Automated Proof Construction in Type Theory Using Resolution

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. − The power of resolution theorem provers becomes available in interactive proof construction systems based on type theory.

• Type: Conference
• Year: 2000
• Where: CADE
• Authors: Marc Bezem, Dimitri Hendriks, Hans de Nivelle
• Keywords: CADE 2000, Logical Reasoning, Resolution Logic, Resolution Theorem Provers, Type Theory