 
Summary: Lambda Calculi plus Letrec
Zena M. Ariola
Department of Computer & Information Sciences
University of Oregon. Eugene, OR 97401, USA
email: ariola@cs.uoregon.edu
Stefan Blom
Department of Mathematics and Computer Science
Vrije Universiteit, De Boelelaan 1081a, 1081 HV Amsterdam
email: sccblom@cs.vu.nl
The paper consists of three parts.
Part I: We establish an isomorphism between the wellformed cyclic lambdagraphs and their syntactic
representations. To define the wellformed cyclic lambdagraphs we introduce the notion of a scoped
lambdagraph. The wellformed lambdagraphs are those that have associated scoped lambdagraphs.
The scoped lambdagraphs are represented by terms defined over lambda calculus extended with the
letrec construct. On this set of terms we define a sound and complete axiom system (the represen
tational calculus) that equates different representations of the same scoped lambdagraph. Since a
wellformed lambdagraph can have different scoped lambdagraphs associated to it, we extend the
representational calculus with axioms that equate different representations of the same wellformed
graph. Finally, we consider the unwinding of wellformed graphs to possibly infinite trees and give a
sound and complete axiomatization of tree unwinding.
