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A duality between proof systems for cyclic term graphs

Published online by Cambridge University Press:  01 June 2007

CLEMENS GRABMAYER
CLEMENS GRABMAYER*
Affiliation:
Department of Computer Science, Vrije Universiteit Amsterdam, de Boelelaan 1081a, 081 HV Amsterdam, the Netherlands Email: clemens@cs.vu.nl.
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Abstract

This paper presents a proof-theoretic observation about two kinds of proof systems for bisimilarity between cyclic term graphs.

First we consider proof systems for demonstrating that μ term specifications of cyclic term graphs have the same tree unwinding. We establish a close connection between adaptations for μ terms over a general first-order signature of the coinductive axiomatisation of recursive type equivalence by Brandt and Henglein (Brandt and Henglein 1998) and of a proof system by Ariola and Klop (Ariola and Klop 1995) for consistency checking. We show that there exists a simple duality by mirroring between derivations in the former system and formalised consistency checks, which are called ‘consistency unfoldings', in the latter. This result sheds additional light on the axiomatisation of Brandt and Henglein: it provides an alternative soundness proof for the adaptation considered here.

We then outline an analogous duality result that holds for a pair of similar proof systems for proving that equational specifications of cyclic term graphs are bisimilar.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 17 , Issue 3 , June 2007 , pp. 439 - 484
Copyright
Copyright © Cambridge University Press 2007

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