A logic programming language with Lambda-abstraction, function variables, and simple unification
Proceedings of the international workshop on Extensions of logic programming
Logic programming in a fragment of intuitionistic linear logic
Papers presented at the IEEE symposium on Logic in computer science
Term rewriting and all that
Deduction versus Computation: The Case of Induction
AISC '02/Calculemus '02 Proceedings of the Joint International Conferences on Artificial Intelligence, Automated Reasoning, and Symbolic Computation
RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
A simple class of Kripke-style models in which logic and computation have equal standing
LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
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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 describe 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.