Proof assistant

For the academic conference, see Interactive Theorem Proving (conference).
Not to be confused with Interactive proof system.
An interactive proof session in CoqIDE, showing the proof script on the left and the proof state on the right.

In computer science and 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. 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.

Comparison of systems

Name Latest version Developer(s) Implementation language Features
Higher-order logic Dependent types Small kernel Proof automation Proof by reflection Code generation
ACL2 7.1 Matt Kaufmann and J Strother Moore Common Lisp No Untyped No Yes Yes[1] Already executable
Agda Ulf Norell, Nils Anders Danielsson, and Andreas Abel (Chalmers and Gothenburg) HaskellYes Yes Yes No Partial Already executable
Albatross 0.3 Helmut Brandl OcamlYes No Yes Yes Unknown not yet implemented
Coq 8.5pl3 INRIA OCaml Yes Yes Yes Yes Yes Yes
F* repository Microsoft Research and Inria F* Yes Yes No Yes Unknown Yes
Lean repository Microsoft Research C++ Yes Yes Yes Yes Yes Unknown
HOL Light repository John Harrison OCaml Yes No Yes Yes No No
HOL4 Kananaskis-8 (or repo) Michael Norrish, Konrad Slind, and others Standard ML Yes No Yes Yes No Yes
Isabelle 2016 Larry Paulson (Cambridge), Tobias Nipkow (München) and Makarius Wenzel (Paris-Sud) Standard ML, Scala Yes No Yes Yes Yes Yes
LEGO 1.3.1 Randy Pollack (Edinburgh) Standard ML Yes Yes Yes No No No
Mizar 8.1.05 Białystok University Free Pascal Partial Yes No No No No
NuPRL 5 Cornell University Common Lisp Yes Yes Yes Yes Unknown Yes
PVS 5.0 SRI International Common Lisp Yes Yes No Yes No Unknown
Twelf 1.7.1 Frank Pfenning and Carsten Schürmann Standard ML Yes Yes Unknown No No Unknown

User interface

A popular front-end for proof assistants is the Emacs-based Proof General, developed at the University of Edinburgh. Coq includes CoqIDE, which is based on OCaml/Gtk. Isabelle includes Isabelle/jEdit, which is based on jEdit and the Isabelle/Scala infrastructure for document-oriented proof processing.

See also


  1. Hunt, Warren; Matt Kaufmann; Robert Bellarmine Krug; J Moore; Eric W. Smith (2005). "Meta Reasoning in ACL2" (PDF). Springer Lecture Notes in Computer Science. 3603: 163–178.

External links

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