AI & ChatGPT searches , social queries for PROOF ASSISTANT
Search references for PROOF ASSISTANT. Phrases containing PROOF ASSISTANT
See searches and references containing PROOF ASSISTANT!
Search references for PROOF ASSISTANT. Phrases containing PROOF ASSISTANT
See searches and references containing PROOF ASSISTANT!PROOF ASSISTANT
Interactive theorem prover software
mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by human–machine collaboration
Proof_assistant
Proof assistant and programming language
Lean is a proof assistant and a functional programming language. It is based on the calculus of constructions with inductive types (specifically, the
Lean_(proof_assistant)
Higher-order logic (HOL) automated theorem prover
core (kernel) to increase the trustworthiness of proofs without requiring, yet supporting, explicit proof objects. Isabelle is available inside a flexible
Isabelle_(proof_assistant)
Interactive theorem proving systems
Nipkow; Markus Wenzel; Lawrence C. Paulson (2002). Isabelle/HOL: A Proof Assistant for Higher-Order Logic. Berlin, Heidelberg: Springer-Verlag. ISBN 978-3-540-45949-1
HOL_(proof_assistant)
Proof assistant
mathematical assertions, mechanical checking of proofs of these assertions, assists in finding formal proofs using proof automation routines and extraction of a
Rocq
Structure editor for monomorphic Martin-Löf type theory
University. It is a predecessor of the Alfa, Agda, Cayenne and Rocq proof assistants and dependently typed programming languages. It was the first language
ALF_(proof_assistant)
Proof assistant program
LEGO is a proof assistant developed by Randy Pollack at the University of Edinburgh. It implements several type theories: the Edinburgh Logical Framework
LEGO_(proof_assistant)
Formal argument for the existence of God
Gödel's ontological proof is a formal argument by the mathematician Kurt Gödel (1906–1978) for the existence of God. The argument is in a line of development
Gödel's_ontological_proof
Functional programming language created in 2007
programming language similar to Haskell, but may also be used as a proof assistant. The Idris type system is similar to Agda's. Compared to Agda, Idris
Idris_(programming_language)
Functional programming language
considered a new language that shares a name and tradition. Agda is also a proof assistant based on the propositions-as-types paradigm (Curry–Howard correspondence)
Agda_(programming_language)
Reasoning for mathematical statements
that a published proof can, in principle, be converted into a formal proof. However, outside the field of automated proof assistants, this is rarely done
Mathematical_proof
Establishment of a theorem using inference from the axioms
Mathematical proof Proof assistant Proof calculus Proof theory Proof (truth) De Bruijn factor Kassios, Yannis (February 20, 2009). "Formal Proof" (PDF). cs
Formal_proof
Computer scientist
computer scientist, and creator of the Z3 Theorem Prover and the Lean proof assistant during his time at Microsoft Research. He currently works at AWS and
Leonardo_de_Moura
1995 publication in mathematics
Wiles's proof of Fermat's Last Theorem is a proof by British mathematician Andrew Wiles of a special case of the modularity theorem for elliptic curves
Wiles's proof of Fermat's Last Theorem
Wiles's_proof_of_Fermat's_Last_Theorem
Area of mathematics using condensed sets
and verified proof. Over a 6-month period, a group led by Johan Commelin verified the central part of the proof using the proof assistant Lean. As of 14
Condensed_mathematics
Proof assistant
Matita is an experimental proof assistant under development at the Computer Science Department of the University of Bologna. It is a tool aiding the development
Matita
Topics referred to by the same term
startup, how to start a company in a lean way Lean (proof assistant), a mathematical proof assistant and programming language Lean (drug), based on cough
Lean
Mathematical proof at least partially generated by computer
new proofs for known theorems.[citation needed] Additionally, interactive proof assistants allow mathematicians to develop human-readable proofs which
Computer-assisted_proof
Proof assistant program
for writing mathematical definitions and proofs, a proof assistant, which is able to mechanically check proofs written in this language, and a library
Mizar_system
1970s automated theorem prover
HOL, HOL Light, and the Isabelle proof assistant that supports various logics. As of 2019, the Isabelle proof assistant still contains an implementation
Logic for Computable Functions
Logic_for_Computable_Functions
Type theory created by Thierry Coquand
and hence consistent. The CoC has been developed alongside the Rocq proof assistant. As features were added (or possible liabilities removed) to the theory
Calculus_of_constructions
General purpose functional programming language
the pair into its three components. HOL (proof assistant) Hope (programming language) Isabelle (proof assistant) Nuprl Gordon, M.; Milner, R.; Wadsworth
ML_(programming_language)
Mathematical theory of data types
theory of types and Per Martin-Löf's intuitionistic type theory. Many proof assistants are based on type theory. For example, the underlying formal language
Type_theory
