Embedding Display Calculi into Logical Frameworks: Comparing Twelf and Isabelle

Abstract

Logical frameworks are computer systems which allow a user to formalise mathematics using specially designed languages based upon mathematical logic and Church's theory of types. They can be used to derive programs from logical specifications, thereby guaranteeing the correctness of the resulting programs. They can also be used to formalise rigorous proofs about logical systems. We compare several methods of implementing the display (sequent) calculus δRA for relation algebra in the logical frameworks Isabelle and Twelf. We aim for an implementation enabling us to formalise, within the logical framework, proof-theoretic results such as the cut-elimination theorem for δRA, and any associated increase in proof length. We discuss issues arising from this requirement. Show more