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Theoretical Pearls: Representing ‘undefined’ in lambda calculus

Part of: JFP Research Articles

Published online by Cambridge University Press:  07 November 2008

Henk Barendregt
Henk Barendregt
Affiliation:
Faculty of Mathematics and Computer Science, Catholic University Nijmegen, Toernooiveld 1, 6525 ED, The Netherlands (e-mail: henk@cs.kun.nl)
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Abstract

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Let ψ be a partial recursive function (of one argument) with λ-defining term F∈Λ°. This meansThere are several proposals for what F⌜n⌝ should be in case ψ(n) is undefined: (1) a term without a normal form (Church); (2) an unsolvable term (Barendregt); (3) an easy term (Visser); (4) a term of order 0 (Statman).

These four possibilities will be covered by one ‘master’ result of Statman which is based on the ‘Anti Diagonal Normalization Theorem’ of Visser (1980). That ingenious theorem about precomplete numerations of Ershov is a powerful tool with applications in recursion theory, metamathematics of arithmetic and lambda calculus.

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Type
Articles
Information
Journal of Functional Programming , Volume 2 , Issue 3 , July 1992 , pp. 367 - 374
Copyright
Copyright © Cambridge University Press 1992

References

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