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

Authors:
B. Intrigila;E. Biasone
Affiliations:
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;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
Venue:
Mathematical Structures in Computer Science
Year:
2000

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Abstract

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.