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Proof assistant
The Rocq Prover (formerly named Coq) is an interactive theorem prover first released in 1989. It allows the expression of mathematical assertions, mechanical
Rocq
Functional programming language
propositions-as-types paradigm (Curry–Howard correspondence), but unlike Rocq, has no separate tactics language, and proofs are written in a functional
Agda_(programming_language)
Municipality in Hainaut Province, Wallonia, Belgium
Seneffe (French pronunciation: [sənɛf] ; Walloon: Sinefe) is a municipality of Wallonia located in the province of Hainaut, Belgium. On 1 January 2006
Seneffe
Interactive theorem prover software
University of Edinburgh. Nowadays, many provers include their own editor. Rocq includes RocqIDE, which is based on OCaml/Gtk. Isabelle includes Isabelle/jEdit
Proof_assistant
Mathematical logician and computer scientist
Paris-Saclay University, best known for developing the interactive theorem prover Rocq. Paulin-Mohring received her PhD in 1989, under the supervision of Gérard
Christine_Paulin-Mohring
Inconsistent pure type systems related to Girard's paradox
restricted variant System U− suffices for a paradox; for example, the Coq/Rocq standard library explicitly presents "Hurkens's paradox … for system U−"
System_U
Graph data structure
Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar NuPRL PVS Rocq Twelf Category Outline Glossary
E-graph
Concept in computer science
Ynot library for the Rocq; the Holfoot embedding of Smallfoot in HOL; Fine-grained Concurrent Separation Logic, and Bedrock (a Rocq library for low-level
Separation_logic
Concepts in theoretical computer science
Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar NuPRL PVS Rocq Twelf Category Outline Glossary
Safety and liveness properties
Safety_and_liveness_properties
Programming paradigm based on applying and composing functions
expressed by the language's type system. Some special purpose languages such as Rocq allow only well-founded recursion and are strongly normalizing (nonterminating
Functional_programming
Type theory created by Thierry Coquand
For this second reason, the CoC and its variants have been the basis for Rocq and other proof assistants. Some of its variants include the calculus of
Calculus_of_constructions
Topics referred to by the same term
word for "rooster" or "cock" Coq, an interactive theorem prover, renamed to Rocq in 2025 CoQ, common term for Coenzyme Q10, a naturally occurring biochemical
Coq
Concurrent Pascal Constraint Handling Rules (CHR) Control Language Coq, renamed Rocq CORAL, Coral 66 CorVision COWSEL CPL Cryptol Crystal Csound Cuneiform Curl
List_of_programming_languages
French computer scientist and mathematician
theoretical computer science, Coquand is also known as the co-creator of the Rocq (formerly named Coq, the name is a reference partly to Coquand's surname)
Thierry_Coquand
Subfield of computer science and logic
essentially another proof assistant for classical higher order logic. Rocq Developed in France, Rocq is another automated proof assistant, which can automatically
Automated_reasoning
Analysis of computer programs without executing them
Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar NuPRL PVS Rocq Twelf Category Outline Glossary
Static_program_analysis
Mathematical theory of data types
are based on type theory. For example, the underlying formal language of Rocq (formerly Coq) is the calculus of inductive constructions, while Lean is
Type_theory
Type whose definition depends on a value
and "there exists". In functional programming languages like Agda, ATS, Rocq (previously known as Coq), F*, Epigram, Idris, and Lean, dependent types
Dependent_type
Concept in programming language design
first-class control continuations Scheme, ML, F# first-class type dependent types Rocq, Idris, Agda first-class data type Generic Haskell, C++ first-class polymorphism
First-class_citizen
Functional programming language created in 2007
interacting with proof assistants: by writing a series of tactic invocations (Rocq style), or by interactively elaborating a proof term (Epigram–Agda style)
Idris_(programming_language)
Proof assistant and programming language
x86-64, AArch64 OS Cross-platform: Linux, macOS, Windows License Apache 2.0 Website lean-lang.org Influenced by ML, Rocq (formerly named Coq), Haskell
Lean_(proof_assistant)
Computer program for the Boolean satisfiability problem
Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar NuPRL PVS Rocq Twelf Category Outline Glossary
SAT_solver
Formally verified C compiler
compiler is specified, programmed and proven in proof assistant software named Rocq. CompCert is to be used to program embedded systems requiring reliability
CompCert
Proving or disproving the correctness of certain intended algorithms
proof assistants (interactive theorem provers) (such as HOL, ACL2, Isabelle, Rocq (previously known as Coq) or PVS), or automatic theorem provers, including
Formal_verification
Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar NuPRL PVS Rocq Twelf Category Outline Glossary
Dependence_analysis
French computer scientist and programmer (born 1968)
optimizing compiler for the C programming language, formally verified in Rocq (former name: Coq). Leroy was also the original author of LinuxThreads, the
Xavier_Leroy
Mathematical constructs and creation rules
encoding the natural numbers using Peano's encoding. It can be defined in Rocq (formerly named Coq) as follows: Inductive nat : Type := | O : nat | S :
Inductive_type
Topics referred to by the same term
Scotland Cockfight Cock ring Cockpit (disambiguation) Cocktail Coq (renamed Rocq), an application used in computer science Coque (disambiguation) Cox (disambiguation)
Cock
General purpose functional programming language
GEDANKEN Influenced Caml, Clojure, Cyclone, C++, Elm, Erlang, F#, F*, Haskell, Idris, Kotlin, Miranda, Nemerle, OCaml, Opa, Rocq, Rust, Scala, Standard ML
ML_(programming_language)
Of a function, an additional effect besides returning a value
Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar NuPRL PVS Rocq Twelf Category Outline Glossary
Side effect (computer science)
Side_effect_(computer_science)
Encapsulation of an optional value in programming or type theory
empty) show_value full -> The value is: 42 show_value empty -> No value In Rocq, the option type is defined as Inductive option (A:Type) : Type := | Some
Option_type
Type of algorithm in computer science
every function must terminate. It is supported by theorem provers Agda and Rocq. Both corecursion and recursion can be thought of as operating on trees,
Corecursion
American singer and television presenter
to the Girl Groups (2003), with Rocq-E Harrell and Lucretia van der Vloot Big, Black & Beautiful XL (2006), with Rocq-E Harrell and Lucretia van der Vloot
Michelle_David
Computer science field
Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar NuPRL PVS Rocq Twelf Category Outline Glossary
Model_checking
Validates computer program operations
Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar NuPRL PVS Rocq Twelf Category Outline Glossary
Typestate_analysis
Set of software engineering methods
Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar NuPRL PVS Rocq Twelf Category Outline Glossary
Program_slicing
French research institution for computer science
brain–computer interfaces. Pharo, an open-source Smalltalk derived from Squeak. Rocq, a proof assistant scikit-learn, a machine learning software package Scilab
French Institute for Research in Computer Science and Automation
French_Institute_for_Research_in_Computer_Science_and_Automation
Programming language
network Coccinelle, a utility for transforming the source code of C programs. Rocq (former name: Coq), a formal proof management system. Easycrypt, a toolset
OCaml
Type system in computer science
The proof assistant Rocq has also supported type classes in recent versions. Unlike in ordinary programming languages, in Rocq, any laws of a type class
Type_class
Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar NuPRL PVS Rocq Twelf Category Outline Glossary
Hyperproperty
2025-12-21. "Inductive types and recursive functions — The Rocq Prover 9.1.0 documentation". rocq-prover.org. Retrieved 2026-01-13. "enum - Rust". doc.rust-lang
Comparison of programming languages (algebraic data type)
Comparison_of_programming_languages_(algebraic_data_type)
Limitative results in mathematical logic
Shankar in 1986 using Nqthm (Shankar 1994), by Russell O'Connor in 2003 using Rocq (previously known as Coq) (O'Connor 2005) and by John Harrison in 2009 using
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
Russian mathematician (1966–2017)
mathematics that Voevodsky worked on in his final years. He worked on a Rocq (then: Coq) library UniMath using univalent ideas. In April 2016, the University
Vladimir_Voevodsky
