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Theoretical Pearls

An unsolvable numeral system in lambda calculus

Part of: JFP Research Articles

Published online by Cambridge University Press:  07 November 2008

Erik Barendsen
Erik Barendsen
Affiliation:
Department of Computer Science, University of Nijmegen, Toernooiveld 1, 6525 ED Nijmegen, The Netherlands. E-mail: erikb@cs.kun.nl.
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Abstract

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For numeral systems in untyped λ-calculus the definability of a successor, a predecessor and a test for zero implies the definability of all recursive functions on that system. Towards a disproof of the converse statement, H. P. Barendregt and the author constructed a numeral system consisting of unsolvable λ-terms, being adequate for unary functions. Then, independently, B. Intrigila found an analogous system for all computable functions.

Type
Articles
Information
Journal of Functional Programming , Volume 1 , Issue 3 , July 1991 , pp. 367 - 372
Copyright
Copyright © Cambridge University Press 1991

References

Barendregt, H. P. (1984) The lambda calculus: its syntax and semantics, Studies in logic 103. North-Holland.Google Scholar
Intrigila, B. 1990. Some results on numeral systems in λ-calculus. Typescript, Rome, Italy.Google Scholar
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