Proof assistants

software for interactive and automated theorem proving

thumb|300x300px|An interactive proof session in CoqIDE, showing the proof script on the left and the proof state on the right.

dependently typed, purely functional programming language and proof assistant

proof assistant

software tool to assist with the development of formal proofs by human-machine collaboration

Metamath is a formal language and an associated computer program (a proof assistant) for archiving and verifying mathematical proofs. Several databases of proved theorems have been developed using Metamath covering standard results in logic, set theory, number theory, algebra, topology and analysis, among others.

functional programming language inspired by ML and aimed at program verification

higher-order logic (HOL) automated theorem prover