Superdeduction in Lambda-Bar-Mu-Mu-Tilde

TL;DR

This paper extends the Lambda bar mu mu tilde calculus to incorporate superdeduction, providing a proof-term language and cut-elimination, and proves strong normalization, bridging superdeduction with lambda-calculus based proof theory.

Contribution

It introduces a lambda-calculus extension for superdeduction, enabling proof-term representation and cut-elimination, and establishes strong normalization for this system.

Findings

Extended Lambda bar mu mu tilde calculus with superdeduction

Developed proof-term language for superdeduction

Proved strong normalization of the extended calculus

Abstract

Superdeduction is a method specially designed to ease the use of first-order theories in predicate logic. The theory is used to enrich the deduction system with new deduction rules in a systematic, correct and complete way. A proof-term language and a cut-elimination reduction already exist for superdeduction, both based on Christian Urban's work on classical sequent calculus. However the computational content of Christian Urban's calculus is not directly related to the (lambda-calculus based) Curry-Howard correspondence. In contrast the Lambda bar mu mu tilde calculus is a lambda-calculus for classical sequent calculus. This short paper is a first step towards a further exploration of the computational content of superdeduction proofs, for we extend the Lambda bar mu mu tilde calculus in order to obtain a proofterm langage together with a cut-elimination reduction for superdeduction. We also prove strong normalisation for this extension of the Lambda bar mu mu tilde calculus.