, BigZ libraries are no longer part of the Coq standard library, they are now provided by a separate repository https://github.com/coq/bignums The split has been done just after the Int31 library.
  • IZR (Reals) has been changed to produce a compact representation of integers. As a consequence, IZR is no longer convertible to INR and lemmas such as INR_IZR_INZ should be used instead.
  • Real constants are now represented using IZR rather than R0 and R1; this might cause rewriting rules to fail to apply to constants.
  • Added new notation {x & P} for sigT (without a type for x)


  • The Ssreflect plugin is now distributed with Coq. Its documentation has been integrated as a chapter of the reference manual. This chapter is work in progress so feedback is welcome.
  • The mathematical proof language (also known as declarative mode) was removed.
  • A new command Extraction TestCompile has been introduced, not meant for the general user but instead for Coq's test-suite.
  • The extraction plugin is no longer loaded by default. It must be explicitly loaded with [Require Extraction], which is backwards compatible.
  • The functional induction plugin (which provides the [Function] vernacular) is no longer loaded by default. It must be explicitly loaded with [Require FunInd], which is backwards compatible.


  • Support for camlp4 has been removed.


  • coq_makefile was completely redesigned to improve its maintainability and the extensibility of generated Makefiles, and to make _CoqProject files more palatable to IDEs. Overview:

    • _CoqProject files contain only Coq specific data (i.e. the list of files, -R options, ...)
    • coq_makefile translates _CoqProject to Makefile.conf and copies in the desired location a standard Makefile (that reads Makefile.conf)
    • Makefile extensions can be implemented in a Makefile.local file (read by the main Makefile) by installing a hook in the extension points provided by the standard Makefile

    The current version contains code for retro compatibility that prints warnings when a deprecated feature is used. Please upgrade your _CoqProject accordingly.

    • Additionally, coq_makefile-made Makefiles now support experimental timing targets pretty-timed, pretty-timed-before, pretty-timed-after, print-pretty-timed-diff, print-pretty-single-time-diff, all.timing.diff, and the variable TIMING=1 (or TIMING=before or TIMING=after); see the documentation for more details.

Build Infrastructure

  • Note that 'make world' does not build the bytecode binaries anymore. For that, you can use 'make byte' (and 'make install-byte' afterwards). Warning: native and byte compilations should not be mixed in the same instance of 'make -j', otherwise both ocamlc and ocamlopt might race for access to the same .cmi files. In short, use "make -j && make -j byte" instead of "make -j world byte".


  • Cumulative inductive types. see prefixes "Cumulative", "NonCumulative" for inductive definitions and the option "Set Polymorphic Inductive Cumulativity" in the reference manual.
  • New syntax foo@{_} to instantiate a polymorphic definition with anonymous universes (can also be used with Type).

XML Protocol and internal changes

See dev/doc/changes.txt

Many bugfixes including #1859, #2884, #3613, #3943, #3994, #4250, #4709, #4720, #4824, #4844, #4911, #5026, #5233, #5275, #5315, #5336, #5360, #5390, #5414, #5417, #5420, #5439, #5449, #5475, #5476, #5482, #5501, #5507, #5520, #5523, #5524, #5553, #5577, #5578, #5589, #5597, #5598, #5607, #5618, #5619, #5620, #5641, #5648, #5651, #5671.

Many bugfixes on OS X and Windows (now the test-suite passes on these platforms too).

Many optimizations.

Many documentation improvements.

Details of changes in 8.7+beta2


  • In CoqIDE, the "Compile Buffer" command takes account of flags in _CoqProject or other project file.

Improvements around some error messages.

Many bug fixes including two important ones:

  • Bug #5730: CoqIDE becomes unresponsive on file open.
  • coq_makefile: make sure compile flags for Coq and coq_makefile are in sync (in particular, make sure the -safe-string option is used to compile plugins).

Details of changes in 8.7.0


  • Users can pass specific flags to the OCaml optimizing compiler by -using the flambda-opts configure-time option.

    Beware that compiling Coq with a flambda-enabled compiler is experimental and may require large amounts of RAM and CPU, see INSTALL for more details.

Details of changes in 8.7.1

Compatibility with OCaml 4.06.0.

Many bug fixes, documentation improvements, and user message improvements (for details see the 8.7.1 milestone at https://github.com/coq/coq/milestone/10?closed=1).

Details of changes in 8.7.2

Fixed a critical bug in the VM handling of universes (#6677). This bug affected all releases since 8.5.

Improved support for building with OCaml 4.06.0 and external num package.

Many other bug fixes, documentation improvements, and user message improvements (for details, see the 8.7.2 milestone at https://github.com/coq/coq/milestone/11?closed=1).

Version 8.6

Summary of changes

Coq version 8.6 contains the result of refinements, stabilization of 8.5’s features and cleanups of the internals of the system. Over the year of (now time-based) development, about 450 bugs were resolved and over 100 contributions integrated. The main user visible changes are:

  • A new, faster state-of-the-art universe constraint checker, by Jacques-Henri Jourdan.
  • In CoqIDE and other asynchronous interfaces, more fine-grained asynchronous processing and error reporting by Enrico Tassi, making Coq capable of recovering from errors and continue processing the document.
  • More access to the proof engine features from Ltac: goal management primitives, range selectors and a typeclasses eauto engine handling multiple goals and multiple successes, by Cyprien Mangin, Matthieu Sozeau and Arnaud Spiwack.
  • Tactic behavior uniformization and specification, generalization of intro-patterns by Hugo Herbelin and others.
  • A brand new warning system allowing to control warnings, turn them into errors or ignore them selectively by Maxime Dénès, Guillaume Melquiond, Pierre-Marie Pédrot and others.
  • Irrefutable patterns in abstractions, by Daniel de Rauglaudre.
  • The ssreflect subterm selection algorithm by Georges Gonthier and Enrico Tassi is now accessible to tactic writers through the ssrmatching plugin.
  • Integration of LtacProf, a profiler for Ltac by Jason Gross, Paul Steckler, Enrico Tassi and Tobias Tebbi.

Coq 8.6 also comes with a bunch of smaller-scale changes and improvements regarding the different components of the system. We shall only list a few of them.

The iota reduction flag is now a shorthand for match, fix and cofix flags controlling the corresponding reduction rules (by Hugo Herbelin and Maxime Dénès).

Maxime Dénès maintained the native compilation machinery.

Pierre-Marie Pédrot separated the Ltac code from general purpose tactics, and generalized and rationalized the handling of generic arguments, allowing to create new versions of Ltac more easily in the future.

In patterns and terms, @, abbreviations and notations are now interpreted the same way, by Hugo Herbelin.

Name handling for universes has been improved by Pierre-Marie Pédrot and Matthieu Sozeau. The minimization algorithm has been improved by Matthieu Sozeau.

The unifier has been improved by Hugo Herbelin and Matthieu Sozeau, fixing some incompatibilities introduced in Coq 8.5. Unification constraints can now be left floating around and be seen by the user thanks to a new option. The Keyed Unification mode has been improved by Matthieu Sozeau.

The typeclass resolution engine and associated proof-search tactic have been reimplemented on top of the proof-engine monad, providing better integration in tactics, and new options have been introduced to control it, by Matthieu Sozeau with help from Théo Zimmermann.

The efficiency of the whole system has been significantly improved thanks to contributions from Pierre-Marie Pédrot, Maxime Dénès and Matthieu Sozeau and performance issue tracking by Jason Gross and Paul Steckler.

Standard library improvements by Jason Gross, Sébastien Hinderer, Pierre Letouzey and others.

Emilio Jesús Gallego Arias contributed many cleanups and refactorings of the pretty-printing and user interface communication components.

Frédéric Besson maintained the micromega tactic.

The OPAM repository for Coq packages has been maintained by Guillaume Claret, Guillaume Melquiond, Matthieu Sozeau, Enrico Tassi and others. A list of packages is now available at https://coq.inria.fr/opam/www/.

Packaging tools and software development kits were prepared by Michael Soegtrop with the help of Maxime Dénès and Enrico Tassi for Windows, and Maxime Dénès and Matthieu Sozeau for MacOS X. Packages are now regularly built on the continuous integration server. Coq now comes with a META file usable with ocamlfind, contributed by Emilio Jesús Gallego Arias, Gregory Malecha, and Matthieu Sozeau.

Matej Košík maintained and greatly improved the continuous integration setup and the testing of Coq contributions. He also contributed many API improvements and code cleanups throughout the system.

The contributors for this version are Bruno Barras, C.J. Bell, Yves Bertot, Frédéric Besson, Pierre Boutillier, Tej Chajed, Guillaume Claret, Xavier Clerc, Pierre Corbineau, Pierre Courtieu, Maxime Dénès, Ricky Elrod, Emilio Jesús Gallego Arias, Jason Gross, Hugo Herbelin, Sébastien Hinderer, Jacques-Henri Jourdan, Matej Košík, Xavier Leroy, Pierre Letouzey, Gregory Malecha, Cyprien Mangin, Erik Martin-Dorel, Guillaume Melquiond, Clément Pit–Claudel, Pierre-Marie Pédrot, Daniel de Rauglaudre, Lionel Rieg, Gabriel Scherer, Thomas Sibut-Pinote, Matthieu Sozeau, Arnaud Spiwack, Paul Steckler, Enrico Tassi, Laurent Théry, Nickolai Zeldovich and Théo Zimmermann. The development process was coordinated by Hugo Herbelin and Matthieu Sozeau with the help of Maxime Dénès, who was also in charge of the release process.

Many power users helped to improve the design of the new features via the bug tracker, the pull request system, the Coq development mailing list or the Coq-Club mailing list. Special thanks to the users who contributed patches and intensive brain-storming and code reviews, starting with Cyril Cohen, Jason Gross, Robbert Krebbers, Jonathan Leivent, Xavier Leroy, Gregory Malecha, Clément Pit–Claudel, Gabriel Scherer and Beta Ziliani. It would however be impossible to mention exhaustively the names of everybody who to some extent influenced the development.

Version 8.6 is the first release of Coq developed on a time-based development cycle. Its development spanned 10 months from the release of Coq 8.5 and was based on a public roadmap. To date, it contains more external contributions than any previous Coq system. Code reviews were systematically done before integration of new features, with an important focus given to compatibility and performance issues, resulting in a hopefully more robust release than Coq 8.5.

Coq Enhancement Proposals (CEPs for short) were introduced by Enrico Tassi to provide more visibility and a discussion period on new features, they are publicly available https://github.com/coq/ceps.

Started during this period, an effort is led by Yves Bertot and Maxime Dénès to put together a Coq consortium.

Paris, November 2016,
Matthieu Sozeau and the Coq development team

Potential sources of incompatibilities

  • Symptom: An obligation generated by Program or an abstracted subproof has different arguments.

    Cause: Set Shrink Abstract and Set Shrink Obligations are on by default and the subproof does not use the argument.


    • Adapt the script.
    • Write an explicit lemma to prove the obligation/subproof and use it instead (compatible with 8.4).
    • Unset the option for the program/proof the obligation/subproof originates from.
  • Symptom: In a goal, order of hypotheses, or absence of an equality of the form "x = t" or "t = x", or no unfolding of a local definition.

    Cause: This might be connected to a number of fixes in the tactic "subst". The former behavior can be reactivated by issuing "Unset Regular Subst Tactic".

Details of changes in 8.6beta1


  • A new, faster state-of-the-art universe constraint checker.

Specification language

  • Giving implicit arguments explicitly to a constant with multiple choices of implicit arguments does not break any more insertion of further maximal implicit arguments.
  • Ability to put any pattern in binders, prefixed by quote, e.g. "fun '(a,b) => ...", "λ '(a,(b,c)), ...", "Definition foo '(x,y) := ...". It expands into a "let 'pattern := ..."


