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Normalization by evaluation in the delay monad: A case study for coinduction via copatterns and sized types

Conference paper
Authors Andreas Abel
James Chapman
Published in Electronic Proceedings in Theoretical Computer Science, EPTCS
ISSN 2075-2180
Publication year 2014
Published at Department of Computer Science and Engineering (GU)
Language en
Subject categories Software Engineering, Theoretical computer science

Abstract

In this paper, we present an Agda formalization of a normalizer for simply-typed lambda terms. The normalizer consists of two coinductively defined functions in the delay monad: One is a standard evaluator of lambda terms to closures, the other a type-directed reifier from values to h-long b-normal forms. Their composition, normalization-by-evaluation, is shown to be a total function a posteriori, using a standard logical-relations argument. The successful formalization serves as a proof-of-concept for coinductive programming and reasoning using sized types and copatterns, a new and presently experimental feature of Agda.

Page Manager: Webmaster|Last update: 9/11/2012
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