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Conditions for the completeness of functional and algebraic equational reasoning

Published online by Cambridge University Press:  01 December 1999

JON G. RIECKE
Affiliation:
Bell Laboratories, Lucent Technologies, 700 Mountain Avenue, Murray Hill, New Jersey 07974, USA
RAMESH SUBRAHMANYAM
Affiliation:
Department of Mathematics, Wesleyan University, Middletown, Connecticut 06459, USA Current address: Lucent Technologies, 2000 Naperville Road, PO Box 3033, Naperville, Illinois 60566-7033, USA.

Abstract

We consider the following question: in the simply-typed λ-calculus with algebraic operations, is the set of equations valid in a particular model exactly those provable from (β), (η) and the set of algebraic equations, E, that are valid in the model? We find conditions for determining whether βηE-equational reasoning is complete. We demonstrate the utility of the results by presenting a number of simple corollaries for particular models.

Type
Research Article
Copyright
1999 Cambridge University Press

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Footnotes

A preliminary version titled ‘Algebraic Reasoning and Completeness in Typed Languages’ appeared in Twentieth ACM Conference on Principles of Programming Languages, pages 185–195, ACM Press, 1993.

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