  • Flag "Bracketing Last Introduction Pattern" is now on by default.
  • Flag "Regular Subst Tactic" is now on by default: it respects the initial order of hypothesis, it contracts cycles, it unfolds no local definitions (common source of incompatibilities, fixable by "Unset Regular Subst Tactic").
  • New flag "Refolding Reduction", now disabled by default, which turns on refolding of constants/fixpoints (as in cbn) during the reductions done during type inference and tactic retyping. Can be extremely expensive. When set off, this recovers the 8.4 behaviour of unification and type inference. Potential source of incompatibility with 8.5 developments (the option is set on in Compat/Coq85.v).
  • New flag "Shrink Abstract" that minimalizes proofs generated by the abstract tactical w.r.t. variables appearing in the body of the proof. On by default and deprecated. Minor source of incompatibility for code relying on the precise arguments of abstracted proofs.
  • Serious bugs are fixed in tactic "double induction" (source of incompatibilities as soon as the inductive types have dependencies in the type of their constructors; "double induction" remains however deprecated).
  • In introduction patterns of the form (pat1,...,patn), n should match the exact number of hypotheses introduced (except for local definitions for which pattern can be omitted, as in regular pattern-matching).
  • Tactic scopes in Ltac like constr: and ltac: now require parentheses around their argument.
  • Every generic argument type declares a tactic scope of the form "name:(...)" where name is the name of the argument. This generalizes the constr: and ltac: instances.
  • When in strict mode (i.e. in a Ltac definition), if the "intro" tactic is given a free identifier, it is not bound in subsequent tactics anymore. In order to introduce a binding, use e.g. the "fresh" primitive instead (potential source of incompatibilities).
  • New tactics is_ind, is_const, is_proj, is_constructor for use in Ltac.
  • New goal selectors. Sets of goals can be selected by listing integers ranges. Example: "1,4-7,24: tac" focuses "tac" on goals 1,4,5,6,7,24.
  • For uniformity with "destruct"/"induction" and for a more natural behavior, "injection" can now work in place by activating option "Structural Injection". In this case, hypotheses are also put in the context in the natural left-to-right order and the hypothesis on which injection applies is cleared.
  • Tactic "contradiction" (hence "easy") now also solve goals with hypotheses of the form "~True" or "t<>t" (possible source of incompatibilities because of more successes in automation, but generally a more intuitive strategy).
  • Option "Injection On Proofs" was renamed "Keep Proof Equalities". When enabled, injection and inversion do not drop equalities between objects in Prop. Still disabled by default.
  • New tactics "notypeclasses refine" and "simple notypeclasses refine" that disallow typeclass resolution when typechecking their argument, for use in typeclass hints.
  • Integration of LtacProf, a profiler for Ltac.
  • Reduction tactics now accept more fine-grained flags: iota is now a shorthand for the new flags match, fix and cofix.
  • The ssreflect subterm selection algorithm is now accessible to tactic writers through the ssrmatching plugin.
  • When used as an argument of an ltac function, "auto" without "with" nor "using" clause now correctly uses only the core hint database by default.


  • Revised the syntax of [Hint Cut] to follow standard notation for regexps.
  • Hint Mode now accepts "!" which means that the mode matches only if the argument's head is not an evar (it goes under applications, casts, and scrutinees of matches and projections).
  • Hints can now take an optional user-given pattern, used only by [typeclasses eauto] with the [Filtered Unification] option on.


  • Many new options and new engine based on the proof monad. The [typeclasses eauto] tactic is now a multi-goal, multi-success tactic. See reference manual for more information. It is planned to replace auto and eauto in the following version. The 8.5 resolution engine is still available to help solve compatibility issues.


  • The "Shrink Obligations" flag now applies to all obligations, not only those solved by the automatic tactic.
  • "Shrink Obligations" is on by default and deprecated. Minor source of incompatibility for code relying on the precise arguments of obligations.


  • "Bind Scope" can once again bind "Funclass" and "Sortclass".

General infrastructure

  • New configurable warning system which can be controlled with the vernacular command "Set Warnings", or, under coqc/coqtop, with the flag "-w". In particular, the default is now that warnings are printed by coqc.
  • In asynchronous mode, Coq is now capable of recovering from errors and continue processing the document.


  • coqc accepts a -o option to specify the output file name
  • coqtop accepts --print-version to print Coq and OCaml versions in easy to parse format
  • Setting [Printing Dependent Evars Line] can be unset to disable the computation associated with printing the "dependent evars: " line in -emacs mode
  • Removed the -verbose-compat-notations flag and the corresponding Set Verbose Compat vernacular, since these warnings can now be silenced or turned into errors using "-w".

XML protocol

  • message format has changed, see dev/doc/changes.txt for more details.

Many bug fixes, minor changes and documentation improvements are not mentioned here.

Details of changes in 8.6


  • Fixed critical bug #5248 in VM long multiplication on 32-bit architectures. Was there only since 8.6beta1, so no stable release impacted.

Other bug fixes in universes, type class shelving,...

Details of changes in 8.6.1

  • Fix #5380: Default colors for CoqIDE are actually applied.
  • Fix plugin warnings
  • Document named evars (including Show ident)
  • Fix Bug #5574, document function scope
  • Adding a test case as requested in bug 5205.
  • Fix Bug #5568, no dup notation warnings on repeated module imports
  • Fix documentation of Typeclasses eauto :=
  • Refactor documentation of records.
  • Protecting from warnings while compiling 8.6
  • Fixing an inconsistency between configure and configure.ml
  • Add test-suite checks for coqchk with constraints
  • Fix bug #5019 (looping zify on dependent types)
  • Fix bug 5550: "typeclasses eauto with" does not work with section variables.
  • Bug 5546, qualify datatype constructors when needed in Show Match
  • Bug #5535, test for Show with -emacs
  • Fix bug #5486, don't reverse ids in tuples
  • Fixing #5522 (anomaly with free vars of pat)
  • Fix bug #5526, don't check for nonlinearity in notation if printing only
  • Fix bug #5255
  • Fix bug #3659: -time should understand multibyte encodings.
  • FIx bug #5300: Anomaly: Uncaught exception Not_found" in "Print Assumptions".
  • Fix outdated description in RefMan.
  • Repairing Set Rewriting Schemes
  • Fixing #5487 (v8.5 regression on ltac-matching expressions with evars).
  • Fix description of command-line arguments for Add (Rec) LoadPath
  • Fix bug #5377: @? patterns broken.
  • add XML protocol doc
  • Fix anomaly when doing [all:Check _.] during a proof.
  • Correction of bug #4306
  • Fix #5435: [Eval native_compute in] raises anomaly.
  • Instances should obey universe binders even when defined by tactics.
  • Intern names bound in match patterns
  • funind: Ignore missing info for current function
  • Do not typecheck twice the type of opaque constants.
  • show unused intro pattern warning
  • [future] Be eager when "chaining" already resolved future values.
  • Opaque side effects
  • Fix #5132: coq_makefile generates incorrect install goal
  • Run non-tactic comands without resilient_command
  • Univs: fix bug #5365, generation of u+k <= v constraints
  • make emit tail recursive
  • Don't require printing-only notation to be productive
  • Fix the way setoid_rewrite handles bindings.
  • Fix for bug 5244 - set printing width ignored when given enough space
  • Fix bug 4969, autoapply was not tagging shelved subgoals correctly

Version 8.5

Summary of changes

Coq version 8.5 contains the result of five specific long-term projects:

  • A new asynchronous evaluation and compilation mode by Enrico Tassi with help from Bruno Barras and Carst Tankink.
  • Full integration of the new proof engine by Arnaud Spiwack helped by Pierre-Marie Pédrot,
  • Addition of conversion and reduction based on native compilation by Maxime Dénès and Benjamin Grégoire.
  • Full universe polymorphism for definitions and inductive types by Matthieu Sozeau.
  • An implementation of primitive projections with \(\eta\)-conversion bringing significant performance improvements when using records by Matthieu Sozeau.

The full integration of the proof engine, by Arnaud Spiwack and Pierre-Marie Pédrot, brings to primitive tactics and the user level Ltac language dependent subgoals, deep backtracking and multiple goal handling, along with miscellaneous features and an improved potential for future modifications. Dependent subgoals allow statements in a goal to mention the proof of another. Proofs of unsolved subgoals appear as existential variables. Primitive backtracking makes it possible to write a tactic with several possible outcomes which are tried successively when subsequent tactics fail. Primitives are also available to control the backtracking behavior of tactics. Multiple goal handling paves the way for smarter automation tactics. It is currently used for simple goal manipulation such as goal reordering.

The way Coq processes a document in batch and interactive mode has been redesigned by Enrico Tassi with help from Bruno Barras. Opaque proofs, the text between Proof and Qed, can be processed asynchronously, decoupling the checking of definitions and statements from the checking of proofs. It improves the responsiveness of interactive development, since proofs can be processed in the background. Similarly, compilation of a file can be split into two phases: the first one checking only definitions and statements and the second one checking proofs. A file resulting from the first phase – with the .vio extension – can be already Required. All .vio files can be turned into complete .vo files in parallel. The same infrastructure also allows terminating tactics to be run in parallel on a set of goals via the par: goal selector.

CoqIDE was modified to cope with asynchronous checking of the document. Its source code was also made separate from that of Coq, so that CoqIDE no longer has a special status among user interfaces, paving the way for decoupling its release cycle from that of Coq in the future.

Carst Tankink developed a Coq back-end for user interfaces built on Makarius Wenzel’s Prover IDE framework (PIDE), like PIDE/jEdit (with help from Makarius Wenzel) or PIDE/Coqoon (with help from Alexander Faithfull and Jesper Bengtson). The development of such features was funded by the Paral-ITP French ANR project.

The full universe polymorphism extension was designed by Matthieu Sozeau. It conservatively extends the universes system and core calculus with definitions and inductive declarations parameterized by universes and constraints. It is based on a modification of the kernel architecture to handle constraint checking only, leaving the generation of constraints to the refinement/type inference engine. Accordingly, tactics are now fully universe aware, resulting in more localized error messages in case of inconsistencies and allowing higher-level algorithms like unification to be entirely type safe. The internal representation of universes has been modified but this is invisible to the user.

The underlying logic has been extended with \(\eta\)-conversion for records defined with primitive projections by Matthieu Sozeau. This additional form of \(\eta\)-conversion is justified using the same principle than the previously added \(\eta\)-conversion for function types, based on formulations of the Calculus of Inductive Constructions with typed equality. Primitive projections, which do not carry the parameters of the record and are rigid names (not defined as a pattern matching construct), make working with nested records more manageable in terms of time and space consumption. This extension and universe polymorphism were carried out partly while Matthieu Sozeau was working at the IAS in Princeton.

The guard condition has been made compliant with extensional equality principles such as propositional extensionality and univalence, thanks to Maxime Dénès and Bruno Barras. To ensure compatibility with the univalence axiom, a new flag -indices-matter has been implemented, taking into account the universe levels of indices when computing the levels of inductive types. This supports using Coq as a tool to explore the relations between homotopy theory and type theory.

Maxime Dénès and Benjamin Grégoire developed an implementation of conversion test and normal form computation using the OCaml native compiler. It complements the virtual machine conversion offering much faster computation for expensive functions.

Coq 8.5 also comes with a bunch of many various smaller-scale changes and improvements regarding the different components of the system. We shall only list a few of them.

Pierre Boutillier developed an improved tactic for simplification of expressions called cbn.

Maxime Dénès maintained the bytecode-based reduction machine. Pierre Letouzey maintained the extraction mechanism.

Pierre-Marie Pédrot has extended the syntax of terms to, experimentally, allow holes in terms to be solved by a locally specified tactic.

Existential variables are referred to by identifiers rather than mere numbers, thanks to Hugo Herbelin who also improved the tactic language here and there.

Error messages for universe inconsistencies have been improved by Matthieu Sozeau. Error messages for unification and type inference failures have been improved by Hugo Herbelin, Pierre-Marie Pédrot and Arnaud Spiwack.

Pierre Courtieu contributed new features for using Coq through Proof General and for better interactive experience (bullets, Search, etc).

The efficiency of the whole system has been significantly improved thanks to contributions from Pierre-Marie Pédrot.

A distribution channel for Coq packages using the OPAM tool has been initiated by Thomas Braibant and developed by Guillaume Claret, with contributions by Enrico Tassi and feedback from Hugo Herbelin.

Packaging tools were provided by Pierre Letouzey and Enrico Tassi (Windows), Pierre Boutillier, Matthieu Sozeau and Maxime Dénès (MacOS X). Maxime Dénès improved significantly the testing and benchmarking support.

Many power users helped to improve the design of the new features via the bug tracker, the coq development mailing list or the Coq-Club mailing list. Special thanks are going to the users who contributed patches and intensive brain-storming, starting with Jason Gross, Jonathan Leivent, Greg Malecha, Clément Pit-Claudel, Marc Lasson, Lionel Rieg. It would however be impossible to mention with precision all names of people who to some extent influenced the development.