Place in Wallonia, Belgium
coats of arms of the Renesse–Rubempré–Egmont families. The Château de la Rocq lies in the vicinity of the village proper. Philippe Parmentier (sculptor
Feluy
Function and primitive data structure in Lisp and other functional programming languages
pronounced "cons". (A good example is the :: operator in ML, Scala, F#, Lean, Rocq, and Elm or the : operator in Haskell, which adds an element to the beginning
Cons
Software used in mathematical applications
SCIP SciPy SNOPT TOMLAB WORHP CVC Yices Z3 Theorem Prover ACL2 Coq (now Rocq) HOL Light HOL4 Isabelle Lean Metamath Mizar NuPRL Twelf Botan Bouncy Castle
Mathematical_software
Type theory in logic and mathematics
significant amounts of "synthetic homotopy theory" in the proof assistant Rocq (previously known as Coq); this formed the basis of the library later called
Homotopy_type_theory
Concept in theoretical computer science
by an online amateur mathematical collective, using a proof formalized in Rocq. These are tables of rules for Turing machines that generate Σ(1) and S(1)
Busy_beaver
Canadian computer scientist
proof of the odd-order theorem. (Both were written using the proof assistant Rocq.) In 2011, as a principal researcher at Microsoft Research Cambridge, he
Georges_Gonthier
Higher-order logic (HOL) automated theorem prover
languages and systems provide similar functions: Agda, written in Haskell Rocq (formerly named Coq), written in OCaml Lean, written in Lean and C++ LEGO
Isabelle_(proof_assistant)
Congress". GovTrack. Washington, D.C. Retrieved May 30, 2015. Margaret Miller Rocq (1976). "Kern County". California Local History: A Bibliography and Union
Timeline of Bakersfield, California
Timeline_of_Bakersfield,_California
Historic fort outside Verdun, France, built in the late 19th century
Feignies Leveau Heron-Fontaine Les Sarts Bersillies La Salmagne Boussois Rocq Cerfontaine Bourdiau Hautmont Oise gap Hirson Ayvelles Fortified region of
Fort_Douaumont
Proof assistant
the calculus of constructions), and is compatible, to some extent, with Rocq. The word "matita" means "pencil" in Italian (a simple and widespread editing
Matita
List of programming languages types and the languages that meet its description
Joy jq (functions are 2nd class) KRC Lean Mercury Miranda Pure PureScript Rocq (former name: Coq) SAC SASL SequenceL Ur APL J Q (programming language from
List of programming languages by type
List_of_programming_languages_by_type
Data type defined by combining other types
Nemerle Nim OCaml Opa OpenCog Perl PureScript Python Racket Reason ReScript Rocq Rust Scala Standard ML Swift Tom TypeScript Visual Prolog Disjoint union
Algebraic_data_type
Topics referred to by the same term
COGS (disambiguation) Coq, in computer science, was the ancient name of Rocq, an interactive theorem prover Kog (disambiguation) System Settings, an application
Cog
Problem in computer science
the given deadline. These include languages such as MISRA C, SPARK, and Rocq.[citation needed] The halting problem requires a decision procedure that
Halting_problem
Aspect of cryptography
Protocol Analyzer (Maude-NPA) ProVerif Scyther Tamarin Prover Squirrel StrandsRocq To formally verify a protocol it is often abstracted and modelled using Alice
Cryptographic_protocol
Relationship between programs and proofs
lambda calculi derived from the Curry–Howard paradigm led to software like Rocq in which proofs seen as programs can be formalized, checked, and run. A converse
Curry–Howard_correspondence
Fundamental problem in computer science
Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar NuPRL PVS Rocq Twelf Category Outline Glossary
Path_explosion
Contractual transaction on a decentralized platform
verification: Bamboo, IELE, Simplicity, Michelson (can be verified with Rocq), Liquidity (compiles to Michelson), Scilla, DAML and Pact. Processes on
Smart_contract
Rules to verify computer program correctness
Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar NuPRL PVS Rocq Twelf Category Outline Glossary
Hoare_logic
Feignies Leveau Heron-Fontaine Les Sarts Bersillies La Salmagne Boussois Rocq Cerfontaine Bourdiau Hautmont Oise gap Hirson Ayvelles Fortified region of
Fort_Souville
Structure editor for monomorphic Martin-Löf type theory
Chalmers University. It is a predecessor of the Alfa, Agda, Cayenne and Rocq proof assistants and dependently typed programming languages. It was the
ALF_(proof_assistant)
American mathematician
