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Jape allows to make proof steps and undo them, and it shows the effect of the added proof steps which helps to understand strategies for finding proofs. [ 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 ]
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 ...
Vampire is an automatic theorem prover for first-order classical logic developed in the Department of Computer Science at the University of Manchester. Up to Version 3, it was developed by Andrei Voronkov together with Kryštof Hoder and previously with Alexandre Riazanov. Since Version 4, the development has involved a wider international team ...
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.
An online Java application for proof building Archived 2006-10-02 at the Wayback Machine; A Web implementation of Fitch proof system (propositional and first-order) at proofmod.mindconnect.cc; The Jape general-purpose proof assistant (see Jape) Resources for typesetting proofs in Fitch notation with LaTeX (see LaTeX)
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.
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Depending on the underlying logic, the problem of deciding the validity of a formula varies from trivial to impossible. For the common case of propositional logic, the problem is decidable but co-NP-complete, and hence only exponential-time algorithms are believed to exist for general proof tasks.