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Concept
Proof assistant
Summary
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.
A recent effort within this field is making these tools use artificial intelligence to automate the formalization of ordinary mathematics.
Dependent type#Comparison and Automated theorem proving#Comparison
ACL2 – 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.
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.
Lean
LEGO
Matita – A light system based on the Calculus of Inductive Constructions.
Official source
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