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Event structures and non-orthogonal term graph rewriting

Published online by Cambridge University Press:  19 April 2018

David Clark  and
Richard Kennaway
David Clark
Affiliation:
Department of Computing, Imperial College, London, UK
Richard Kennaway
Affiliation:
School of Information Systems, University of East Anglia, Norwich, UK
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Abstract

We show that for every term graph in a left-linear but non-orthogonal term graph rewrite system, one can construct an event structure that represents all the possible reductions that can occur in reduction sequences starting from that term graph. Every finite reduction sequence from that graph corresponds to a configuration of the event structure, and Lévy-equivalent sequences correspond to the same configuration.

Garbage collection is modelled in the event structure by an ‘erases’ relation. The asymmetric conflicts that arise in non-orthogonal rewrite systems are modelled by introducing a ‘prevents’ relation. The configurations of the event structure then form the state space of an event automaton. Taking the directed completion of this space yields a prime algebraic domain.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 6 , Issue 6 , December 1996 , pp. 545 - 578
Copyright
Copyright © Cambridge University Press 1996

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