NDLI: Nested proof search as reduction in the Lambda-calculus

Content Provider	ACM Digital Library
Author	Guenot, Nicolas
Abstract	We present a system for propositional implicative intuitionistic logic in the calculus of structures, which is a generalisation of the sequent calculus to the deep inference methodology. We show that it is sound and complete with respect to the usual sequent calculus, and consider a restricted system for a smaller class of formulas. Then, we encode lambda-terms with explicit substitutions in these formulas and exhibit a correspondence between proof search in this system and reduction in a lambda-calculus with explicit substitutions. Finally, we present a further restriction to allow a correspondence with the standard lambda-calculus, and show that we can prove results on lambda-calculi by proving results on derivations in the proof systems.
Starting Page	183
Ending Page	194
Page Count	12
File Format	PDF
ISBN	9781450307765
DOI	10.1145/2003476.2003501
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2011-07-20
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Intuitionistic logic Explicit substitutions Focusing Lambda calculus Evaluation strategies Proof search Deep inference
Content Type	Text
Resource Type	Article

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Nested proof search as reduction in the Lambda-calculus