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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.
An interactive proof session in CoqIDE, showing the proof script on the left and the proof state on the right. Coq is an interactive theorem prover first released in 1989. It allows for expressing mathematical assertions, mechanically checks proofs of these assertions, helps find formal proofs, and extracts a certified program from the constructive proof of its formal specification.
In computer science and mathematical logic, Cooperating Validity Checker (CVC) is a family of satisfiability modulo theories (SMT) solvers. The latest major versions of CVC are CVC4 and CVC5 (stylized cvc5); earlier versions include CVC, CVC Lite, and CVC3. [ 2 ]
The Isabelle [a] automated theorem prover is a higher-order logic (HOL) theorem prover, written in Standard ML and Scala.As a Logic for Computable Functions (LCF) style theorem prover, it is based on a small logical core (kernel) to increase the trustworthiness of proofs without requiring, yet supporting, explicit proof objects.
[2]: 60 When the user adds and removes the proof steps, the proof tree is constructed which Jape can show either in a tree shape or in box forms. [5] Jape allows to display proofs at different levels of abstraction. It is also possible to present a forward proof in a natural deduction style by using the specialized modes of display for proofs. [6]
CTL: Computation Tree Logic; a branching-time logic, meaning that its model of time is a tree-like structure in which the future is not determined; there are different paths in the future, any one of which might be an actual path that is realized. Invariants: Predicates over a system state.
Metamath is a formal language and an associated computer program (a proof assistant) for archiving and verifying mathematical proofs. [2] 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.
Among subsequent implementations is Cambridge LCF. Later systems simplified the logic to use total instead of partial functions, leading to HOL, HOL Light, and the Isabelle proof assistant that supports various logics. As of 2019, the Isabelle proof assistant still contains an implementation of an LCF logic, Isabelle/LCF.