Abstract
In this work we have axiomatized permutation equivalence in the λ-calculus. Most of the axioms result from the methodology developed by Meseguer in [12]. The completeness result is obtained by adding some axioms modelling the interplay between substitution and β-conversion.
The main goal of our research is to axiomatize permutation equivalence for a large class of rewriting systems. We conjecture that permutation equivalence is fully axiomatized for term rewriting systems (where terms are freely generated) by Meseguer's machinery whilst suitable axioms stating the relationships between the rewriting rules and the operation of substitution must be added for completely characterizing permutation equivalence in combinatory reduction systems [8].
Research supported in part by EEC Basic Research Action n. 3011 CEDISYS
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
M. Bednarczyk. Categories of asynchronous systems. PhD thesis, Computer Science, University of Sussex, Brighton, 1987.
G. Boudol. Computational semantics of term rewriting systems. In Algebraic methods in semantics, Eds. M. Nivat and J.C. Reynolds, Cambridge University Press 1985, pp. 169–236.
G. Boudol and I. Castellani. A non-interleaving semantics for CCS based on proved transitions. Fundamenta Informaticae, 11(4):433–452, 1988.
A. Corradini and U. Montanari. An algebraic semantics for strucured transition systems and its application to logic programs. Theoretical Computer Science, 1992. in press.
H.B. Curry and R. Feys. Combinatory Logic, volume 1. North-Holland, 1974.
P. Degano, J. Meseguer, and U. Montanari. Axiomatizing net computations and processes. In Proceedings 4th Annual Symposium on Logic in Computer Science, Asilomar, California, to appear in Information and Computation.
R.M. Keller. Formal verification of parallel programs. Communications of the ACM, 19(7):371–384, 1976.
J.W. Klop. Combinatory Reduction Systems Mathematical Centre Tracts. Nr.127, Centre for Mathematics and Computer Science, Amsterdam, 1980.
J.J. Lévy. Optimal reductions in the lambda-calculus. In J.P. Seldin and J.R. Hindley, editors, To H.B. Curry, Essays on Combinatory Logic, Lambda Calculus and Formalism. Academic Press, 1980.
J.J. Lévy and G. Huet. Computations in orthogonal rewriting systems, 1. In J.L. Lassez and G. Plotkin, editors, Computational Logic, Essays in honour of A. Robinson, chapter 11. MIT Press, 1991.
V. Manca, A. Salibra, and G. Scollo. Equational type logic. Theoretical Computer Science, 77:131–159, 1990.
J. Meseguer. Conditional rewriting systems. Theoretical Computer Science, 1992. in press.
J. Meseguer and U. Montanari. Petri nets are monoids: a new algebraic foundation for net theory. In Proceedings 3th Annual Symposium on Logic in Computer Science, Edinburgh, pages 155–164, Washington, 1988. IEEE Computer Society Press.
R. Milner. Communication and Concurrency. Prentice-Hall International, Englewood Cliffs, 1989.
E.W. Stark. Concurrent transition systems. Theoretical Computer Science, 64:221–269, 1989.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1992 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Laneve, C., Montanari, U. (1992). Axiomatizing permutation equivalence in the λ-calculus. In: Kirchner, H., Levi, G. (eds) Algebraic and Logic Programming. ALP 1992. Lecture Notes in Computer Science, vol 632. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0013837
Download citation
DOI: https://doi.org/10.1007/BFb0013837
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-55873-6
Online ISBN: 978-3-540-47302-2
eBook Packages: Springer Book Archive