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Operational aspects of untyped Normalisation by Evaluation

Published online by Cambridge University Press:  05 August 2004

KLAUS AEHLIG
Affiliation:
Mathematisches Institut der Ludwig-Maximilians-Universität München, Theresienstrasse 39, 80333 München, Germany
FELIX JOACHIMSKI
Affiliation:
Mathematisches Institut der Ludwig-Maximilians-Universität München, Theresienstrasse 39, 80333 München, Germany

Abstract

A purely syntactic and untyped variant of Normalisation by Evaluation for the $\lambda$-calculus is presented in the framework of a two-level $\lambda$-calculus with rewrite rules to model the inverse of the evaluation functional. Among its operational properties there is a standardisation theorem that formally establishes the adequacy of implementation in functional programming languages. An example implementation in Haskell is provided. The relation to the usual type-directed Normalisation by Evaluation is highlighted, using a short analysis of $\eta$-expansion that leads to a perspicuous strong normalisation and confluence proof for $\beta\eta\!\up$-reduction as a byproduct.

Type
Paper
Copyright
2004 Cambridge University Press

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