Extensional rewriting with sums

Authors:
Sam Lindley
Affiliations:
Laboratory for Foundations of Computer Science, School of Informatics, The University of Edinburgh
Venue:
TLCA'07 Proceedings of the 8th international conference on Typed lambda calculi and applications
Year:
2007

Citing 8
Cited 2

Proofs and types

Proofs and types
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ßn-Equality for Coproducts

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Normalization by Evaluation for Typed Lambda Calculus with Coproducts

LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
Extensional normalisation and type-directed partial evaluation for typed lambda calculus with sums

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Reducibility and ⊤⊤-lifting for computation types

TLCA'05 Proceedings of the 7th international conference on Typed Lambda Calculi and Applications
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Proceedings of the 18th ACM SIGPLAN international conference on Functional programming

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Abstract

Inspired by recent work on normalisation by evaluation for sums, we propose a normalising and confluent extensional rewriting theory for the simply-typed λ-calculus extended with sum types. As a corollary of confluence we obtain decidability for the extensional equational theory of simply-typed λ-calculus extended with sum types. Unlike previous decidability results, which rely on advanced rewriting techniques or advanced category theory, we only use standard techniques.