Summary: Cyclic Lambda Calculi
Zena M. Ariola 1 and Stefan Blom 2
1 Department of Computer & Information Sciences
University of Oregon. Eugene, OR 97401, USA
email: ariola@cs.uoregon.edu
2 Department of Mathematics and Computer Science
Vrije Universiteit, De Boelelaan 1081a, 1081 HV Amsterdam
email: sccblom@cs.vu.nl
Abstract. We precisely characterize a class of cyclic lambda­graphs,
and then give a sound and complete axiomatization of the terms that
represent a given graph. The equational axiom system is an extension of
lambda calculus with the letrec construct. In contrast to current theo­
ries, which impose restrictions on where the rewriting can take place, our
theory is very liberal, e.g., it allows rewriting under lambda­abstractions
and on cycles. As shown previously, the reduction theory is non­confluent.
We thus introduce an approximate notion of confluence. Using this no­
tion we define the infinite normal form or L'evy­Longo tree of a cyclic
term. We show that the infinite normal form defines a congruence on
the set of terms. We relate our cyclic lambda calculus to the traditional
lambda calculus and to the infinitary lambda calculus.

Source: Ariola, Zena M. - Department of Computer and Information Science, University of Oregon

Collections: Computer Technologies and Information Sciences