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Theoretical Pearls Enumerators of lambda terms are reducing

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JohnHughes (Ed); Functional Programming Langauges and Computer Architecture. Proceedings of the fifth conference (Cambridge, MA, 28–30081991) Volume 523 of Lecture Notes in Computer Science, Springer-Verlag. 666 pp.

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 of Nijmegen, The Netherlands
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Abstract

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A closed λ-term E is called an enumerator if

Here ⋀0 is the set of closed λ-terms,. is the set of natural numbers and the ⌜n⌝ are the Church's numerals λfx.fnx. Such an E is called reducing if, moreover

An ingenious recursion theoretic proof by Statman will be presented, showing that every enumerator is reducing. I do not know any direct proof.

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Type
Articles
Information
Journal of Functional Programming , Volume 2 , Issue 2 , April 1992 , pp. 233 - 236
Copyright
Copyright © Cambridge University Press 1992

References

Barendregt, H. P. 1971. Some extensional term models for lambda calculi and combinatory logics. PhD thesis, Utrecht University.Google Scholar
Barendregt, H. P. 1991. Theoretical pearls: Self-interpretation in lambda calculus. J. Functional Programming, 1 (2), 229–234.CrossRefGoogle Scholar
Kleene, S. C. 1936. λ-definability and recursiveness. Duke Math. J., 2, 340–353.CrossRefGoogle Scholar
Mulder, J. C. 1990. Case studies in process specification and verification. PhD thesis, University of Amsterdam.Google Scholar
Statman, R. 1987. Two recursion theoretic problems in lambda calculus. Manuscript, Department of Mathematics, Carnegie Mellon University, Pittsburgh, PA.Google Scholar
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