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Rewriting on cyclic structures: Equivalence between the operational and the categorical description

Published online by Cambridge University Press:  15 August 2002

Andrea Corradini  and
Fabio Gadducci
Andrea Corradini
Affiliation:
Dipartimento di Informatica, University of Pisa, Corso Italia 40, 56125 Pisa, Italy; andrea@di.unipi.it.
Fabio Gadducci
Affiliation:
Division of Informatics, University of Edinburgh, Mayfield Road, EH9 3JZ Edinburgh, U.K.; fabio@dcs.ed.ac.uk.
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Abstract

We present a categorical formulation of the rewriting of possibly cyclic term graphs, based on a variation of algebraic 2-theories. We show that this presentation is equivalent to the well-accepted operational definition proposed by Barendregt et al. – but for the case of circular redexes , for which we propose (and justify formally) a different treatment. The categorical framework allows us to model in a concise way also automatic garbage collection and rules for sharing/unsharing and folding/unfolding of structures, and to relate term graph rewriting to other rewriting formalisms.

Keywords

Term graphsdirected acyclic graphsterm graph rewritingcategorical modelstraced monoidal categories2-categoriesalgebraic theoriesgs-monoidal theories.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 33 , Issue 4-5 , July 1999 , pp. 467 - 493
Copyright
© EDP Sciences, 1999

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