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A (machine-oriented) logic based on pattern matching

Published online by Cambridge University Press:  05 July 2023

Tim Lethen Open the ORCID record for Tim Lethen [Opens in a new window]
Tim Lethen*
Affiliation:
Department of Philosophy, University of Helsinki, Helsinki, Finland
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Email: tim.lethen@gmx.de
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Abstract

Robinson’s unification algorithm can be identified as the underlying machinery of both C. Meredith’s rule D (condensed detachment) in propositional logic and of the construction of principal types in lambda calculus and combinatory logic. In combinatory logic, it also plays a crucial role in the construction of Meyer, Bunder & Powers’ Fool’s model. This paper now considers pattern matching, the unidirectional variant of unification, as a basis for logical inference, typing, and a very simple and natural model for untyped combinatory logic. An analysis of the new typing scheme will enable us to characterize a large class of terms of combinatory logic which do not change their principal type when being weakly reduced. We also consider the question whether the major or the minor premisse should be used as the fixed pattern.

Keywords

Pattern matchingUnificationCondensed detachmentPrincipal typesCombinatory logicFool’s model

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Type
Paper
Information
Mathematical Structures in Computer Science , Volume 33 , Issue 7 , August 2023 , pp. 647 - 659
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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