Abstract
In this paper we present the part of the Coccinelle library which deals with list permutations. Indeed permutations naturally arise when formally modeling rewriting in Coq, for instance RPO with multiset status and equality modulo AC. Moreover the needed permutations are up to an equivalence relation, and may be used to inductively define the same relation (equivalence modulo RPO). This is why we introduce the notion of permutation w. r. t. an arbitrary relation. The advantages of our approach are a very simple inductive definition (with only 2 constructors), the adequacy with the mathematical definition, the ability to define a relation using recursively permutations up to this very relation, and a fine grained modularity (if R enjoys a property, so does permut R).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Blanqui, F., Coupet-Grimal, S., Delobel, W., Hinderer, S., Koprowski, A.: CoLoR, a Coq Library on Rewriting and termination. In: Extended Abstracts of the 8th International Workshop on Termination, WST 2006 (2006). http://color.loria.fr/
Boudet, A., Contejean, E.: “Syntactic” AC-unification. In: Jouannaud, J.-P. (ed.) CCL 1994. LNCS, vol. 845, pp. 136–151. Springer, Heidelberg (1994)
Contejean, E.: A certified AC matching algorithm. In: van Oostrom, V. (ed.) RTA 2004. LNCS, vol. 3091, pp. 70–84. Springer, Heidelberg (2004)
Contejean, E. Coccinelle, (2005) http://www.lri.fr/~contejea/Coccinelle/coccinelle.html
Coupet-Grimal, S., Delobel, W.: Une preuve effective de la bonne fondation de l’ordre récursif multi-ensemble sur les chemins. In: Dix-septièmes Journées Francophones des Langages Applicatifs. INRIA, INRIA, (January 2006)
Dershowitz, N.: Orderings for term rewriting systems. Theoretical Computer Science 17(3), 279–301 (March 1982)
Dershowitz, N., Jouannaud, J.-P.: Rewrite systems. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science, vol, pp. 243–320. North-Holland, Amsterdam (1990)
Hullot, J.-M.: Associative commutative pattern matching. In: Proc. 6th IJCAI Tokyo, vol. I, pp. 406–412 (August 1979)
Jouannaud, J.-P.: Syntactic theories. In: Rovan, B. (ed.) Mathematical Foundations of Computer Science, LNCS, vol. 452, Springer, Heidelberg (1990)
Kirchner, C., Klay, F.: Syntactic theories and unification. In: Proc. 5th IEEE Symp. Logic in Computer Science, Philadelphia (June 1990)
Koprowski, A.: Certified Higher-Order Recursive Path Ordering. In: Pfenning, F. (ed.) RTA 2006. LNCS, vol. 4098, pp. 227–241. Springer, Heidelberg (2006)
The Coq Development Team. The Coq Proof Assistant Reference Manual – Version V8.1 (July 2006) http://coq.inria.fr
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Contejean, E. (2007). Modeling Permutations in Coq for Coccinelle . In: Comon-Lundh, H., Kirchner, C., Kirchner, H. (eds) Rewriting, Computation and Proof. Lecture Notes in Computer Science, vol 4600. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73147-4_13
Download citation
DOI: https://doi.org/10.1007/978-3-540-73147-4_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73146-7
Online ISBN: 978-3-540-73147-4
eBook Packages: Computer ScienceComputer Science (R0)