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

Authors:
Joseph P. Near;William E. Byrd;Daniel P. Friedman
Affiliations:
Indiana University, Bloomington, IN 47405,;Indiana University, Bloomington, IN 47405,;Indiana University, Bloomington, IN 47405,
Venue:
ICLP '08 Proceedings of the 24th International Conference on Logic Programming
Year:
2008

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Abstract

We present α lean TA P , adeclarative tableau-based theorem prover written as a purerelation. Like lean TA P , on which it is based,α lean TA P can prove groundtheorems in first-order classical logic. Since it is declarative,α lean TA P generates theorems and accepts non-ground theorems and proofs. The lack ofmode restrictions also allows the user to provide guidance inproving complex theorems and to ask the prover to instantiatenon-ground parts of theorems. We present a complete implementationof α lean TA P , beginning with atranslation of lean TA P intoα Kanren, an embedding of nominal logic programmingin Scheme. We then show how to use a combination of tagging andnominal unification to eliminate the impure operators inheritedfrom lean TA P , resulting in a purely declarativetheorem prover.