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
Formal language and associated computer program
language and an associated computer program (a proof assistant) for archiving and verifying mathematical proofs. Several databases of proved theorems have
Metamath
Type theory in logic and mathematics
make possible); and the formalization of each of these in computer proof assistants. There is a large overlap between the work referred to as homotopy
Homotopy_type_theory
Formally verified C compiler
Automation (INRIA). The compiler is specified, programmed and proven in proof assistant software named Rocq. CompCert is to be used to program embedded systems
CompCert
proved in January 2026 by Enrique Barschkis; the proof was formally verified in the Lean proof assistant. In March 2026, Erdős problem 369 was solved by
List of conjectures by Paul Erdős
List_of_conjectures_by_Paul_Erdős
Proof assistant program
Jape is a configurable, graphical proof assistant, originally developed by Richard Bornat at Queen Mary, University of London and Bernard Sufrin the University
Jape_(software)
Software for automated theorem proving
IsaPlanner is a proof planner for the interactive proof assistant, Isabelle, originally developed by Lucas Dixon. IsaPlanner 2: A Proof Planner in Isabelle
IsaPlanner
electronic programs that perform proof assistance with theorems in mathematical logic. In the 21st century, these proof assistant programs have given birth to
Logical_machine
Programming language
Dafny also allows the proof of properties between one function and another. As is common for a proof assistant, such proofs are often inductive in nature
Dafny
Sub-field of artificial intelligence
mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by human-machine collaboration
Argument_technology
Relationship between programs and proofs
language theory and proof theory, the Curry–Howard correspondence is a direct relationship between computer programs and mathematical proofs. It is also known
Curry–Howard_correspondence
Subfield of automated reasoning and mathematical logic
consequently more easily understandable and checkable, have been developed. Proof assistants require a human user to give hints to the system. Depending on the
Automated_theorem_proving
Analysis of computer programs without executing them
Union-find Tools Constraint solvers CHC SAT SMT Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar
Static_program_analysis
Canadian computer scientist
four color theorem and Feit–Thompson proof of the odd-order theorem. (Both were written using the proof assistant Rocq.) In 2011, as a principal researcher
Georges_Gonthier
Proof assistant program
MINLOG is a proof assistant developed at LMU Munich by the team of Helmut Schwichtenberg. MINLOG is based on first order natural deduction calculus. It
MINLOG
Data type in type theory
quotient types were defined and implemented as part of the Nuprl proof assistant, in work led by Robert L. Constable and others. Quotient types have
Quotient_type
Programming paradigm restricted to provably terminating programs
Total functional programming (also known as strong functional programming, to be contrasted with ordinary, or weak functional programming) is a programming
Total_functional_programming
Basic framework of mathematics
theory have also gained prevalence, being commonly used in computer proof assistants. It results from this that the basic mathematical concepts, such as
Foundations_of_mathematics
Concept in computer science
interactive theorem provers such as Rocq (previously known as Coq) and HOL (proof assistant). In comparison to the program analysis work, these tools require more
Separation_logic
Line-by-line system for natural deduction proofs
2025. "The Jape general-purpose proof assistant". GitHub. Retrieved 6 May 2025. (see Jape) "Resources for typesetting proofs in Fitch notation with LaTeX"
Fitch_notation
theories have semantics in various types of cubical sets. The Agda proof assistant includes an implementation of cubical type theory. Cubical type theory
Cubical_type_theory
Proof assistant program
In automated theorem proving, PhoX is a proof assistant based on higher-order logic which is eXtensible. The user gives PhoX an initial goal and guides
PhoX
Class of mathematical expression
by zero, which can 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
Division_by_zero
French computer scientist and mathematician
(formerly named Coq, the name is a reference partly to Coquand's surname) proof assistant, which he began developing in 1984 while working at INRIA (a French
Thierry_Coquand
Topics referred to by the same term
one of the álfar alf, ISO-639-3 code for the Alege language ALF (proof assistant), dependently typed programming language/theorem prover Action Language
ALF
German computer scientist (born 1958)
interactive and automatic theorem proving, in particular for the Isabelle proof assistant; he was the editor of the Journal of Automated Reasoning up to January
Tobias_Nipkow
Software projects developed at universities
Mizar – proof assistant and formal mathematics system (Białystok, Alberta, and Shinshu) Murφ – explicit-state model checker (Stanford) Nuprl – proof development
List of software developed at universities
List_of_software_developed_at_universities
