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.
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Near, J.P., Byrd, W.E., Friedman, D.P. (2008). α lean TA P: A Declarative Theorem Prover for First-Order Classical Logic. In: Garcia de la Banda, M., Pontelli, E. (eds) Logic Programming. ICLP 2008. Lecture Notes in Computer Science, vol 5366. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89982-2_26
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DOI: https://doi.org/10.1007/978-3-540-89982-2_26
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