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Many more predecessors: A representation workout

Part of: JFP Functional Pearls

Published online by Cambridge University Press:  30 March 2020

OLEG KISELYOV Open the ORCID record for OLEG KISELYOV [Opens in a new window]
OLEG KISELYOV*
Affiliation:
Tohoku University, Japan, (e-mail: oleg@okmij.org)
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Abstract

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From the outset, lambda calculus represented natural numbers through iterated application. The successor hence adds one more application, and the predecessor removes. In effect, the predecessor un-applies a term—which seemed impossible, even to Church. It took Kleene a rather oblique glance to sight a related representation of numbers, with an easier predecessor. Let us see what we can do if we look at this old problem with today’s eyes. We discern the systematic ways to derive more predecessors—smaller, faster, and sharper—while keeping all teeth.

Type
Functional Pearl
Information
Journal of Functional Programming , Volume 30 , 2020 , e7
Copyright
© The Author(s) 2020. Published by Cambridge University Press

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