proofs (e.g. verification of proofs within Zermelo–Fraenkel set theory using Rocq). In his Ph.D. dissertation, Simpson studied the notion of system of Hodge
Carlos_Simpson
Reformulation of Floyd-Hoare logic
language, separation logic and type theory. This system is implemented as a Rocq library named Ynot. In this language, evaluation of expressions corresponds
Predicate transformer semantics
Predicate_transformer_semantics
Topics referred to by the same term
Esenboğa International Airport. The Ltac tactic language embedded in the Rocq proof assistant This disambiguation page lists articles associated with the
LTAC
Software testing software
Logtalk Lua Mathematica Objective-C OCaml Perl Prolog PHP Pony Python R Racket Rocq Ruby Rust Scala Scheme Smalltalk Standard ML Swift TypeScript Whiley Metamorphic
QuickCheck
Feignies Leveau Heron-Fontaine Les Sarts Bersillies La Salmagne Boussois Rocq Cerfontaine Bourdiau Hautmont Oise gap Hirson Ayvelles Fortified region of
Fort_de_la_Pompelle
1991 studio album by Vanessa Williams
Jones, Donna McElroy, Rick Nelson, Valerie Pinkston-Mayo, Angel Rogers, Rocq-E Harrell, Andres "Dres" Vargas-Titus, Tata Vega - backing vocals Vocals
The_Comfort_Zone_(album)
Style of computer programming
which allow the addition of constructs with user defined syntax include Rocq, Racket, Camlp4, OpenC++, Seed7, Red, Rebol, and Felix. While it is acceptable
Extensible_programming
Functional programming language inspired by ML and aimed at program verification
Cross-platform: Linux, macOS, Windows License Apache 2.0 Filename extensions .fst Website fstar-lang.org Influenced by Dafny, F#, Lean, OCaml, Rocq, Standard ML
F*_(programming_language)
Application of model-based design
notations, and mathematical formalisms such as Z, B (Event-B), Alloy or Rocq. There are various known ways to deploy model-based testing, which include
Model-based_testing
Russian computer scientist
basic concepts of mechanized reasoning and interactive theorem proving using Rocq (previously known as Coq). Sergey holds a joint appointment at Yale-NUS College
Ilya_Sergey
1995 live album by Scorpions
Don't Cry" Kinderchor Majell Lustenhouwer – children's choir on "White Dove" Rocq-E Harrel – additional vocals on "White Dove" Production Keith Olsen – producer
Live_Bites
Siege during World War I
forts, except between Boussois and Le Sarts where two were built. Ouvrage de Rocq in the south-east had an infantry parapet and some masonry shelters, the
Siege_of_Maubeuge
everything must be directly constructible. Used in: Proof assistants like Rocq, Agda. Not strictly intuitionistic, but very constructive. Founder: J. Girard
Constructive_logic
Algorithm for computing Gröbner bases
Buchberger’s algorithm has been proved correct within the proof assistant Rocq (formerly named Coq). In the SymPy library for Python, the (improved) Buchberger
Buchberger's_algorithm
Nantucket dBase 1984 Common Lisp Guy L. Steele, Jr., many others LISP 1984 Rocq (then: Coq) INRIA 1984 RPL Hewlett-Packard Forth, Lisp 1984 Standard ML ML
Timeline of programming languages
Timeline_of_programming_languages
Determination of whether a given program halts for each input
dependently typed programming language and theorem proving systems like Rocq and Agda. These systems use Curry-Howard isomorphism between programs and
Termination_analysis
Approach to static program analysis
Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar NuPRL PVS Rocq Twelf Category Outline Glossary
Abstract_interpretation
Feignies Leveau Heron-Fontaine Les Sarts Bersillies La Salmagne Boussois Rocq Cerfontaine Bourdiau Hautmont Oise gap Hirson Ayvelles Fortified region of
Fort_de_Saint-Cyr
Dynamic window manager for X Window System
other research projects. This has included re-implementing xmonad using the Rocq proof assistant, a determination xmonad is an imperative program, and studies
Xmonad
Data structure for storing non-overlapping sets
data structure and formalized its correctness using the proof assistant Rocq (then: Coq). "Semi-persistent" means that previous versions of the structure
Disjoint-set_data_structure
Computer science professor
automates proofs by both induction and coinduction, and has been implemented in Rocq, Isabelle/HOL, Dafny, and as part of the CIRC theorem prover. Grigore Rosu's
Grigore_Roșu
Libre OCaml formal C verifier
provers like Z3, Simplify, Alt-Ergo or interactive theorem provers like Rocq or Why. Using Jessie, an implementation of bubble-sort or a toy e-voting