Topics referred to by the same term
villages), mines, and dams Locale (Isabelle), a module of the Isabelle proof assistant Locale ('Ndrangheta), the main local organizational unit of the 'Ndrangheta
Locale
Topics referred to by the same term
Hol, a community in Duk County in Jonglei State in South Sudan HOL (proof assistant), a family of interactive theorem proving systems Head-of-line blocking
Hol
Controlled language
been used in the fields of software specifications, theorem proving, proof assistants, text summaries, ontologies, rules, querying, medical documentation
Attempto_Controlled_English
Rules to verify computer program correctness
deficiency in the axioms and rules quoted above is that they give no basis for a proof that a program successfully terminates. Failure to terminate may be due
Hoare_logic
incorrect (or no) proofs? Moritz. Theorems demoted back to conjectures Mei Zhang, Proofs shown to be wrong after formalization with proof assistant Steven-Owen
List_of_incomplete_proofs
Algorithm for computing Gröbner bases
implementation of Buchberger’s algorithm has been proved correct within the proof assistant Rocq (formerly named Coq). In the SymPy library for Python, the (improved)
Buchberger's_algorithm
Sequence of operations for a task
"The Spirit of Truth" for a history leading to, and a discussion of, his proof. Kleene, Stephen C. (1936). "General Recursive Functions of Natural Numbers"
Algorithm
Data structure for storing non-overlapping sets
disjoint-set forest data structure and formalized its correctness using the proof assistant Rocq (then: Coq). "Semi-persistent" means that previous versions of
Disjoint-set_data_structure
Computer program for the Boolean satisfiability problem
used to assist in proving mathematical theorems through computer-assisted proof. In Ramsey theory, several previously unknown Van der Waerden numbers were
SAT_solver
Italian computer scientist
a non-profit organization supporting the development of the Lean proof assistant and its ecosystem. Mathematics Genealogy Project https://www.phasecraft
Simone_Severini
Field of knowledge
include proof assistants and proof checkers is another area of computational mathematics that is used for formal verification and allowed formal proof of difficult
Mathematics
Classification theorem in group theory
more leisurely style. A fully formal proof, checked with the Rocq proof assistant, was announced in September 2012 by Georges Gonthier and fellow researchers
Feit–Thompson_theorem
Functional programming language
dependent types bring may be found in The Epigram Tutorial. ALF, a proof assistant among the predecessors of Epigram. McBride, Conor; McKinna, James (2004)
Epigram (programming language)
Epigram_(programming_language)
Dynamic window manager for X Window System
projects. This has included re-implementing xmonad using the Rocq proof assistant, a determination xmonad is an imperative program, and studies of package
Xmonad
Number in {..., –2, –1, 0, 1, 2, ...}
or pair(2,2), etc.. This technique of construction is used by the proof assistant Isabelle; however, many other tools use alternative construction techniques
Integer
Limitative results in mathematical logic
completely verified by proof assistant software. Gödel's original proofs of the incompleteness theorems, like most mathematical proofs, were written in natural
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
Of a function, an additional effect besides returning a value
Union-find Tools Constraint solvers CHC SAT SMT Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar
Side effect (computer science)
Side_effect_(computer_science)
Proof assistant program
HOL Light is a proof assistant for classical higher-order logic. It is a member of the HOL theorem prover family. Compared with other HOL systems, HOL
HOL_Light
Topics referred to by the same term
Theorem prover may refer to: Automated theorem prover Proof assistant, an interactive theorem prover This disambiguation page lists articles associated
Theorem_prover
Functional programming language inspired by ML and aimed at program verification
combination of satisfiability modulo theories (SMT) solving and manual proofs. For execution, programs written in F* can be translated to OCaml, F#, C
F*_(programming_language)
Math theorem about sphere packing
of a formal proof of the Kepler conjecture using a combination of the Isabelle and HOL Light proof assistants. In 2017, the formal proof was accepted
Kepler_conjecture
Area of mathematics
theorems (for example the four color theorem), and the design and use of proof assistants. Computational mathematics emerged as a distinct part of applied mathematics
Computational_mathematics
Software used in mathematical applications
Statistical software Numerical-analysis software Numerical libraries Proof assistants Solvers Discrete Computer algebra Computational number theory Combinatorics
Mathematical_software
Proof assistant program
under the GNU General Public License (GPL). Formal methods List of proof assistants Rosetta-lang Owre, Shankar, and Rushby, 1992. PVS: A Prototype Verification
Prototype_Verification_System
Incubator for philanthropic ventures
