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Implementing a normalizer using sized heterogeneous types

Part of: JFP Research Articles

Published online by Cambridge University Press:  01 July 2009

ANDREAS ABEL
ANDREAS ABEL*
Affiliation:
Institut für Informatik, Ludwig-Maximilians-Universität München, Oettingenstraße 67, D-80538 München, Germany (e-mail: andreas.abel@ifi.lmu.de)

Abstract

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In the simply typed λ-calculus, a hereditary substitution replaces a free variable in a normal form r by another normal form s of type a, removing freshly created redexes on the fly. It can be defined by lexicographic induction on a and r, thus giving rise to a structurally recursive normalizer for the simply typed λ-calculus. We implement hereditary substitutions in a functional programming language with sized heterogeneous inductive types , arriving at an interpreter whose termination can be tracked by the type system of its host programming language.

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Type
Articles
Information
Journal of Functional Programming , Volume 19 , Issue 3-4 , July 2009 , pp. 287 - 310
Copyright
Copyright © Cambridge University Press 2009

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