Frama-C
Mathematical construction of a set with an equivalence relation
13 (2): 261–293, doi:10.1017/S0956796802004501, MR 1985376, S2CID 10069160. Implementation of setoids in Rocq Setoid at the nLab Bishop set at the nLab
Setoid
Class of mathematical expression
be handled in another part of the program. Many proof assistants, such as Rocq and Lean, define 1/0 = 0. This is to make all functions total. Such a definition
Division_by_zero
Proof assistant program
discipline Weak, static Filename extensions .miz .voc Website www.mizar.org Influenced OMDoc, HOL Light and Rocq mizar modes; Isabelle's Isar proof language
Mizar_system
Various systems of symbolic logic
mathematical proof. As such, the use of proof assistants (such as Agda or Rocq) is enabling modern mathematicians and logicians to develop and prove extremely
Intuitionistic_logic
Specification language for Java programs
static verification tool based on the Why verification platform and using the Rocq proof assistant. JMLEclipse, a plugin for the Eclipse integrated development
Java_Modeling_Language
team members at Xerox PARC in 1980, BBC BASIC by Sophie Wilson in 1981, Rocq (previously knows as Coq) by Christine Paulin-Mohring along with eight development
List of inventions and discoveries by women
List_of_inventions_and_discoveries_by_women
Feignies Leveau Heron-Fontaine Les Sarts Bersillies La Salmagne Boussois Rocq Cerfontaine Bourdiau Hautmont Oise gap Hirson Ayvelles Fortified region of
Batterie_de_Bouviers
Process of analyzing computer program behavior
Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar NuPRL PVS Rocq Twelf Category Outline Glossary
Program_analysis
Theorem classifying finite simple groups
multiplier of M22. 2012 Gonthier and collaborators announce a computer-checked version of the Feit–Thompson theorem using the Rocq (then: Coq) proof assistant.
Classification of finite simple groups
Classification_of_finite_simple_groups
French academic and programmer
assisted using Zenon and results are formally machine checked using the Rocq proof checker. In 2008, Doligez worked with Leslie Lamport and others to
Damien_Doligez
French computer scientist
calculus of constructions in 1984 with Thierry Coquand. He led the Coq (renamed Rocq) proof assistant project in the 1990s with Christine Paulin-Mohring, who
Gérard_Huet
2013 PL Software Award, and 2015 ACM Software System Award for Coq (renamed Rocq) proof assistant Patrick Cousot, for contributions to programming languages
List of programming language researchers
List_of_programming_language_researchers
Computer algebra system
use proof technology to prove the correctness of the algorithms (such as Rocq and ACL2). Binary AXIOM packages are available for installation on a wide
Axiom (computer algebra system)
Axiom_(computer_algebra_system)
Logical problem studied in computer science
needed] SMT solvers have been integrated with proof assistants, including Rocq and Isabelle/HOL. SMT solvers are a core building block in program synthesis
Satisfiability modulo theories
Satisfiability_modulo_theories
ROCQ
ROCQ
Surname or Lastname
English
English : topographic name for someone who lived by a rocky crag or outcrop, from Old French roche (later replaced in England by rock, from the Norman byform rocque), or a habitational name from any of the places named with this word, such as Roach in Devon, or Roche in Cornwall and South Yorkshire.English and Irish (of Norman origin) : habitational name from any of various places in Normandy, as for example Les Roches in Seine-Maritime, named with Old French roche, or from Roche Castle in Wales.
ROCQ
ROCQ
Girl/Female
Irish Scottish English
Abbreviation of Christine. Follower of Christ.
Boy/Male
Scottish American Teutonic
From the island of the lime tree. Although in the past, Lindsay was a common boys' name, today...
Surname or Lastname
English
English : variant spelling of Hewitt 1.
Boy/Male
Bengali, Buddhist, Hindu, Indian, Kannada, Marathi, Sanskrit, Tamil, Telugu
One who Seeks Enlightment; A Name of Lord Buddha; Man who Achieves Impossible
Surname or Lastname
English
English : variant of Holton.
Boy/Male
Indian, Punjabi, Sikh
Brave Warrior
Girl/Female
British, English
Goddess
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Sindhi
The Moon
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi
A Sage
Boy/Male
Australian, Biblical
God's Day; Son of God
ROCQ
ROCQ
ROCQ
ROCQ
ROCQ