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Lambda Calculus with Explicit Recursion Zena M. Ariola

Summary: Lambda Calculus with Explicit Recursion
Zena M. Ariola
Computer and Information Science Department
University of Oregon. Eugene, OR 97401, USA
email: ariola@cs.uoregon.edu
Jan Willem Klop
CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands
Department of Mathematics and Computer Science
Vrije Universiteit, De Boelelaan 1081a, 1081 HV Amsterdam
email: jwk@cwi.nl
This paper is concerned with the study of –­calculus with explicit recursion, namely of cyclic –­graphs. The
starting point is to treat a –­graph as a system of recursion equations involving –­terms, and to manipulate
such systems in an unrestricted manner, using equational logic, just as is possible for first­order term rewriting.
Surprisingly, now the confluence property breaks down in an essential way.
Confluence can be restored by introducing a restraining mechanism on the `substitution' operation. This
leads to a family of –­graph calculi, which can be seen as an extension of the family of –oe­calculi (–­calculi
with explicit substitution). While the –oe­calculi treat the let­construct as a first­class citizen, our calculi
support the letrec, a feature that is essential to reason about time and space behavior of functional languages


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


Collections: Computer Technologies and Information Sciences