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- W3194008643 abstract "Weak reduction relations in the lambda-calculus are characterized by the rejection of the so-called xi-rule, which allows arbitrary reductions under abstractions. A notable instance of weak reduction can be found in the literature under the name restricted reduction or weak lambda-reduction.In this work, we attack the problem of algorithmically computing normal forms for lambda-wk, the lambda-calculus with weak lambda-reduction. We do so by first contrasting it with other weak systems, arguing that their notion of reduction is not strong enough to compute lambda-wk-normal forms. We observe that some aspects of weak lambda-reduction prevent us from normalizing lambda-wk directly, thus devise a new, better-behaved weak calculus lambda-ex, and reduce the normalization problem for lambda-w to that of lambda-ex. We finally define type systems for both calculi and apply Normalization by Evaluation to lambda-ex, obtaining a normalization proof for lambda-wk as a corollary. We formalize all our results in Agda, a proof-assistant based on intensional Martin-Lof Type Theory." @default.
- W3194008643 created "2021-08-30" @default.
- W3194008643 creator A5081750865 @default.
- W3194008643 date "2019-01-01" @default.
- W3194008643 modified "2023-09-24" @default.
- W3194008643 title "Normalization by Evaluation for Typed Weak lambda-Reduction" @default.
- W3194008643 doi "https://doi.org/10.4230/lipics.types.2018.6" @default.
- W3194008643 hasPublicationYear "2019" @default.
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