Version 8.5 is one of the most important releases of Coq. Its development spanned over about 3 years and a half with about one year of beta-testing. General maintenance during part or whole of this period has been done by Pierre Boutillier, Pierre Courtieu, Maxime Dénès, Hugo Herbelin, Pierre Letouzey, Guillaume Melquiond, Pierre-Marie Pédrot, Matthieu Sozeau, Arnaud Spiwack, Enrico Tassi as well as Bruno Barras, Yves Bertot, Frédéric Besson, Xavier Clerc, Pierre Corbineau, Jean-Christophe Filliâtre, Julien Forest, Sébastien Hinderer, Assia Mahboubi, Jean-Marc Notin, Yann Régis-Gianas, François Ripault, Carst Tankink. Maxime Dénès coordinated the release process.

Paris, January 2015, revised December 2015,
Hugo Herbelin, Matthieu Sozeau and the Coq development team

Potential sources of incompatibilities

List of typical changes to be done to adapt files from Coq 8.4 to Coq 8.5 when not using compatibility option -compat 8.4.

  • Symptom: "The reference omega was not found in the current environment".

    Cause: "Require Omega" does not import the tactic "omega" any more

    Possible solutions:

    • use "Require Import OmegaTactic" (not compatible with 8.4)
    • use "Require Import Omega" (compatible with 8.4)
    • add definition "Ltac omega := Coq.omega.Omega.omega."
  • Symptom: "intuition" cannot solve a goal (not working anymore on non standard connective)

    Cause: "intuition" had an accidental non uniform behavior fixed on non standard connectives

    Possible solutions:

    • use "dintuition" instead; it is stronger than "intuition" and works uniformly on non standard connectives, such as n-ary conjunctions or disjunctions (not compatible with 8.4)
    • do the script differently
  • Symptom: The constructor foo (in type bar) expects n arguments.

    Cause: parameters must now be given in patterns

    Possible solutions:

    • use option "Set Asymmetric Patterns" (compatible with 8.4)
    • add "_" for the parameters (not compatible with 8.4)
    • turn the parameters into implicit arguments (compatible with 8.4)
  • Symptom: "NPeano.Nat.foo" not existing anymore

    Possible solutions:

    • use "Nat.foo" instead

    Symptom: typing problems with proj1_sig or similar

    Cause: coercion from sig to sigT and similar coercions have been removed so as to make the initial state easier to understand for beginners

    Solution: change proj1_sig into projT1 and similarly (compatible with 8.4)

Other detailed changes

  • options for coq compilation (see below for ocaml).

    • [-I foo] is now deprecated and will not add directory foo to the coq load path (only for ocaml, see below). Just replace [-I foo] by [-Q foo ""] in your project file and re-generate makefile. Or perform the same operation directly in your makefile if you edit it by hand.
    • Option -R Foo bar is the same in v8.5 than in v8.4 concerning coq load path.
    • Option [-I foo -as bar] is unchanged but discouraged unless you compile ocaml code. Use -Q foo bar instead.

    for more details: see section "Customization at launch time" of the reference manual.

  • Command line options for ocaml Compilation of ocaml code (plugins)

    • [-I foo] is not deprecated to add foo to the ocaml load path.
    • [-I foo -as bar] adds foo to the ocaml load path and adds foo to the coq load path with logical name bar (shortcut for -I foo -Q foo bar).

    for more details: section "Customization at launch time" of the reference manual.

  • Universe Polymorphism.

  • Refinement, unification and tactics are now aware of universes, resulting in more localized errors. Universe inconsistencies should no more get raised at Qed time but during the proof. Unification always produces well-typed substitutions, hence some rare cases of unifications that succeeded while producing ill-typed terms before will now fail.

  • The [change p with c] tactic semantics changed, now typechecking [c] at each matching occurrence [t] of the pattern [p], and converting [t] with [c].

  • Template polymorphic inductive types: the partial application of a template polymorphic type (e.g. list) is not polymorphic. An explicit parameter application (e.g [fun A => list A]) or [apply (list _)] will result in a polymorphic instance.

  • The type inference algorithm now takes opacity of constants into account. This may have effects on tactics using type inference (e.g. induction). Extra "Transparent" might have to be added to revert opacity of constants.

Type classes.

  • When writing an Instance foo : Class A := {| proj := t |} (note the vertical bars), support for typechecking the projections using the type information and switching to proof mode is no longer available. Use { } (without the vertical bars) instead.

Tactic abstract.

  • Auxiliary lemmas generated by the abstract tactic are removed from the global environment and inlined in the proof term when a proof is ended with Qed. The behavior of 8.4 can be obtained by ending proofs with "Qed exporting" or "Qed exporting ident, .., ident".

Details of changes in 8.5beta1


  • Primitive projections for records allow for a compact representation of projections, without parameters and avoid the behavior of defined projections that can unfold to a case expression. To turn the use of native projections on, use [Set Primitive Projections]. Record, Class and Structure types defined while this option is set will be defined with primitive projections instead of the usual encoding as a case expression. For compatibility, when p is a primitive projection, @p can be used to refer to the projection with explicit parameters, i.e. [@p] is definitionally equal to [λ params r. r.(p)]. Records with primitive projections have eta-conversion, the canonical form being [mkR pars (p1 t) ... (pn t)].
  • New universe polymorphism (see reference manual)
  • New option -type-in-type to collapse the universe hierarchy (this makes the logic inconsistent).
  • The guard condition for fixpoints is now a bit stricter. Propagation of subterm value through pattern matching is restricted according to the return predicate. Restores compatibility of Coq's logic with the propositional extensionality axiom. May create incompatibilities in recursive programs heavily using dependent types.
  • Trivial inductive types are no longer defined in Type but in Prop, which leads to a non-dependent induction principle being generated in place of the dependent one. To recover the old behavior, explicitly define your inductive types in Set.

Vernacular commands

  • A command "Variant" allows to define non-recursive variant types.
  • The command "Record foo ..." does not generate induction principles (foo_rect, foo_rec, foo_ind) anymore by default (feature wish #2693). The command "Variant foo ..." does not either. A flag "Set/Unset Nonrecursive Elimination Schemes" allows changing this. The tactic "induction" on a "Record" or a "Variant" is now actually doing "destruct".
  • The "Open Scope" command can now be given also a delimiter (e.g. Z).
  • The "Definition" command now allows the "Local" modifier, allowing for non-importable definitions. The same goes for "Axiom" and "Parameter".
  • Section-specific commands such as "Let" (resp. "Variable", "Hypothesis") used out of a section now behave like the corresponding "Local" command, i.e. "Local Definition" (resp. "Local Parameter", "Local Axiom"). (potential source of rare incompatibilities).
  • The "Let" command can now define local (co)fixpoints.
  • Command "Search" has been renamed into "SearchHead". The command name "Search" now behaves like former "SearchAbout". The latter name is deprecated.
  • "Search", "About", "SearchHead", "SearchRewrite" and "SearchPattern" now search for hypothesis (of the current goal by default) first. They now also support the goal selector prefix to specify another goal to search: e.g. "n:Search id". This is also true for SearchAbout although it is deprecated.
  • The coq/user-contrib directory and the XDG directories are no longer recursively added to the load path, so files from installed libraries now need to be fully qualified for the "Require" command to find them. The tools/update-require script can be used to convert a development.
  • A new Print Strategies command allows visualizing the opacity status of the whole engine.
  • The "Locate" command now searches through all sorts of qualified namespaces of Coq: terms, modules, tactics, etc. The old behavior of the command can be retrieved using the "Locate Term" command.
  • New "Derive" command to help writing program by derivation.
  • New "Refine Instance Mode" option that allows to deactivate the generation of obligations in incomplete typeclass instances, raising an error instead.
  • "Collection" command to name sets of section hypotheses. Named collections can be used in the syntax of "Proof using" to assert which section variables are used in a proof.
  • The "Optimize Proof" command can be placed in the middle of a proof to force the compaction of the data structure used to represent the ongoing proof (evar map). This may result in a lower memory footprint and speed up the execution of the following tactics.
  • "Optimize Heap" command to tell the OCaml runtime to perform a major garbage collection step and heap compaction.
  • Instance no longer treats the {|...|} syntax specially; it handles it in the same way as other commands, e.g. "Definition". Use the {...} syntax (no pipe symbols) to recover the old behavior.

Specification Language

  • Slight changes in unification error messages.
  • Added a syntax $(...)$ that allows putting tactics in terms (may break user notations using "$(", fixable by inserting a space or rewriting the notation).
  • Constructors in pattern-matching patterns now respect the same rules regarding implicit arguments as in applicative position. The old behavior can be recovered by the command "Set Asymmetric Patterns". As a side effect, notations for constructors explicitly mentioning non-implicit parameters can now be used in patterns. Considering that the pattern language is already rich enough, binding local definitions is however now forbidden in patterns (source of incompatibilities for local definitions that delta-reduce to a constructor).
  • Type inference algorithm now granting opacity of constants. This might also affect behavior of tactics (source of incompatibilities, solvable by re-declaring transparent constants which were set opaque).
  • Existential variables are now referred to by an identifier and the relevant part of their instance is displayed by default. They can be reparsed. The naming policy is yet unstable and subject to changes in future releases.


