Skip to Main content Skip to Navigation
Journal articles

Sufficient Completeness Verification for Conditional and Constrained Term Rewriting Systems

Adel Bouhoula 1 Florent Jacquemard 2 
2 MuTant - Synchronous Realtime Processing and Programming of Music Signals
IRCAM - Institut de Recherche et Coordination Acoustique/Musique, Inria Paris-Rocquencourt, UPMC - Université Pierre et Marie Curie - Paris 6, CNRS - Centre National de la Recherche Scientifique
Abstract : We present a procedure for checking sufficient completeness of conditional and constrained term rewriting systems containing axioms for constructors which may be constrained (by e.g. equalities, disequalities, ordering, membership...). Such axioms allow to specify complex data structures like e.g. sets, sorted lists or powerlists. Our approach is integrated into a framework for inductive theorem proving based on tree grammars with constraints, a formalism which permits an exact representation of languages of ground constructor terms in normal form. The procedure is presented by an inference system which is shown sound and complete. A precondition of one inference of this system refers to a (undecidable) property called strong ground reducibility which is discharged to the above inductive theorem proving system. We have successfully applied our method to several examples, yielding readable proofs and, in case of negative answer, a counter-example suggesting how to complete the specification. Moreover, we show that it is a decision procedure when the TRS is unconditional but constrained, for an expressive class of constrained constructor axioms.
Document type :
Journal articles
Complete list of metadata

Cited literature [34 references]  Display  Hide  Download
Contributor : Florent Jacquemard Connect in order to contact the contributor
Submitted on : Monday, November 21, 2011 - 11:49:45 AM
Last modification on : Friday, January 21, 2022 - 3:21:46 AM
Long-term archiving on: : Wednesday, February 22, 2012 - 2:25:26 AM


Files produced by the author(s)




Adel Bouhoula, Florent Jacquemard. Sufficient Completeness Verification for Conditional and Constrained Term Rewriting Systems. Journal of Applied Logic, Elsevier, 2012, 10 (1), pp.127-143. ⟨10.1016/j.jal.2011.09.001⟩. ⟨hal-00643136⟩



Record views


Files downloads