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**1 - 1**of**1**### WFLP 2008 Term sequent logic

"... We consider a term sequent logic for the lambda-calculus. Term sequents are a judgement form similar to the logical judgement form of entailment between sentences, but denoting equality or reducibility between terms. Using term sequents, it is possible to treat lambda-terms almost like logical sente ..."

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We consider a term sequent logic for the lambda-calculus. Term sequents are a judgement form similar to the logical judgement form of entailment between sentences, but denoting equality or reducibility between terms. Using term sequents, it is possible to treat lambda-terms almost like logical sentences, and to use proof-theoretic methods to establish their properties. We prove a cut-elimination result for untyped lambda-calculus and de-scribe how this generalises the usual confluence result. We give a notion of uniform proof for lambda-terms, and suggest how this can be viewed as a mixed logic-programming/functional programming framework with the ability to assume arbitrary reductions. Finally, we discuss related and future work.