How to circumvent church numerals

Authors:
Mayer Goldberg;Mads Torgersen
Affiliations:
Department of Computer Science, Ben Gurion University Be'er Sheva 84105, Israel;Department of Computer Science, University of Aarhus Aabogade 34, DK-8200 Aarhus N, Denmark
Venue:
Nordic Journal of Computing
Year:
2002

Citing 4
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Abstract

In this work we consider a standard numeral system in the lambda-calculus, and the elementary arithmetic and Boolean functions and predicates defined on this numeral system, and show how to construct terms that "circumvent" or "defeat" these functions: The equality predicate is satisfied when comparing these special terms to any numeral, the zero predicate is satisfied for these terms, etc. We believe this exercise offers an instructive look at what definability means in the untyped lambda-calculus.