A sequent calculus with implicit term representation

Authors:
Stefan Hetzl
Affiliations:
Laboratoire Preuves, Programmes et Systèmes, Université Paris Diderot, Paris, France
Venue:
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
Year:
2010

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Abstract

We investigate a modification of the sequent calculus which separates a first-order proof into its abstract deductive structure and a unifier which renders this structure a valid proof. We define a cutelimination procedure for this calculus and show that it produces the same cut-free proofs as the standard calculus, but, due to the implicit representation of terms, it provides exponentially shorter normal forms. This modified calculus is applied as a tool for theoretical analyses of the standard calculus and as a mechanism for a more efficient implementation of cut-elimination.