venture capital and transform into startups. Development for Lean (proof assistant) is supported by a FRO. E11 bio has a goal of creating a single-cell
Convergent_Research
Study of discrete mathematical structures
it can be easily verified with a truth table. The study of mathematical proof is particularly important in logic, and has accumulated to automated theorem
Discrete_mathematics
Branch of computer science
substantial subset of Standard ML programming language using the HOL proof assistant. Another approach to obtain a formally correct compiler is to use semantics-directed
Compiler_correctness
Topics referred to by the same term
Phox may refer to: Phox (band) PhoX, a proof assistant based on high order logic PHOX2A, a protein PHOX2B, a protein Phosphinooxazolines, a class of chiral
Phox
Topics referred to by the same term
processing JAPE, an automated pun generator Jape (software), a Java-based proof assistant Java Annotations Pattern Engine – see General Architecture for Text
Jape
Free and open-source VPN protocol
INRIA published a machine-checked proof of the WireGuard protocol, produced using the CryptoVerif proof assistant. WireGuard supports pre-shared symmetric
WireGuard
Planar maps require at most four colors
This proof remains unpublished, however. In 2005, Benjamin Werner and Georges Gonthier formalized a proof of the theorem inside the Coq proof assistant. This
Four_color_theorem
Computer science field
the violation is feasible, it is reported to the user. If it is not, the proof of infeasibility is used to refine the abstraction and checking begins again
Model_checking
Branch of mathematics concerning probability
both discrete and continuous distributions as well as others; separate proofs are not required for discrete and continuous distributions. Certain random
Probability_theory
Symmetry between bosons and fermions
four-dimensional gauge theories that interchanges particles and monopoles. The proof of the Atiyah–Singer index theorem is much simplified by the use of supersymmetric
Supersymmetry
Decidable first-order theory of the natural numbers with addition
example, the Rocq and Lean proof assistant systems feature the tactic omega for Presburger arithmetic and the Isabelle proof assistant contains a verified quantifier
Presburger_arithmetic
Study of abstract machines and automata
language. The pumping lemma for regular languages, also useful in regularity proofs, was proven in this period by Michael O. Rabin and Dana Scott, along with
Automata_theory
Formula for area of a grid polygon
of different proof assistants. As of 2024[update], Pick's theorem had been formalized and proven in only two of the ten proof assistants recorded by Wiedijk
Pick's_theorem
Process of analyzing computer program behavior
Union-find Tools Constraint solvers CHC SAT SMT Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar
Program_analysis
Study of the properties of codes and their fitness
Statistical software Numerical-analysis software Numerical libraries Proof assistants Solvers Discrete Computer algebra Computational number theory Combinatorics
Coding_theory
Method of forming inferences
goal. It is used in automated theorem provers, inference engines, proof assistants, and other artificial intelligence applications. In game theory, researchers
Backward_chaining
Formal languages for expressing mathematical theories
very influential in the later development of logical frameworks and proof assistants. The Mizar system, a system of writing and checking formalized mathematics
Automath
Programming language and theorem prover
Centaur Technology, IBM, Intel, Oracle, and Collins Aerospace. List of proof assistants "XDOC — Note-1-7". www.cs.utexas.edu. "ACM: Press Release, March 15
ACL2
Union-find Tools Constraint solvers CHC SAT SMT Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar
Hyperproperty
improve the proofs generated by automated theorem proving tools such as SAT solvers, SMT-solvers, first-order theorem provers and proof assistants. In propositional
Proof_compression
Approach to static program analysis
Union-find Tools Constraint solvers CHC SAT SMT Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar
Abstract_interpretation
Union-find Tools Constraint solvers CHC SAT SMT Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar
Dependence_analysis
Union-find Tools Constraint solvers CHC SAT SMT Lightweight Alloy TLA+ Proof assistants ACL2 Agda F* HOL Light HOL4 Idris Isabelle Isabelle/HOL Lean LEGO Mizar
Polyvariance
Association for Computing Machinery (ACM) special interest group
Prover 2014: GNU Compiler Collection (GCC) 2013: Rocq (then: Coq) proof assistant 2012: Jikes Research Virtual Machine (RVM) awarded to Bowen Alpern
SIGPLAN
Methods in artificial intelligence research
to be useful in a few domains such as computer algebra systems and proof assistants. A short history of symbolic AI to the present day follows below. Time
Symbolic artificial intelligence
Symbolic_artificial_intelligence
French computer scientist
constructions in 1984 with Thierry Coquand. He led the Coq (renamed Rocq) proof assistant project in the 1990s with Christine Paulin-Mohring, who developed Coq
Gérard_Huet
PROOF ASSISTANT
PROOF ASSISTANT
PROOF ASSISTANT
PROOF ASSISTANT
PROOF ASSISTANT
PROOF ASSISTANT
PROOF ASSISTANT
PROOF ASSISTANT
PROOF ASSISTANT