  • New tactic engine allowing dependent subgoals, fully backtracking (also known as multiple success) tactics, as well as tactics which can consider multiple goals together. In the new tactic engine, instantiation information of existential variables is always propagated to tactics, removing the need to manually use the "instantiate" tactics to mark propagation points.
    • New tactical (a+b) inserts a backtracking point. When (a+b);c fails during the execution of c, it can backtrack and try b instead of a.
    • New tactical (once a) removes all the backtracking points from a (i.e. it selects the first success of a).
    • Tactic "constructor" is now fully backtracking. In case of incompatibilities (e.g. combinatoric explosion), the former behavior of "constructor" can be retrieved by using instead "[> once constructor ..]". Thanks to backtracking, undocumented "constructor <tac>" syntax is now equivalent to "[> once (constructor; tac) ..]".
    • New "multimatch" variant of "match" tactic which backtracks to new branches in case of a later failure. The "match" tactic is equivalent to "once multimatch".
    • New selector "all:" such that "all:tac" applies tactic "tac" to all the focused goals, instead of just the first one as is the default.
    • A corresponding new option Set Default Goal Selector "all" makes the tactics in scripts be applied to all the focused goal by default
    • New selector "par:" such that "par:tac" applies the (terminating) tactic "tac" to all the focused goal in parallel. The number of worker can be selected with -async-proofs-tac-j and also limited using the coqworkmgr utility.
    • New tactics "revgoals", "cycle" and "swap" to reorder goals.
    • The semantics of recursive tactics (introduced with "Ltac t := ..." or "let rec t := ... in ...") changed slightly as t is now applied to every goal, not each goal independently. In particular it may be applied when no goals are left. This may cause tactics such as "let rec t := constructor;t" to loop indefinitely. The simple fix is to rewrite the recursive calls as follows: "let rec t := constructor;[t..]" which recovers the earlier behavior (source of rare incompatibilities).
    • New tactic language feature "numgoals" to count number of goals. It is accompanied by a "guard" tactic which fails if a Boolean test over integers does not pass.
    • New tactical "[> ... ]" to apply tactics to individual goals.
    • New tactic "gfail" which works like "fail" except it will also fail if every goal has been solved.
    • The refine tactic is changed not to use an ad hoc typing algorithm to generate subgoals. It also uses the dependent subgoal feature to generate goals to materialize every existential variable which is introduced by the refinement (source of incompatibilities).
    • A tactic shelve is introduced to manage the subgoals which may be solved by unification: shelve removes every goal it is applied to from focus. These goals can later be called back into focus by the Unshelve command.
    • A variant shelve_unifiable only removes those goals which appear as existential variables in other goals. To emulate the old refine, use "refine c;shelve_unifiable". This can still cause incompatibilities in rare occasions.
    • New "give_up" tactic to skip over a goal. A proof containing given up goals cannot be closed with "Qed", but only with "Admitted".
  • The implementation of the admit tactic has changed: no axiom is generated for the admitted sub proof. "admit" is now an alias for "give_up". Code relying on this specific behavior of "admit" can be made to work by:
    • Adding an "Axiom" for each admitted subproof.
    • Adding a single "Axiom proof_admitted : False." and the Ltac definition "Ltac admit := case proof_admitted.".
  • Matching using "lazymatch" was fundamentally modified. It now behaves like "match" (immediate execution of the matching branch) but without the backtracking mechanism in case of failure.
  • New "tryif t then u else v" tactical which executes "u" in case of success of "t" and "v" in case of failure.
  • New conversion tactic "native_compute": evaluates the goal (or an hypothesis) with a call-by-value strategy, using the OCaml native compiler. Useful on very intensive computations.
  • New "cbn" tactic, a well-behaved simpl.
  • Repeated identical calls to omega should now produce identical proof terms.
  • Tactics btauto, a reflexive Boolean tautology solver.
  • Tactic "tauto" was exceptionally able to destruct other connectives than the binary connectives "and", "or", "prod", "sum", "iff". This non-uniform behavior has been fixed (bug #2680) and tauto is slightly weaker (possible source of incompatibilities). On the opposite side, new tactic "dtauto" is able to destruct any record-like inductive types, superseding the old version of "tauto".
  • Similarly, "intuition" has been made more uniform and, where it now fails, "dintuition" can be used (possible source of incompatibilities).
  • New option "Unset Intuition Negation Unfolding" for deactivating automatic unfolding of "not" in intuition.
  • Tactic notations can now be defined locally to a module (use "Local" prefix).
  • Tactic "red" now reduces head beta-iota redexes (potential source of rare incompatibilities).
  • Tactic "hnf" now reduces inner beta-iota redexes (potential source of rare incompatibilities).
  • Tactic "intro H" now reduces beta-iota redexes if these hide a product (potential source of rare incompatibilities).
  • In Ltac matching on patterns of the form "_ pat1 ... patn" now behaves like if matching on "?X pat1 ... patn", i.e. accepting "_" to be instantiated by an applicative term (experimental at this stage, potential source of incompatibilities).
  • In Ltac matching on goal, types of hypotheses are now interpreted in the %type scope (possible source of incompatibilities).
  • "change ... in ..." and "simpl ... in ..." now properly consider nested occurrences (possible source of incompatibilities since this alters the numbering of occurrences), but do not support nested occurrences.
  • Tactics simpl, vm_compute and native_compute can be given a notation string to a constant as argument.
  • When given a reference as argument, simpl, vm_compute and native_compute now strictly interpret it as the head of a pattern starting with this reference.
  • The "change p with c" tactic semantics changed, now type-checking "c" at each matching occurrence "t" of the pattern "p", and converting "t" with "c".
  • Now "appcontext" and "context" behave the same. The old buggy behavior of "context" can be retrieved at parse time by setting the "Tactic Compat Context" flag (possible source of incompatibilities).
  • New introduction pattern p/c which applies lemma c on the fly on the hypothesis under consideration before continuing with introduction pattern p.
  • New introduction pattern [= x1 .. xn] applies "injection as [x1 .. xn]" on the fly if injection is applicable to the hypothesis under consideration (idea borrowed from Georges Gonthier). Introduction pattern [=] applies "discriminate" if a discriminable equality.
  • New introduction patterns * and ** to respectively introduce all forthcoming dependent variables and all variables/hypotheses dependent or not.
  • Tactic "injection c as ipats" now clears c if c refers to an hypothesis and moves the resulting equations in the hypotheses independently of the number of ipats, which has itself to be less than the number of new hypotheses (possible source of incompatibilities; former behavior obtainable by "Unset Injection L2R Pattern Order").
  • Tactic "injection" now automatically simplifies subgoals "existT n p = existT n p'" into "p = p'" when "n" is in an inductive type for which a decidable equality scheme has been generated with "Scheme Equality" (possible source of incompatibilities).
  • New tactic "rewrite_strat" for generalized rewriting with user-defined strategies, subsuming autorewrite.
  • Injection can now also deduce equality of arguments of sort Prop, by using the option "Set Injection On Proofs" (disabled by default). Also improved the error messages.
  • Tactic "subst id" now supports id occurring in dependent local definitions.
  • Bugs fixed about intro-pattern "*" might lead to some rare incompatibilities.
  • New tactical "time" to display time spent executing its argument.
  • Tactics referring or using a constant dependent in a section variable which has been cleared or renamed in the current goal context now fail (possible source of incompatibilities solvable by avoiding clearing the relevant hypotheses).
  • New construct "uconstr:c" and "type_term c" to build untyped terms.
  • Binders in terms defined in Ltac (either "constr" or "uconstr") can now take their names from identifiers defined in Ltac. As a consequence, a name cannot be used in a binder "constr:(fun x => ...)" if an Ltac variable of that name already exists and does not contain an identifier. Source of occasional incompatibilities.
  • The "refine" tactic now accepts untyped terms built with "uconstr" so that terms with holes can be constructed piecewise in Ltac.
  • New bullets --, ++, , ---, +++, *, ... made available.
  • More informative messages when wrong bullet is used.
  • Bullet suggestion when a subgoal is solved.
  • New tactic "enough", symmetric to "assert", but with subgoals swapped, as a more friendly replacement of "cut".
  • In destruct/induction, experimental modifier "!" prefixing the hypothesis name to tell not erasing the hypothesis.
  • Bug fixes in "inversion as" may occasionally lead to incompatibilities.
  • Behavior of introduction patterns -> and <- made more uniform (hypothesis is cleared, rewrite in hypotheses and conclusion and erasing the variable when rewriting a variable).
  • New experimental option "Set Standard Proposition Elimination Names" so that case analysis or induction on schemes in Type containing propositions now produces "H"-based names.
  • Tactics from plugins are now active only when the corresponding module is imported (source of incompatibilities, solvable by adding an "Import"; in the particular case of Omega, use "Require Import OmegaTactic").
  • Semantics of destruct/induction has been made more regular in some edge cases, possibly leading to incompatibilities:
    • new goals are now opened when the term does not match a subterm of the goal and has unresolved holes, while in 8.4 these holes were turned into existential variables
    • when no "at" option is given, the historical semantics which selects all subterms syntactically identical to the first subterm matching the given pattern is used
    • non-dependent destruct/induction on an hypothesis with premises in an inductive type with indices is fixed
    • residual local definitions are now correctly removed.
  • The rename tactic may now replace variables in parallel.
  • A new "Info" command replaces the "info" tactical discontinued in v8.4. It still gives informative results in many cases.
  • The "info_auto" tactic is known to be broken and does not print a trace anymore. Use "Info 1 auto" instead. The same goes for "info_trivial". On the other hand "info_eauto" still works fine, while "Info 1 eauto" prints a trivial trace.
  • When using a lemma of the prototypical form "forall A, {a:A & P a}", "apply" and "apply in" do not instantiate anymore "A" with the current goal and use "a" as the proof, as they were sometimes doing, now considering that it is a too powerful decision.


  • "Solve Obligations using" changed to "Solve Obligations with", consistent with "Proof with".
  • Program Lemma, Definition now respect automatic introduction.
  • Program Lemma, Definition, etc.. now interpret "->" like Lemma and Definition as a non-dependent arrow (potential source of incompatibility).
  • Add/document "Set Hide Obligations" (to hide obligations in the final term inside an implicit argument) and "Set Shrink Obligations" (to minimize dependencies of obligations defined by tactics).


  • The syntax "x -> y" is now declared at level 99. In particular, it has now a lower priority than "<->": "A -> B <-> C" is now "A -> (B <-> C)" (possible source of incompatibilities)
  • Notations accept term-providing tactics using the $(...)$ syntax.
  • "Bind Scope" can no longer bind "Funclass" and "Sortclass".
  • A notation can be given a (compat "8.x") annotation, making it behave like a "only parsing" notation, but the annotation may lead to eventually issue warnings or errors in further versions when this notation is used.
  • More systematic insertion of spaces as a default for printing notations ("format" still available to override the default).
  • In notations, a level modifier referring to a non-existent variable is now considered an error rather than silently ignored.


  • Option -I now only adds directories to the ml path.
  • Option -Q behaves as -R, except that the logical path of any loaded file has to be fully qualified.
  • Option -R no longer adds recursively to the ml path; only the root directory is added. (Behavior with respect to the load path is unchanged.)
  • Option -nois prevents coq/theories and coq/plugins to be recursively added to the load path. (Same behavior as with coq/user-contrib.)
  • coqdep accepts a -dumpgraph option generating a dot file.
  • Makefiles generated through coq_makefile have three new targets "quick" "checkproofs" and "vio2vo", allowing respectively to asynchronously compile the files without playing the proof scripts, asynchronously checking that the quickly generated proofs are correct and generating the object files from the quickly generated proofs.
  • The XML plugin was discontinued and removed from the source.
  • A new utility called coqworkmgr can be used to limit the number of concurrent workers started by independent processes, like make and CoqIDE. This is of interest for users of the par: goal selector.


  • CoqIDE supports asynchronous edition of the document, ongoing tasks and errors are reported in the bottom right window. The number of workers taking care of processing proofs can be selected with -async-proofs-j.
  • CoqIDE highlights in yellow "unsafe" commands such as axiom declarations, and tactics like "give_up".
  • CoqIDE supports Proof General like key bindings; to activate the PG mode go to Edit -> Preferences -> Editor. For the documentation see Help -> Help for PG mode.
  • CoqIDE automatically retracts the locked area when one edits the locked text.
  • CoqIDE search and replace got regular expressions power. See the documentation of OCaml's Str module for the supported syntax.
  • Many CoqIDE windows, including the query one, are now detachable to improve usability on multi screen work stations.
  • Coqtop/coqc outputs highlighted syntax. Colors can be configured thanks to the COQ_COLORS environment variable, and their current state can be displayed with the -list-tags command line option.
  • Third party user interfaces can install their main loop in $COQLIB/toploop and call coqtop with the -toploop flag to select it.

Internal Infrastructure

  • Many reorganizations in the ocaml source files. For instance, many internal a.s.t. of Coq are now placed in mli files in a new directory intf/, for instance constrexpr.mli or glob_term.mli. More details in dev/doc/changes.
  • The file states/initial.coq does not exist anymore. Instead, coqtop initially does a "Require" of Prelude.vo (or nothing when given the options -noinit or -nois).
  • The format of vo files has slightly changed: cf final comments in checker/cic.mli.
  • The build system does not produce anymore programs named coqtop.opt and a symbolic link to coqtop. Instead, coqtop is now directly an executable compiled with the best OCaml compiler available. The bytecode program coqtop.byte is still produced. Same for other utilities.
  • Some options of the ./configure script slightly changed:
    • The -coqrunbyteflags and its blank-separated argument is replaced by option -vmbyteflags which expects a comma-separated argument.
    • The -coqtoolsbyteflags option is discontinued, see -no-custom instead.


  • ML plugins now require a "DECLARE PLUGIN "foo"" statement. The "foo" name must be exactly the name of the ML module that will be loaded through a "Declare ML "foo"" command.

Details of changes in 8.5beta2


  • The VM now supports inductive types with up to 8388851 non-constant constructors and up to 8388607 constant ones.

Specification language

  • Syntax "$(tactic)$" changed to "ltac: tactic".


  • A script using the admit tactic can no longer be concluded by either Qed or Defined. In the first case, Admitted can be used instead. In the second case, a subproof should be used.
  • The easy tactic and the now tactical now have a more predictable behavior, but they might now discharge some previously unsolved goals.


  • Definitions extracted to Haskell GHC should no longer randomly segfault when some Coq types cannot be represented by Haskell types.
  • Definitions can now be extracted to Json for post-processing.


  • Option -I -as has been removed, and option -R -as has been deprecated. In both cases, option -R can be used instead.
  • coq_makefile now generates double-colon rules for rules such as clean.


  • The interface of [change] has changed to take a [change_arg], which can be built from a [constr] using [make_change_arg].

Details of changes in 8.5beta3

Vernacular commands

  • New command "Redirect" to redirect the output of a command to a file.
  • New command "Undelimit Scope" to remove the delimiter of a scope.
  • New option "Strict Universe Declaration", set by default. It enforces the declaration of all polymorphic universes appearing in a definition when introducing it.
  • New command "Show id" to show goal named id.
  • Option "Virtual Machine" removed.


