The Lean 4 Theorem Prover and Programming Language

The Lean Theorem Prover (System Description)

Lean is a new open source theorem prover being developed at Microsoft Research and Carnegie Mellon University, with a small trusted kernel based on dependent type theory. It aims to bridge the gap between interactive and automated theorem proving, by situating automated tools and methods in a framework that supports user interaction and the construction of fully specified axiomatic proofs. Lean...

Formalizing Mathematics using the Lean Theorem Prover

Java Embedding a Programming Language in a Theorem Prover

This paper introduces the subset Java of Java essentially by omitting everything but classes The type system and semantics of this language and a corresponding abstract Machine JVM are for malized in the theorem prover Isabelle HOL Type safety both of Java and the JVM are mechanically veri ed To make the paper self contained it begins with introductions to Isabelle HOL and the art of embedding ...

LangPro: Natural Language Theorem Prover

LangPro is an automated theorem prover for natural language. Given a set of premises and a hypothesis, it is able to prove semantic relations between them. The prover is based on a version of analytic tableau method specially designed for natural logic. The proof procedure operates on logical forms that preserve linguistic expressions to a large extent. The nature of proofs is deductive and tra...

The Heuristic Theorem Prover: Yet Another SMT Modulo Theorem Prover

HTP is an SMT Modulo theorem prover similar to many others.[2–6, 9, 11] As input, HTP accepts problems using the SMT-LIB format[8]. As output, HTP will answer either SAT, UNSAT or UNKNOWN. Alternatively, HTP can be run in a preprocessing mode in which the output is the simplified problem in SMTLIB format. An evidence file showing the derivation in a human readable form can be produced. There is...