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.
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Bezem, M., Hendriks, D. & de Nivelle, H. Automated Proof Construction in Type Theory Using Resolution. Journal of Automated Reasoning 29, 253–275 (2002). https://doi.org/10.1023/A:1021939521172
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DOI: https://doi.org/10.1023/A:1021939521172