In

Theorem Prover Museum

in ''Certified Programming with Dependent Types''.

Introduction to the Coq Proof Assistant

(with a general introduction to interactive theorem proving)

A list of theorem proving tools

; Catalogues

*

Science: Math: Logic and Foundations: Computational Logic: Logical Frameworks

Argument technology Automated theorem proving de:Maschinengestütztes Beweisen

computer science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to practical disciplines (includi ...

and mathematical logic
Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal ...

, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proof
In logic and mathematics, a formal proof or derivation is a finite sequence of sentences (called well-formed formulas in the case of a formal language), each of which is an axiom, an assumption, or follows from the preceding sentences in the sequ ...

s by human-machine collaboration. This involves some sort of interactive proof editor, or other interface, with which a human can guide the search for proofs, the details of which are stored in, and some steps provided by, a computer
A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations ( computation) automatically. Modern digital electronic computers can perform generic sets of operations known as programs. These p ...

.
System comparison

*ACL2
ACL2 ("A Computational Logic for Applicative Common Lisp") is a software system consisting of a programming language, created by Timothy Still it was an extensible theory in a first-order logic, and an automated theorem prover. ACL2 is designed t ...

– a programming language, a first-order logical theory, and a theorem prover (with both interactive and automatic modes) in the Boyer–Moore tradition.
* Coq – Allows the expression of mathematical assertions, mechanically checks proofs of these assertions, helps to find formal proofs, and extracts a certified program from the constructive proof of its formal specification.
* HOL theorem provers – A family of tools ultimately derived from the LCF theorem prover. In these systems the logical core is a library of their programming language. Theorems represent new elements of the language and can only be introduced via "strategies" which guarantee logical correctness. Strategy composition gives users the ability to produce significant proofs with relatively few interactions with the system. Members of the family include:
** HOL4 – The "primary descendant", still under active development. Support for both Moscow ML and Poly/ML. Has a BSD-style license
BSD licenses are a family of permissive free software licenses, imposing minimal restrictions on the use and distribution of covered software. This is in contrast to copyleft licenses, which have share-alike requirements. The original BSD lic ...

.
** HOL Light – A thriving "minimalist fork". OCaml
OCaml ( , formerly Objective Caml) is a general-purpose, multi-paradigm programming language which extends the Caml dialect of ML with object-oriented features. OCaml was created in 1996 by Xavier Leroy, Jérôme Vouillon, Damien Doligez, ...

based.
**ProofPower – Went proprietary, then returned to open source. Based on Standard ML.
* IMPS, An Interactive Mathematical Proof System
* Isabelle is an interactive theorem prover, successor of HOL. The main code-base is BSD-licensed, but the Isabelle distribution bundles many add-on tools with different licenses.
* Jape – Java based.
* Lean
Lean, leaning or LEAN may refer to:
Business practices
* Lean thinking, a business methodology adopted in various fields
** Lean construction, an adaption of lean manufacturing principles to the design and construction process
** Lean governm ...

* LEGO
Lego ( , ; stylized as LEGO) is a line of plastic construction toys that are manufactured by The Lego Group, a privately held company based in Billund, Denmark. The company's flagship product, Lego, consists of variously colored interlockin ...

* Matita – A light system based on the Calculus of Inductive Constructions.
* MINLOG – A proof assistant based on first-order minimal logic.
* Mizar – A proof assistant based on first-order logic, in a natural deduction style, and Tarski–Grothendieck set theory.
* PhoX
PHOX was an American six-piece alternative folk / indie pop band from Baraboo, Wisconsin. Active from 2011 until 2017, they released their self-titled debut LP on June 24, 2014.
History
Prior to the formation of PHOX, many eventual members co ...

– A proof assistant based on higher-order logic which is eXtensible.
* Prototype Verification System (PVS) – a proof language and system based on higher-order logic.
* TPS and ETPS – Interactive theorem provers also based on simply-typed lambda calculus, but based on an independent formulation of the logical theory and independent implementation.
User interfaces

A popular front-end for proof assistants is theEmacs
Emacs , originally named EMACS (an acronym for "Editor MACroS"), is a family of text editors that are characterized by their extensibility. The manual for the most widely used variant, GNU Emacs, describes it as "the extensible, customizable, ...

-based Proof General, developed at the University of Edinburgh
The University of Edinburgh ( sco, University o Edinburgh, gd, Oilthigh Dhùn Èideann; abbreviated as ''Edin.'' in post-nominals) is a public research university based in Edinburgh, Scotland. Granted a royal charter by King James VI in 1 ...

.
Coq includes CoqIDE, which is based on OCaml/Gtk
GTK (formerly GIMP ToolKit and GTK+) is a free and open-source cross-platform widget toolkit for creating graphical user interfaces (GUIs). It is licensed under the terms of the GNU Lesser General Public License, allowing both free and proprie ...

. Isabelle includes Isabelle/jEdit, which is based on jEdit and the Isabelle/ Scala infrastructure for document-oriented proof processing. More recently, a Visual Studio Code extension for Isabelle has also been developed by Makarius Wenzel.
See also

* * * * * *Notes

References

* * * * * *External links

{{external links, date=December 2022Theorem Prover Museum

in ''Certified Programming with Dependent Types''.

Introduction to the Coq Proof Assistant

(with a general introduction to interactive theorem proving)

A list of theorem proving tools

; Catalogues

*

DMOZ
DMOZ (from ''directory.mozilla.org'', an earlier domain name, stylized in lowercase in its logo) was a multilingual open-content directory of World Wide Web links. The site and community who maintained it were also known as the Open Directory ...

Science: Math: Logic and Foundations: Computational Logic: Logical Frameworks

Argument technology Automated theorem proving de:Maschinengestütztes Beweisen