  • New flag "Regular Subst Tactic" which fixes "subst" in situations where it failed to substitute all substitutable equations or failed to simplify cycles, or accidentally unfolded local definitions (flag is off by default).
  • New flag "Loose Hint Behavior" to handle hints loaded but not imported in a special way. It accepts three distinct flags: * "Lax", which is the default one, sets the old behavior, i.e. a non-imported hint behaves the same as an imported one. * "Warn" outputs a warning when a non-imported hint is used. Note that this is an over-approximation, because a hint may be triggered by an eauto run that will eventually fail and backtrack. * "Strict" changes the behavior of an unloaded hint to the one of the fail tactic, allowing to emulate the hopefully future import-scoped hint mechanism.
  • New compatibility flag "Universal Lemma Under Conjunction" which let tactics working under conjunctions apply sublemmas of the form "forall A, ... -> A".
  • New compatibility flag "Bracketing Last Introduction Pattern" which can be set so that the last disjunctive-conjunctive introduction pattern given to "intros" automatically complete the introduction of its subcomponents, as the the disjunctive-conjunctive introduction patterns in non-terminal position already do.
  • New flag "Shrink Abstract" that minimalizes proofs generated by the abstract tactical w.r.t. variables appearing in the body of the proof.


  • The "Shrink Obligations" flag now applies to all obligations, not only those solved by the automatic tactic.
  • Importing Program no longer overrides the "exists" tactic (potential source of incompatibilities).
  • Hints costs are now correctly taken into account (potential source of incompatibilities).
  • Documented the Hint Cut command that allows control of the proof-search during typeclass resolution (see reference manual).


  • Some functions from pretyping/typing.ml and their derivatives were potential source of evarmap leaks, as they dropped their resulting evarmap. The situation was clarified by renaming them according to a unsafe_* scheme. Their sound variant is likewise renamed to their old name. The following renamings were made.

    • Typing.type_of -> unsafe_type_of
    • Typing.e_type_of -> type_of
    • A new e_type_of function that matches the e_ prefix policy
    • Tacmach.pf_type_of -> pf_unsafe_type_of
    • A new safe pf_type_of function.

    All uses of unsafe_* functions should be eventually eliminated.


  • Added an option -w to control the output of coqtop warnings.
  • Configure now takes an optional -native-compiler (yes|no) flag replacing -no-native-compiler. The new flag is set to no by default under Windows.
  • Flag -no-native-compiler was removed and became the default for coqc. If precompilation of files for native conversion test is desired, use -native-compiler.
  • The -compile command-line option now takes the full path of the considered file, including the ".v" extension, and outputs a warning if such an extension is lacking.
  • The -require and -load-vernac-object command-line options now take a logical path of a given library rather than a physical path, thus they behave like Require [Import] path.
  • The -vm command-line option has been removed.

Standard Library

  • There is now a Coq.Compat.Coq84 library, which sets the various compatibility options and does a few redefinitions to make Coq behave more like Coq v8.4. The standard way of putting Coq in v8.4 compatibility mode is to pass the command line flags "-require Coq.Compat.Coq84 -compat 8.4".

Details of changes in 8.5


  • Flag "-compat 8.4" now loads Coq.Compat.Coq84. The standard way of putting Coq in v8.4 compatibility mode is to pass the command line flag "-compat 8.4". It can be followed by "-require Coq.Compat.AdmitAxiom" if the 8.4 behavior of admit is needed, in which case it uses an axiom.

Specification language

  • Syntax "$(tactic)$" changed to "ltac:(tactic)".


  • Syntax "destruct !hyp" changed to "destruct (hyp)", and similarly for induction (rare source of incompatibilities easily solvable by removing parentheses around "hyp" when not for the purpose of keeping the hypothesis).
  • Syntax "p/c" for on-the-fly application of a lemma c before introducing along pattern p changed to p%c1..%cn. The feature and syntax are in experimental stage.
  • "Proof using" does not clear unused section variables.
  • Tactic "refine" has been changed back to the 8.4 behavior of shelving subgoals that occur in other subgoals. The "refine" tactic of 8.5beta3 has been renamed "simple refine"; it does not shelve any subgoal.
  • New tactical "unshelve tac" which grab existential variables put on the tactic shelve by the execution of "tac".

Details of changes in 8.5pl1

Critical bugfix

  • The subterm relation for the guard condition was incorrectly defined on primitive projections (#4588)

Plugin development tools

  • add a .merlin target to the makefile

Various performance improvements (time, space used by .vo files)

Other bugfixes

  • Fix order of arguments to Big.compare_case in ExtrOcamlZBigInt.v
  • Added compatibility coercions from Specif.v which were present in Coq 8.4.
  • Fixing a source of inefficiency and an artificial dependency in the printer in the congruence tactic.
  • Allow to unset the refinement mode of Instance in ML
  • Fixing an incorrect use of prod_appvect on a term which was not a product in setoid_rewrite.
  • Add -compat 8.4 econstructor tactics, and tests
  • Add compatibility Nonrecursive Elimination Schemes
  • Fixing the "No applicable tactic" non informative error message regression on apply.
  • Univs: fix get_current_context (bug #4603, part I)
  • Fix a bug in Program coercion code
  • Fix handling of arity of definitional classes.
  • #4630: Some tactics are 20x slower in 8.5 than 8.4.
  • #4627: records with no declared arity can be template polymorphic.
  • #4623: set tactic too weak with universes (regression)
  • Fix incorrect behavior of CS resolution
  • #4591: Uncaught exception in directory browsing.
  • CoqIDE is more resilient to initialization errors.
  • #4614: "Fully check the document" is uninterruptible.
  • Try eta-expansion of records only on non-recursive ones
  • Fix bug when a sort is ascribed to a Record
  • Primitive projections: protect kernel from erroneous definitions.
  • Fixed bug #4533 with previous Keyed Unification commit
  • Win: kill unreliable hence do not waitpid after kill -9 (Close #4369)
  • Fix strategy of Keyed Unification
  • #4608: Anomaly "output_value: abstract value (outside heap)".
  • #4607: do not read native code files if native compiler was disabled.
  • #4105: poor escaping in the protocol between CoqIDE and coqtop.
  • #4596: [rewrite] broke in the past few weeks.
  • #4533 (partial): respect declared global transparency of projections in unification.ml
  • #4544: Backtrack on using full betaiota reduction during keyed unification.
  • #4540: CoqIDE bottom progress bar does not update.
  • Fix regression from 8.4 in reflexivity
  • #4580: [Set Refine Instance Mode] also used for Program Instance.
  • #4582: cannot override notation [ x ]. MAY CREATE INCOMPATIBILITIES, see #4683.
  • STM: Print/Extraction have to be skipped if -quick
  • #4542: CoqIDE: STOP button also stops workers
  • STM: classify some variants of Instance as regular `` Fork ` nodes.
  • #4574: Anomaly: Uncaught exception Invalid_argument("splay_arity").
  • Do not give a name to anonymous evars anymore. See bug #4547.
  • STM: always stock in vio files the first node (state) of a proof
  • STM: not delegate proofs that contain Vernac(Module|Require|Import), #4530
  • Don't fail fatally if PATH is not set.
  • #4537: Coq 8.5 is slower in typeclass resolution.
  • #4522: Incorrect "Warning..." on windows.
  • #4373: coqdep does not know about .vio files.
  • #3826: "Incompatible module types" is uninformative.
  • #4495: Failed assertion in metasyntax.ml.
  • #4511: evar tactic can create non-typed evars.
  • #4503: mixing universe polymorphic and monomorphic variables and definitions in sections is unsupported.
  • #4519: oops, global shadowed local universe level bindings.
  • #4506: Anomaly: File "pretyping/indrec.ml", line 169, characters 14-20: Assertion failed.
  • #4548: Coqide crashes when going back one command

Details of changes in 8.5pl2

Critical bugfix

  • Checksums of .vo files dependencies were not correctly checked.
  • Unicode-to-ASCII translation was not injective, leading in a soundness bug in the native compiler.

Other bugfixes

  • #4097: more efficient occur-check in presence of primitive projections
  • #4398: type_scope used consistently in "match goal".
  • #4450: eauto does not work with polymorphic lemmas
  • #4677: fix alpha-conversion in notations needing eta-expansion.
  • Fully preserve initial order of hypotheses in "Regular Subst Tactic" mode.
  • #4644: a regression in unification.
  • #4725: Function (Error: Conversion test raised an anomaly) and Program (Error: Cannot infer this placeholder of type)
  • #4747: Problem building Coq 8.5pl1 with OCaml 4.03.0: Fatal warnings
  • #4752: CoqIDE crash on files not ended by ".v".
  • #4777: printing inefficiency with implicit arguments
  • #4818: "Admitted" fails due to undefined universe anomaly after calling "destruct"
  • #4823: remote counter: avoid thread race on sockets
  • #4841: -verbose flag changed semantics in 8.5, is much harder to use
  • #4851: [nsatz] cannot handle duplicated hypotheses
  • #4858: Anomaly: Uncaught exception Failure("hd"). Please report. in variant of nsatz
  • #4880: [nsatz_compute] generates invalid certificates if given redundant hypotheses
  • #4881: synchronizing "Declare Implicit Tactic" with backtrack.
  • #4882: anomaly with Declare Implicit Tactic on hole of type with evars
  • Fix use of "Declare Implicit Tactic" in refine. triggered by CoqIDE
  • #4069, #4718: congruence fails when universes are involved.


  • Disallow silently dropping universe instances applied to variables (forward compatible)
  • Allow explicit universe instances on notations, when they can apply to the head reference of their expansion.

Build infrastructure

  • New update on how to find camlp5 binary and library at configure time.

Details of changes in 8.5pl3

Critical bugfix

  • #4876: Guard checker incompleteness when using primitive projections

Other bugfixes

  • #4780: Induction with universe polymorphism on was creating ill-typed terms.
  • #4673: regression in setoid_rewrite, unfolding let-ins for type unification.
  • #4754: Regression in setoid_rewrite, allow postponed unification problems to remain.
  • #4769: Anomaly with universe polymorphic schemes defined inside sections.
  • #3886: Program: duplicate obligations of mutual fixpoints.
  • #4994: Documentation typo.
  • #5008: Use the "md5" command on OpenBSD.
  • #5007: Do not assume the "TERM" environment variable is always set.
  • #4606: Output a break before a list only if there was an empty line.
  • #5001: metas not cleaned properly in clenv_refine_in.
  • #2336: incorrect glob data for module symbols (bug #2336).
  • #4832: Remove extraneous dot in error message.
  • Anomaly in printing a unification error message.
  • #4947: Options which take string arguments are not backwards compatible.
  • #4156: micromega cache files are now hidden files.
  • #4871: interrupting par:abstract kills coqtop.
  • #5043: [Admitted] lemmas pick up section variables.
  • Fix name of internal refine ("simple refine").
  • #5062: probably a typo in Strict Proofs mode.
  • #5065: Anomaly: Not a proof by induction.
  • Restore native compiler optimizations, they were disabled since 8.5!
  • #5077: failure on typing a fixpoint with evars in its type.
  • Fix recursive notation bug.
  • #5095: non relevant too strict test in let-in abstraction.
  • Ensuring that the evar name is preserved by "rename".
  • #4887: confusion between using and with in documentation of firstorder.
  • Bug in subst with let-ins.
  • #4762: eauto weaker than auto.
  • Remove if_then_else (was buggy). Use tryif instead.
  • #4970: confusion between special "{" and non special "{{" in notations.
  • #4529: primitive projections unfolding.
  • #4416: Incorrect "Error: Incorrect number of goals".
  • #4863: abstract in typeclass hint fails.
  • #5123: unshelve can impact typeclass resolution
  • Fix a collision about the meta-variable ".." in recursive notations.
  • Fix printing of info_auto.
  • #3209: Not_found due to an occur-check cycle.
  • #5097: status of evars refined by "clear" in ltac: closed wrt evars.
  • #5150: Missing dependency of the test-suite subsystems in prerequisite.
  • Fix a bug in error printing of unif constraints
  • #3941: Do not stop propagation of signals when Coq is busy.
  • #4822: Incorrect assertion in cbn.
  • #3479 parsing of "{" and "}" when a keyword starts with "{" or "}".
  • #5127: Memory corruption with the VM.
  • #5102: bullets parsing broken by calls to parse_entry.

Various documentation improvements

Version 8.4

Summary of changes

Coq version 8.4 contains the result of three long-term projects: a new modular library of arithmetic by Pierre Letouzey, a new proof engine by Arnaud Spiwack and a new communication protocol for CoqIDE by Vincent Gross.

