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On the number of fixed points of a combinator in lambda calculus

Published online by Cambridge University Press:  10 November 2000

B. INTRIGILA  and
E. BIASONE
B. INTRIGILA
Affiliation:
Dipartimento di Matematica Pura e Applicata, Universitá Di L'Aquila, Via Vetoio, 67010 Coppito, L'Aquila, Italy. Email: intrigil@univaq.it and e.biasone@reply.it
E. BIASONE
Affiliation:
Dipartimento di Matematica Pura e Applicata, Universitá Di L'Aquila, Via Vetoio, 67010 Coppito, L'Aquila, Italy. Email: intrigil@univaq.it and e.biasone@reply.it
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Abstract

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We consider the problem of determining the number of fixed points of a combinator (a closed λ-term). This appears to be a still unsolved problem. We give a partial answer by showing that if there is a fixed point in normal form, then this fixed point is unique or there are infinitely many fixed points.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 10 , Issue 5 , October 2000 , pp. 595 - 615
Copyright
2000 Cambridge University Press