Automated Proof Construction in Type Theory Using Resolution

Abstract

We provide techniques to integrate resolution logic with equality in type theory. The results may be rendered as follows. • A clausification procedure in type theory, equipped with a correctness proof, all encoded using higher-order primitive recursion. • A novel representation of clauses in minimal logic such that the λ-representation of resolution steps is linear in the size of the premisses. • A translation of resolution proofs into lambda terms, yielding a verification procedure for those proofs. • Availability of the power of resolution theorem provers in interactive proof construction systems based on type theory.