Proof assistant

Comparison of systems

• ACL2 – a programming language, a first-order logical theory, and a theorem prover in the Boyer–Moore tradition.
• Coq – Which 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:
• * – The "primary descendant", still under active development. Support for both Moscow ML and Poly/ML. Has a BSD-style license.
• *HOL Light – A thriving "minimalist fork". OCaml 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.
• 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 – A proof assistant based on higher-order logic which is eXtensible.
• Prototype Verification System – a proof language and system based on higher-order logic.
• – 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