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Axiomatizing permutation equivalence†

Published online by Cambridge University Press:  04 March 2009

Cosimo Laneve  and
Ugo Montanari
Cosimo Laneve
Affiliation:
Dip. di Matematica, Universitá di Bologna, P.za di Porta S.Donato, 40127, Bologna, Italy. (1aneve@cs.unibo.it)
Ugo Montanari
Affiliation:
Dip. di Informatica, Università di Pisa, C.so Italia 40, 56125 Pisa, Italy, (ugo@di.unipi.it)
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Abstract

We axiomatize permutation equivalence in term rewriting systems and Klop’s orthogonal Combinatory Reduction Systems (Klop 1980). The axioms for the former are provided by the general approach proposed by Meseguer (Meseguer 1992). The latter need extra axioms modelling the interplay between reductions and the operation of substitution.

As a consequence of this work, the definition of permutation equivalence is rid of residual calculi, which are heavy in general.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 6 , Issue 3 , June 1996 , pp. 219 - 249
Copyright
Copyright © Cambridge University Press 1996

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References

Abadi, M., Cardelli, L., Curien, P. L. and Lévy, J. J. (1990) Explicit substitutions. In: Proceedings 17th ACM Symposium on Principles of Programmining Languages 59–71.CrossRefGoogle Scholar
Aczel, P. (1978) A general Church-Rosser theorem. Draft, Manchester.Google Scholar
Boudol, G. (1985) Computational semantics of term rewriting systems. In: Nivat, M. and Reynolds, J. C. (eds.) Algebraic Methods in Semantics, Cambridge University Press 169–236.Google Scholar
Boudol, G. and Castellani, I. (1988) A non-interleaving semantics for CCS based on proved transitions. Fundamenta Informaticae 11 (4) 433–452.CrossRefGoogle Scholar
Corradini, A. and Montanari, U. (1992) An algebraic semantics for structured transition systems and its application to logic programs. Theoretical Computer Science 103 51–106.CrossRefGoogle Scholar
Curry, H. B. and Feys, R. (1974) Combinatory Logic, volume 1, North-Holland.Google Scholar
Klop, J. W. (1980) Combinatory Reduction System, Ph.D. thesis, Mathematisch Centrum, Amsterdam.Google Scholar
Klop, J. W., van Oostrom, V. and van Raamsdonk, F. (1993) Combinatory Reduction System: introduction and survey. Theoretical Computer Science 121 279–308.CrossRefGoogle Scholar
Laneve, C. (1994) Distributive Evaluations of λ-calculus. Fundamenta Informaticae 20 (4) 333–352.CrossRefGoogle Scholar
Laneve, C. and Montanari, U. (1992) Axiomatizing permutation equivalence in the λ-calculus. In: 3rd Int. Conf. on Algebraic and Logic Programming. Springer-Verlag Lecture Notes in Computer Science 632 350–363.CrossRefGoogle Scholar
Lévy, J. J. (1980) Optimal reductions in the lambda-calculus. In: Seldin, J. P. and Hindley, J. R. (eds.) To H.B. Curry, Essays on Combinatory Logic, Lambda Calculus and Formalism, Academic Press 159–191.Google Scholar
Manca, V., Salibra, A. and Scollo, G. (1990) Equational type logic. Theoretical Computer Science 77 131–159.CrossRefGoogle Scholar
Meseguer, J. (1992) Conditional rewriting logic as a unified model of concurrency. Theoretical Computer Science 96 73–155.CrossRefGoogle Scholar
Meseguer, J. and Goguen, J. A. (1985) Initiality, Induction and Computability. In: Nivat, M. and Reynolds, J. C. (eds.) Algebraic Methods in Semantics, Cambridge University Press.Google Scholar
Meseguer, J. and Montanari, U. (1990) Petri nets are monoids. Information and Computation 88 155–164.CrossRefGoogle Scholar
Talcott, C. (1993) A theory of binding structures and applications to rewritings. Theoretical Computer Science 112 99–143.CrossRefGoogle Scholar