The new modular library of arithmetic extends, generalizes and unifies the existing libraries on Peano arithmetic (types nat, N and BigN), positive arithmetic (type positive), integer arithmetic (Z and BigZ) and machine word arithmetic (type Int31). It provides with unified notations (e.g. systematic use of add and mul for denoting the addition and multiplication operators), systematic and generic development of operators and properties of these operators for all the types mentioned above, including gcd, pcm, power, square root, base 2 logarithm, division, modulo, bitwise operations, logical shifts, comparisons, iterators, ...

The most visible feature of the new proof engine is the support for structured scripts (bullets and proof brackets) but, even if yet not user-available, the new engine also provides the basis for refining existential variables using tactics, for applying tactics to several goals simultaneously, for reordering goals, all features which are planned for the next release. The new proof engine forced Pierre Letouzey to reimplement info and Show Script differently.

Before version 8.4, CoqIDE was linked to Coq with the graphical interface living in a separate thread. From version 8.4, CoqIDE is a separate process communicating with Coq through a textual channel. This allows for a more robust interfacing, the ability to interrupt Coq without interrupting the interface, and the ability to manage several sessions in parallel. Relying on the infrastructure work made by Vincent Gross, Pierre Letouzey, Pierre Boutillier and Pierre-Marie Pédrot contributed many various refinements of CoqIDE.

Coq 8.4 also comes with a bunch of various smaller-scale changes and improvements regarding the different components of the system.

The underlying logic has been extended with \(\eta\)-conversion thanks to Hugo Herbelin, Stéphane Glondu and Benjamin Grégoire. The addition of \(\eta\)-conversion is justified by the confidence that the formulation of the Calculus of Inductive Constructions based on typed equality (such as the one considered in Lee and Werner to build a set-theoretic model of CIC [LW11]) is applicable to the concrete implementation of Coq.

The underlying logic benefited also from a refinement of the guard condition for fixpoints by Pierre Boutillier, the point being that it is safe to propagate the information about structurally smaller arguments through \(\beta\)-redexes that are blocked by the “match” construction (blocked commutative cuts).

Relying on the added permissiveness of the guard condition, Hugo Herbelin could extend the pattern matching compilation algorithm so that matching over a sequence of terms involving dependencies of a term or of the indices of the type of a term in the type of other terms is systematically supported.

Regarding the high-level specification language, Pierre Boutillier introduced the ability to give implicit arguments to anonymous functions, Hugo Herbelin introduced the ability to define notations with several binders (e.g. exists x y z, P), Matthieu Sozeau made the typeclass inference mechanism more robust and predictable, Enrico Tassi introduced a command Arguments that generalizes Implicit Arguments and Arguments Scope for assigning various properties to arguments of constants. Various improvements in the type inference algorithm were provided by Matthieu Sozeau and Hugo Herbelin with contributions from Enrico Tassi.

Regarding tactics, Hugo Herbelin introduced support for referring to expressions occurring in the goal by pattern in tactics such as set or destruct. Hugo Herbelin also relied on ideas from Chung-Kil Hur’s Heq plugin to introduce automatic computation of occurrences to generalize when using destruct and induction on types with indices. Stéphane Glondu introduced new tactics constr_eq, is_evar, and has_evar, to be used when writing complex tactics. Enrico Tassi added support to fine-tuning the behavior of simpl. Enrico Tassi added the ability to specify over which variables of a section a lemma has to be exactly generalized. Pierre Letouzey added a tactic timeout and the interruptibility of vm_compute. Bug fixes and miscellaneous improvements of the tactic language came from Hugo Herbelin, Pierre Letouzey and Matthieu Sozeau.

Regarding decision tactics, Loïc Pottier maintained nsatz, moving in particular to a typeclass based reification of goals while Frédéric Besson maintained Micromega, adding in particular support for division.

Regarding vernacular commands, Stéphane Glondu provided new commands to analyze the structure of type universes.

Regarding libraries, a new library about lists of a given length (called vectors) has been provided by Pierre Boutillier. A new instance of finite sets based on Red-Black trees and provided by Andrew Appel has been adapted for the standard library by Pierre Letouzey. In the library of real analysis, Yves Bertot changed the definition of \(\pi\) and provided a proof of the long-standing fact yet remaining unproved in this library, namely that \(sin \frac{\pi}{2} = 1\).

Pierre Corbineau maintained the Mathematical Proof Language (C-zar).

Bruno Barras and Benjamin Grégoire maintained the call-by-value reduction machines.

The extraction mechanism benefited from several improvements provided by Pierre Letouzey.

Pierre Letouzey maintained the module system, with contributions from Élie Soubiran.

Julien Forest maintained the Function command.

Matthieu Sozeau maintained the setoid rewriting mechanism.

Coq related tools have been upgraded too. In particular, coq_makefile has been largely revised by Pierre Boutillier. Also, patches from Adam Chlipala for coqdoc have been integrated by Pierre Boutillier.

Bruno Barras and Pierre Letouzey maintained the coqchk checker.

Pierre Courtieu and Arnaud Spiwack contributed new features for using Coq through Proof General.

The Dp plugin has been removed. Use the plugin provided with Why 3 instead (http://why3.lri.fr/).

Under the hood, the Coq architecture benefited from improvements in terms of efficiency and robustness, especially regarding universes management and existential variables management, thanks to Pierre Letouzey and Yann Régis-Gianas with contributions from Stéphane Glondu and Matthias Puech. The build system is maintained by Pierre Letouzey with contributions from Stéphane Glondu and Pierre Boutillier.

A new backtracking mechanism simplifying the task of external interfaces has been designed by Pierre Letouzey.

The general maintenance was done by Pierre Letouzey, Hugo Herbelin, Pierre Boutillier, Matthieu Sozeau and Stéphane Glondu with also specific contributions from Guillaume Melquiond, Julien Narboux and Pierre-Marie Pédrot.

Packaging tools were provided by Pierre Letouzey (Windows), Pierre Boutillier (MacOS), Stéphane Glondu (Debian). Releasing, testing and benchmarking support was provided by Jean-Marc Notin.

Many suggestions for improvements were motivated by feedback from users, on either the bug tracker or the Coq-Club mailing list. Special thanks are going to the users who contributed patches, starting with Tom Prince. Other patch contributors include Cédric Auger, David Baelde, Dan Grayson, Paolo Herms, Robbert Krebbers, Marc Lasson, Hendrik Tews and Eelis van der Weegen.

Paris, December 2011
Hugo Herbelin

Potential sources of incompatibilities

The main known incompatibilities between 8.3 and 8.4 are consequences of the following changes:

  • The reorganization of the library of numbers:

    Several definitions have new names or are defined in modules of different names, but a special care has been taken to have this renaming transparent for the user thanks to compatibility notations.

    However some definitions have changed, what might require some adaptations. The most noticeable examples are:

    • The "?=" notation which now bind to Pos.compare rather than former Pcompare (now Pos.compare_cont).
    • Changes in names may induce different automatically generated names in proof scripts (e.g. when issuing "destruct Z_le_gt_dec").
    • Z.add has a new definition, hence, applying "simpl" on subterms of its body might give different results than before.
    • BigN.shiftl and BigN.shiftr have reversed arguments order, the power function in BigN now takes two BigN.
  • Other changes in libraries:

    • The definition of functions over "vectors" (list of fixed length) have changed.
    • TheoryList.v has been removed.
  • Slight changes in tactics:

    • Less unfolding of fixpoints when applying destruct or inversion on a fixpoint hiding an inductive type (add an extra call to simpl to preserve compatibility).
    • Less unexpected local definitions when applying "destruct" (incompatibilities solvable by adapting name hypotheses).
    • Tactic "apply" might succeed more often, e.g. by now solving pattern-matching of the form ?f x y = g(x,y) (compatibility ensured by using "Unset Tactic Pattern Unification"), but also because it supports (full) betaiota (using "simple apply" might then help).
    • Tactic autorewrite does no longer instantiate pre-existing existential variables.
    • Tactic "info" is now available only for auto, eauto and trivial.
  • Miscellaneous changes:

    • The command "Load" is now atomic for backtracking (use "Unset Atomic Load" for compatibility).

Details of changes in 8.4beta


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

Specification language and notations

  • Maximal implicit arguments can now be set locally by { }. The registration traverses fixpoints and lambdas. Because there is conversion in types, maximal implicit arguments are not taken into account in partial applications (use eta expanded form with explicit { } instead).
  • Added support for recursive notations with binders (allows for instance to write "exists x y z, P").
  • Structure/Record printing can be disable by "Unset Printing Records". In addition, it can be controlled on type by type basis using "Add Printing Record" or "Add Printing Constructor".
  • Pattern-matching compilation algorithm: in "match x, y with ... end", possible dependencies of x (or of the indices of its type) in the type of y are now taken into account.


  • New proof engine.
  • Scripts can now be structured thanks to bullets - * + and to subgoal delimitation via { }. Note: for use with Proof General, a cvs version of Proof General no older than mid-July 2011 is currently required.
  • Support for tactical "info" is suspended.
  • Support for command "Show Script" is suspended.
  • New tactics constr_eq, is_evar and has_evar for use in Ltac (DOC TODO).
  • Removed the two-argument variant of "decide equality".
  • New experimental tactical "timeout <n> <tac>". Since <n> is a time in second for the moment, this feature should rather be avoided in scripts meant to be machine-independent.
  • Fix in "destruct": removal of unexpected local definitions in context might result in some rare incompatibilities (solvable by adapting name hypotheses).
  • Introduction pattern "_" made more robust.
  • Tactic (and Eval command) vm_compute can now be interrupted via Ctrl-C.
  • Unification in "apply" supports unification of patterns of the form ?f x y = g(x,y) (compatibility ensured by using "Unset Tactic Pattern Unification"). It also supports (full) betaiota.
  • Tactic autorewrite does no longer instantiate pre-existing existential variables (theoretical source of possible incompatibilities).
  • Tactic "dependent rewrite" now supports equality in "sig".
  • Tactic omega now understands Zpred (wish #1912) and can prove any goal from a context containing an arithmetical contradiction (wish #2236).
  • Using "auto with nocore" disables the use of the "core" database (wish #2188). This pseudo-database "nocore" can also be used with trivial and eauto.
  • Tactics "set", "destruct" and "induction" accepts incomplete terms and use the goal to complete the pattern assuming it is non ambiguous.
  • When used on arguments with a dependent type, tactics such as "destruct", "induction", "case", "elim", etc. now try to abstract automatically the dependencies over the arguments of the types (based on initial ideas from Chung-Kil Hur, extension to nested dependencies suggested by Dan Grayson)
  • Tactic "injection" now failing on an equality showing no constructors while it was formerly generalizing again the goal over the given equality.
  • In Ltac, the "context [...]" syntax has now a variant "appcontext [...]" allowing to match partial applications in larger applications.
  • When applying destruct or inversion on a fixpoint hiding an inductive type, recursive calls to the fixpoint now remain folded by default (rare source of incompatibility generally solvable by adding a call to simpl).
  • In an ltac pattern containing a "match", a final "| _ => _" branch could be used now instead of enumerating all remaining constructors. Moreover, the pattern "match _ with _ => _ end" now allows to match any "match". A "in" annotation can also be added to restrict to a precise inductive type.
  • The behavior of "simpl" can be tuned using the "Arguments" vernacular. In particular constants can be marked so that they are always/never unfolded by "simpl", or unfolded only when a set of arguments evaluates to a constructor. Last one can mark a constant so that it is unfolded only if the simplified term does not expose a match in head position.

Vernacular commands

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

Module System

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


  • Extension of the abstract part of Numbers, which now provide axiomatizations and results about many more integer functions, such as pow, gcd, lcm, sqrt, log2 and bitwise functions. These functions are implemented for nat, N, BigN, Z, BigZ. See in particular file NPeano for new functions about nat.

  • The definition of types positive, N, Z is now in file BinNums.v

  • Major reorganization of ZArith. The initial file ZArith/BinInt.v now contains an internal module Z implementing the Numbers interface for integers. This module Z regroups:

    • all functions over type Z : Z.add, Z.mul, ...
    • the minimal proofs of specifications for these functions : Z.add_0_l, ...
    • an instantiation of all derived properties proved generically in Numbers : Z.add_comm, Z.add_assoc, ...

    A large part of ZArith is now simply compatibility notations, for instance Zplus_comm is an alias for Z.add_comm. The direct use of module Z is now recommended instead of relying on these compatibility notations.

