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'''Interactive [[theorem proving]]''' is the field of [[computer science]] and [[mathematical logic]] concerned with tools to develop [[formal proof]]s by man-machine collaboration. This involves some sort of '''proof assistant''': an interactive proof editor, or other [[User interface|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]].
Examples include:
* [[HOL theorem prover]]s - 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:
**[http://hol.sourceforge.net/ HOL4] - The "primary descendant". [[Moscow ML]] based.
**[[HOL Light theorem prover|HOL Lite]] - A thriving "minimalist fork". [[OCaml]] based.
**[[Isabelle theorem prover|Isabelle]] - With a [[BSD license]]. Based on [[Standard ML]].
**[[ProofPower]] - Went commercial... then returned to open source. Based on [[Standard ML]].
* [[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.
* [[PhoX]] - A proof assistant based on higher-order logic which is eXtensible
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[[Category:Theorem provers]]
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