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arXiv · 1406.2059

Normalization by Evaluation in the Delay Monad: A Case Study for Coinduction via Copatterns and Sized Types

Andreas Abel·James Chapman
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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 eta-long beta-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.

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Andreas Abel, James Chapman. 2014-06-09. Normalization by Evaluation in the Delay Monad: A Case Study for Coinduction via Copatterns and Sized Types. https://doi.org/10.4204/eptcs.153.4

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