  • Similar major reorganization of NArith, via a module N in NArith/BinNat.v

  • Concerning the positive datatype, BinPos.v is now in a specific directory PArith, and contains an internal submodule Pos. We regroup there functions such as Pos.add Pos.mul etc as well as many results about them. These results are here proved directly (no Number interface for strictly positive numbers).

  • Note that in spite of the compatibility layers, all these reorganizations may induce some marginal incompatibilies in scripts. In particular:

    • the "?=" notation for positive now refers to a binary function Pos.compare, instead of the infamous ternary Pcompare (now Pos.compare_cont).
    • some hypothesis names generated by the system may changed (typically for a "destruct Z_le_gt_dec") since naming is done after the short name of the head predicate (here now "le" in module Z instead of "Zle", etc).
    • the internals of Z.add has changed, now relying of Z.pos_sub.
  • Also note these new notations:

    • "<?" "<=?" "=?" for boolean tests such as Z.ltb Z.leb Z.eqb.
    • "÷" for the alternative integer division Z.quot implementing the Truncate convention (former ZOdiv), while the notation for the Coq usual division Z.div implementing the Flooring convention remains "/". Their corresponding modulo functions are Z.rem (no notations) for Z.quot and Z.modulo (infix "mod" notation) for Z.div.
  • Lemmas about conversions between these datatypes are also organized in modules, see for instance modules Z2Nat, N2Z, etc.

  • When creating BigN, the macro-generated part NMake_gen is much smaller. The generic part NMake has been reworked and improved. Some changes may introduce incompatibilities. In particular, the order of the arguments for BigN.shiftl and BigN.shiftr is now reversed: the number to shift now comes first. By default, the power function now takes two BigN.

  • Creation of Vector, an independent library for lists indexed by their length. Vectors' names overwrite lists' one so you should not "Import" the library. All old names changed: function names follow the ocaml ones and, for example, Vcons becomes Vector.cons. You can get [..;..;..]-style notations by importing Vector.VectorNotations.

  • Removal of TheoryList. Requiring List instead should work most of the time.

  • New syntax "rew Heq in H" and "rew <- Heq in H" for eq_rect and eq_rect_r (available by importing module EqNotations).

  • Wf.iter_nat is now Peano.nat_iter (with an implicit type argument).

Internal infrastructure

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


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


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


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

Details of changes in 8.4beta2

Vernacular commands

  • Commands "Back" and "BackTo" are now handling the proof states. They may perform some extra steps of backtrack to avoid states where the proof state is unavailable (typically a closed proof).
  • The commands "Suspend" and "Resume" have been removed.
  • A basic Show Script has been reintroduced (no indentation).
  • New command "Set Parsing Explicit" for deactivating parsing (and printing) of implicit arguments (useful for teaching).
  • New command "Grab Existential Variables" to transform the unresolved evars at the end of a proof into goals.


  • Still no general "info" tactical, but new specific tactics info_auto, info_eauto, info_trivial which provides information on the proofs found by auto/eauto/trivial. Display of these details could also be activated by "Set Info Auto"/"Set Info Eauto"/"Set Info Trivial".
  • Details on everything tried by auto/eauto/trivial during a proof search could be obtained by "debug auto", "debug eauto", "debug trivial" or by a global "Set Debug Auto"/"Set Debug Eauto"/"Set Debug Trivial".
  • New command "r string" in Ltac debugger that interprets "idtac string" in Ltac code as a breakpoint and jumps to its next use.
  • Tactics from the Dp plugin (simplify, ergo, yices, cvc3, z3, cvcl, harvey, zenon, gwhy) have been removed, since Why2 has not been maintained for the last few years. The Why3 plugin should be a suitable replacement in most cases.


  • MSetRBT: a new implementation of MSets via Red-Black trees (initial contribution by Andrew Appel).
  • MSetAVL: for maximal sharing with the new MSetRBT, the argument order of Node has changed (this should be transparent to regular MSets users).

Module System

  • The names of modules (and module types) are now in a fully separated namespace from ordinary definitions: "Definition E:=0. Module E. End E." is now accepted.


  • Coqide now supports the "Restart" command, and "Undo" (with a warning). Better support for "Abort".

Details of changes in 8.4

Vernacular commands

  • The "Reset" command is now supported again in files given to coqc or Load.
  • "Show Script" now indents again the displayed scripts. It can also work correctly across Load'ed files if the option "Unset Atomic Load" is used.
  • "Open Scope" can now be given the delimiter (e.g. Z) instead of the full scope name (e.g. Z_scope).


  • Most compatibility notations of the standard library are now tagged as (compat xyz), where xyz is a former Coq version, for instance "8.3". These notations behave as (only parsing) notations, except that they may triggers warnings (or errors) when used while Coq is not in a corresponding -compat mode.
  • To activate these compatibility warnings, use "Set Verbose Compat Notations" or the command-line flag -verbose-compat-notations.
  • For a strict mode without these compatibility notations, use "Unset Compat Notations" or the command-line flag -no-compat-notations.


  • An annotation "eqn:H" or "eqn:?" can be added to a "destruct" or "induction" to make it generate equations in the spirit of "case_eq". The former syntax "_eqn" is discontinued.
  • The name of the hypothesis introduced by tactic "remember" can be set via the new syntax "remember t as x eqn:H" (wish #2489).


  • Reals: changed definition of PI, no more axiom about sin(PI/2).
  • SetoidPermutation: a notion of permutation for lists modulo a setoid equality.
  • BigN: fixed the ocaml code doing the parsing/printing of big numbers.
  • List: a couple of lemmas added especially about no-duplication, partitions.
  • Init: Removal of the coercions between variants of sigma-types and subset types (possible source of incompatibility).

Version 8.3

Summary of changes

Coq version 8.3 is before all a transition version with refinements or extensions of the existing features and libraries and a new tactic 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 FSets and a new round of evolutions in the modular development of arithmetic (library Numbers). The reason for making 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 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 (including 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 <+ for nesting functor application that provides a light notation for inheriting the properties of cascading modules.

The new tactic nsatz is due to Loïc Pottier. It works by computing Gröbner bases. Regarding the existing tactics, various improvements have been done by Matthieu Sozeau, Hugo Herbelin and Pierre Letouzey.

Matthieu Sozeau extended and refined the typeclasses and Program features (the Russell language). Pierre Letouzey maintained and improved the extraction mechanism. Bruno Barras and Élie Soubiran maintained the Coq checker, Julien Forest maintained the Function mechanism for reasoning over recursively defined functions. Matthieu Sozeau, Hugo Herbelin and Jean-Marc Notin maintained coqdoc. Frédéric Besson maintained the Micromega platform 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 (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.

Paris, April 2010
Hugo Herbelin

Details of changes

Rewriting tactics

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

Automation tactics

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

Other tactics

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

Tactic definitions

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


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

Specification language

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

Module system

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


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


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

Type classes

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

Vernacular commands

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


  • Use "standard" Coq names for the properties of eq and identity (e.g. refl_equal is now eq_refl). Support for compatibility is provided.

  • The function Compare_dec.nat_compare is now defined directly, instead of relying on lt_eq_lt_dec. The earlier version is still available under the name nat_compare_alt.

  • Lemmas in library Relations and Reals have been homogenized a bit.

  • The implicit argument of Logic.eq is now maximally inserted, allowing to simply write "eq" instead of "@eq _" in morphism signatures.

  • Wrongly named lemmas (Zlt_gt_succ and Zlt_succ_gt) fixed (potential source of incompatibilities)

  • List library:

    • Definitions of list, length and app are now in Init/Datatypes. Support for compatibility is provided.
    • Definition of Permutation is now in Sorting/Permtation.v
    • Some other light revisions and extensions (possible source of incompatibilities solvable by qualifying names accordingly).
  • In ListSet, set_map has been fixed (source of incompatibilities if used).

  • Sorting library:

    • new mergesort of worst-case complexity O(n*ln(n)) made available in Mergesort.v;
    • former notion of permutation up to setoid from Permutation.v is deprecated and moved to PermutSetoid.v;
    • heapsort from Heap.v of worst-case complexity O(n*n) is deprecated;
    • new file Sorted.v for some definitions of being sorted.
  • Structure library. This new library is meant to contain generic structures such as types with equalities or orders, either in Module version (for now) or Type Classes (still to do):

    • DecidableType.v and OrderedType.v: initial notions for FSets/FMaps, left for compatibility but considered as deprecated.
    • Equalities.v and Orders.v: evolutions of the previous files, with fine-grain Module architecture, many variants, use of Equivalence and other relevant Type Classes notions.
    • OrdersTac.v: a generic tactic for solving chains of (in)equalities over variables. See {Nat,N,Z,P}OrderedType.v for concrete instances.
    • GenericMinMax.v: any ordered type can be equipped with min and max. We derived here all the generic properties of these functions.
  • MSets library: an important evolution of the FSets library. "MSets" stands for Modular (Finite) Sets, by contrast with a forthcoming library of Class (Finite) Sets contributed by S. Lescuyer which will be integrated with the next release of Coq. The main features of MSets are:

    • The use of Equivalence, Proper and other Type Classes features easing the handling of setoid equalities.
    • The interfaces are now stated in iff-style. Old specifications are now derived properties.
    • The compare functions are now pure, and return a "comparison" value. Thanks to the CompSpec inductive type, reasoning on them remains easy.
    • Sets structures requiring invariants (i.e. sorted lists) are built first as "Raw" sets (pure objects and separate proofs) and attached with their proofs thanks to a generic functor. "Raw" sets have now a proper interface and can be manipulated directly.

    Note: No Maps yet in MSets. The FSets library is still provided for compatibility, but will probably be considered as deprecated in the next release of Coq.

  • Numbers library:

    • The abstract layer (NatInt, Natural/Abstract, Integer/Abstract) has been simplified and enhance thanks to new features of the module system such as Include (see above). It has been extended to Euclidean division (three flavors for integers: Trunc, Floor and Math).
    • The arbitrary-large efficient numbers (BigN, BigZ, BigQ) has also been reworked. They benefit from the abstract layer improvements (especially for div and mod). Note that some specifications have slightly changed (compare, div, mod, shift{r,l}). Ring/Field should work better (true recognition of constants).


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


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

Internal infrastructure

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

Version 8.2

Summary of changes

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 typeclasses. Typeclasses, which come with a few convenient features such as type-based resolution of implicit arguments, play a new landmark role in the architecture of Coq with respect to automation. For instance, thanks to typeclass 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 arithmetic 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 automation in presence of various number-theory concepts.

Frédéric Besson contributed a reflective 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 arithmetic for efficiently computing with the library of integers he developed.

Beside the libraries, various improvements were 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 Russell language, ending in an convenient way to write programs of given specifications, Pierre Corbineau extended the Mathematical Proof Language and the automation tools that accompany it, Pierre Letouzey supervised and extended various parts of the standard library, Stéphane Glondu contributed a few tactics and improvements, Jean-Marc Notin provided help in debugging, general maintenance and coqdoc support, Vincent Siles contributed extensions of the Scheme command and of injection.

Bruno Barras implemented the coqchk tool: this is a stand-alone type checker that can be used to certify .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 Kaliszyk, Milad Niqui contributed to improve 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 Radboud university in Nijmegen, reporters of bugs and participants to the Coq-Club mailing list.

Palaiseau, June 2008
Hugo Herbelin

Details of changes


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

Vernacular commands

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


  • Several parts of the libraries are now in Type, in particular FSets, SetoidList, ListSet, Sorting, Zmisc. This may induce a few incompatibilities. In case of trouble while fixing existing development, it may help to simply declare Set as an alias for Type (see file SetIsType).

  • New arithmetical library in theories/Numbers. It contains:

    • an abstract modular development of natural and integer arithmetics in Numbers/Natural/Abstract and Numbers/Integer/Abstract
    • an implementation of efficient computational bounded and unbounded integers that can be mapped to processor native arithmetics. See Numbers/Cyclic/Int31 for 31-bit integers and Numbers/Natural/BigN for unbounded natural numbers and Numbers/Integer/BigZ for unbounded integers.
    • some proofs that both older libraries Arith, ZArith and NArith and newer BigN and BigZ implement the abstract modular development. This allows in particular BigN and BigZ to already come with a large database of basic lemmas and some generic tactics (ring),

    This library has still an experimental status, as well as the processor-acceleration mechanism, but both its abstract and its concrete parts are already quite usable and could challenge the use of nat, N and Z in actual developments. Moreover, an extension of this framework to rational numbers is ongoing, and an efficient Q structure is already provided (see Numbers/Rational/BigQ), but this part is currently incomplete (no abstract layer and generic lemmas).

