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Lambda Calculi plus Letrec Zena M. Ariola

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.


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


Collections: Computer Technologies and Information Sciences