α lean TA P: A Declarative Theorem Prover for First-Order Classical Logic

Abstract

We present α lean TA P, a declarative tableau-based theorem prover written as a pure relation. Like lean TA P, on which it is based, α lean TA P can prove ground theorems in first-order classical logic. Since it is declarative, α lean TA P generates theorems and accepts non-ground theorems and proofs. The lack of mode restrictions also allows the user to provide guidance in proving complex theorems and to ask the prover to instantiate non-ground parts of theorems. We present a complete implementation of α lean TA P, beginning with a translation of lean TA P into αKanren, an embedding of nominal logic programming in Scheme. We then show how to use a combination of tagging and nominal unification to eliminate the impure operators inherited from lean TA P, resulting in a purely declarative theorem prover.KeywordsLogic ProgrammingTheorem ProverLogic VariableAutomate DeductionLogic Programming LanguageThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.