  • Many changes in FSets/FMaps. In practice, compatibility with earlier version should be fairly good, but some adaptations may be required.

    • Interfaces of unordered ("weak") and ordered sets have been factorized thanks to new features of Coq modules (in particular Include), see FSetInterface. Same for maps. Hints in these interfaces have been reworked (they are now placed in a "set" database).
    • To allow full subtyping between weak and ordered sets, a field "eq_dec" has been added to OrderedType. The old version of OrderedType is now called MiniOrderedType and functor MOT_to_OT allow to convert to the new version. The interfaces and implementations of sets now contain also such a "eq_dec" field.
    • FSetDecide, contributed by Aaron Bohannon, contains a decision procedure allowing to solve basic set-related goals (for instance, is a point in a particular set ?). See FSetProperties for examples.
    • Functors of properties have been improved, especially the ones about maps, that now propose some induction principles. Some properties of fold need less hypothesis.
    • More uniformity in implementations of sets and maps: they all use implicit arguments, and no longer export unnecessary scopes (see bug #1347)
    • Internal parts of the implementations based on AVL have evolved a lot. The main files FSetAVL and FMapAVL are now much more lightweight now. In particular, minor changes in some functions has allowed to fully separate the proofs of operational correctness from the proofs of well-balancing: well-balancing is critical for efficiency, but not anymore for proving that these trees implement our interfaces, hence we have moved these proofs into appendix files FSetFullAVL and FMapFullAVL. Moreover, a few functions like union and compare have been modified in order to be structural yet efficient. The appendix files also contains alternative versions of these few functions, much closer to the initial Ocaml code and written via the Function framework.
  • Library IntMap, subsumed by FSets/FMaps, has been removed from Coq Standard Library and moved into a user contribution Cachan/IntMap

  • Better computational behavior of some constants (eq_nat_dec and le_lt_dec more efficient, Z_lt_le_dec and Positive_as_OT.compare transparent, ...) (exceptional source of incompatibilities).

  • Boolean operators moved from module Bool to module Datatypes (may need to rename qualified references in script and force notations || and && to be at levels 50 and 40 respectively).

  • The constructors xI and xO of type positive now have postfix notations "~1" and "~0", allowing to write numbers in binary form easily, for instance 6 is 1~1~0 and 4*p is p~0~0 (see BinPos.v).

  • Improvements to NArith (Nminus, Nmin, Nmax), and to QArith (in particular a better power function).

  • Changes in ZArith: several additional lemmas (used in theories/Numbers), especially in Zdiv, Znumtheory, Zpower. Moreover, many results in Zdiv have been generalized: the divisor may simply be non-null instead of strictly positive (see lemmas with name ending by "_full"). An alternative file ZOdiv proposes a different behavior (the one of Ocaml) when dividing by negative numbers.

  • Changes in Arith: EqNat and Wf_nat now exported from Arith, some constructions on nat that were outside Arith are now in (e.g. iter_nat).

  • In SetoidList, eqlistA now expresses that two lists have similar elements at the same position, while the predicate previously called eqlistA is now equivlistA (this one only states that the lists contain the same elements, nothing more).

  • Changes in Reals:

    • Most statement in "sigT" (including the completeness axiom) are now in "sig" (in case of incompatibility, use proj1_sig instead of projT1, sig instead of sigT, etc).
    • More uniform naming scheme (identifiers in French moved to English, consistent use of 0 -- zero -- instead of O -- letter O --, etc).
    • Lemma on prod_f_SO is now on prod_f_R0.
    • Useless hypothesis of ln_exists1 dropped.
    • New Rlogic.v states a few logical properties about R axioms.
    • RIneq.v extended and made cleaner.
  • Slight restructuration of the Logic library regarding choice and classical logic. Addition of files providing intuitionistic axiomatizations of descriptions: Epsilon.v, Description.v and IndefiniteDescription.v.

  • Definition of pred and minus made compatible with the structural decreasing criterion for use in fixpoints.

  • Files Relations/Rstar.v and Relations/Newman.v moved out to the user contribution repository (contribution CoC_History). New lemmas about transitive closure added and some bound variables renamed (exceptional risk of incompatibilities).

  • Syntax for binders in terms (e.g. for "exists") supports anonymous names.

Notations, coercions, implicit arguments and type inference

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

Tactic Language

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


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


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

Type Classes

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

Setoid rewriting

  • Complete (and still experimental) rewrite of the tactic based on typeclasses. The old interface and semantics are almost entirely respected, except:
    • Import Setoid is now mandatory to be able to call setoid_replace and declare morphisms.
    • "-->", "++>" and "==>" are now right associative notations declared at level 55 in scope signature_scope. Their introduction may break existing scripts that defined them as notations with different levels.
    • One needs to use [Typeclasses unfold [cst]] if [cst] is used as an abbreviation hiding products in types of morphisms, e.g. if ones redefines [relation] and declares morphisms whose type mentions [relation].
    • The [setoid_rewrite]'s semantics change when rewriting with a lemma: it can rewrite two different instantiations of the lemma at once. Use [setoid_rewrite H at 1] for (almost) the usual semantics. [setoid_rewrite] will also try to rewrite under binders now, and can succeed on different terms than before. In particular, it will unify under let-bound variables. When called through [rewrite], the semantics are unchanged though.
    • [Add Morphism term : id] has different semantics when used with parametric morphism: it will try to find a relation on the parameters too. The behavior has also changed with respect to default relations: the most recently declared Setoid/Relation will be used, the documentation explains how to customize this behavior.
    • Parametric Relation and Morphism are declared differently, using the new [Add Parametric] commands, documented in the manual.
    • Setoid_Theory is now an alias to Equivalence, scripts building objects of type Setoid_Theory need to unfold (or "red") the definitions of Reflexive, Symmetric and Transitive in order to get the same goals as before. Scripts which introduced variables explicitly will not break.
    • The order of subgoals when doing [setoid_rewrite] with side-conditions is always the same: first the new goal, then the conditions.
  • New standard library modules Classes.Morphisms declares standard morphisms on refl / sym / trans relations. Classes.Morphisms_Prop declares morphisms on propositional connectives and Classes.Morphisms_Relations on generalized predicate connectives. Classes.Equivalence declares notations and tactics related to equivalences and Classes.SetoidTactics defines the setoid_replace tactics and some support for the Add * interface, notably the tactic applied automatically before each Add Morphism proof.
  • User-defined subrelations are supported, as well as higher-order morphisms and rewriting under binders. The tactic is also extensible entirely in Ltac. The documentation has been updated to cover these features.
  • [setoid_rewrite] and [rewrite] now support the [at] modifier to select occurrences to rewrite, and both use the [setoid_rewrite] code, even when rewriting with leibniz equality if occurrences are specified.


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


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


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


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

Version 8.1

Summary of changes

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 (now called template polymorphism).

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 for rings and semirings.

Laurent Théry and Bruno Barras developed a new, significantly more efficient simplification algorithm for 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 cvcl, Simplify and zenon. Hugo Herbelin implemented an experimental protocol for calling external tools from the tactic language.

Matthieu Sozeau developed 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 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, Radboud University, University of Pennsylvania and Yale University.

Palaiseau, July 2006
Hugo Herbelin

Details of changes in 8.1beta


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


  • 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.


  • 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 bug #5941)
  • "rewrite ... in" now accepts a clause as place where to rewrite instead of just a simple hypothesis name. For instance: rewrite H in H1,H2 |- * means rewrite H in H1; rewrite H in H2; rewrite H rewrite H in * |- will do try rewrite H in Hi for all hypothesis Hi <> H.
  • Added "dependent rewrite term" and "dependent rewrite term in hyp".
  • Added "autorewrite with ... in hyp [using ...]".
  • Tactic "replace" now accepts a "by" tactic clause.
  • Added "clear - id" to clear all hypotheses except the ones depending in id.
  • The argument of Declare Left Step and Declare Right Step is now a term (it used to be a reference).
  • Omega now handles arbitrary precision integers.
  • Several bug fixes in Reflexive Omega (romega).
  • Idtac can now be left implicit in a [...|...] construct: for instance, [ foo | | bar ] stands for [ foo | idtac | bar ].
  • Fixed a "fold" bug (non critical but possible source of incompatibilities).
  • Added classical_left and classical_right which transforms |- A \/ B into ~B |- A and ~A |- B respectively.
  • Added command "Declare Implicit Tactic" to set up a default tactic to be used to solve unresolved subterms of term arguments of tactics.
  • Better support for coercions to Sortclass in tactics expecting type arguments.
  • Tactic "assert" now accepts "as" intro patterns and "by" tactic clauses.
  • New tactic "pose proof" that generalizes "assert (id:=p)" with intro patterns.
  • New introduction pattern "?" for letting Coq choose a name.
  • Introduction patterns now support side hypotheses (e.g. intros [|] on "(nat -> nat) -> nat" works).
  • New introduction patterns "->" and "<-" for immediate rewriting of introduced hypotheses.
  • Introduction patterns coming after non trivial introduction patterns now force full introduction of the first pattern (e.g. intros [[|] p] on nat->nat->nat now behaves like intros [[|?] p])
  • Added "eassumption".
  • Added option 'using lemmas' to auto, trivial and eauto.
  • Tactic "congruence" is now complete for its intended scope (ground equalities and inequalities with constructors). Furthermore, it tries to equates goal and hypotheses.
  • New tactic "rtauto" solves pure propositional logic and gives a reflective version of the available proof.
  • Numbering of "pattern", "unfold", "simpl", ... occurrences in "match with" made consistent with the printing of the return clause after the term to match in the "match-with" construct (use "Set Printing All" to see hidden occurrences).
  • Generalization of induction "induction x1...xn using scheme" where scheme is an induction principle with complex predicates (like the ones generated by function induction).
  • Some small Ltac tactics has been added to the standard library (file Tactics.v):
    • f_equal : instead of using the different f_equalX lemmas
    • case_eq : a "case" without loss of information. An equality stating the current situation is generated in every sub-cases.
    • swap : for a negated goal ~B and a negated hypothesis H:~A, swap H asks you to prove A from hypothesis B
    • revert : revert H is generalize H; clear H.


  • 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.


  • 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'.


  • 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)


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


  • 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.

Details of changes in 8.1gamma


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

Language and commands

  • Added sort-polymorphism for definitions in Type (but finally abandoned).
  • 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.


  • 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).

Details of changes in 8.1

Bug fixes

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


  • 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).


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

Version 8.0

Summary of changes

Coq version 8 is a major revision of the Coq proof assistant. First, the underlying logic is slightly different. The so-called impredicativity of the sort 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 mathematics within classical logic. Moreover, even in an constructive setting, the impredicativity of 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 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

  • a more uniform, purified style: all constructions are now lowercase, with a functional programming perfume (e.g. abstraction is now written fun), and more directly accessible to the novice (e.g. dependent product is now written forall and allows omission of types). Also, parentheses are no longer mandatory for function application.
  • 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.

Together with the revision of the concrete syntax, a new mechanism of 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 restructuring and uniformization 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 with Coq. Close in style to 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.

Bruno Barras and Hugo Herbelin have been the main contributors of the reflection 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 implementer of the notion of interpretation scopes and of the commands for easily adding new notations.

Hugo Herbelin is the main implementer of the restructured standard library.

Pierre Corbineau is the main designer and implementer 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 Chrząszcz respectively maintained the extraction tool and module system of Coq.

Jean-Christophe Filliâtre, Pierre Letouzey, Hugo Herbelin and other contributors from Sophia-Antipolis and Nijmegen participated in extending 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 responsibility of Christine Paulin.

Palaiseau & Orsay, Apr. 2004
Hugo Herbelin & Christine Paulin
(updated Apr. 2006)

Details of changes in 8.0beta old syntax


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

Syntax for arithmetic

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

Vernacular commands

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


  • 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


  • New file about the factorial function in Arith
  • An additional elimination Acc_iter for Acc, simpler 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


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

Extraction (See details in plugins/extraction/CHANGES)

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


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


  • Implicit parameters of inductive types definition now taken into account for inferring other implicit arguments


  • 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

Details of changes in 8.0beta new syntax

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


  • 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 (switch 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

Details of changes in 8.0

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 functionalities 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)