Termination of a set of rules modulo a set of equations

Jouannaud, Jean-Pierre; Muñoz, Miguel Luis López-Guadalupe

doi:10.1007/bfb0047121

Cited by 10 publications

(10 citation statements)

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“…These general results have led us to the development of various particular transforms, including methods for proving termination of equational rewrite systems R/E, where E contains associativity, commutativity, and identity axioms. It should be possible to automate, to a certain degree, the process of developing transforms for certain classes of rewrite systems by using a "completion-like" procedure as suggested by Jouannaud and Munoz (1984).…”

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confidence: 99%

Commutation, transformation, and termination

Bachmair

Dershowitz

1986

8th International Conference on Automated Deduction

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In this paper we study the use of commutation properties for proving termination of rewrite systems. Commutation properties may be used to prove termination of a combined system RUS by proving termination of R and S separately. We present termination methods for ordinary and for equational rewrite systems. Commutation is also important for transformation techniques. We outline the application of transforms-mappings from terms to terms-to termination in general, and describe various specific transforms, including transforms for associative-commutative rewrite systems.

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confidence: 99%

Commutation, transformation, and termination

Bachmair

Dershowitz

1986

8th International Conference on Automated Deduction

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“…Such conditions are well known in first-order rewriting theory: the notion of compatibility of Peterson and Stickel [PS81], the notion of local E-commutation of Jouannaud and Muñoz [JM84] and, more generally, the notion of local coherence modulo E of Jouannaud and Kirchner [JK86]. Similarly, the addition of extension rules to make a system compatible, locally commute or locally coherent is also well known since Lankford and Ballantyne [LB77].…”

Section: Lemma 22mentioning

confidence: 94%

“…Hence, if we also have ← η → R,βη ⊆ → R,βη = η , then ↔ η → R,βη ⊆ → + R,βη = η , a property that, after [JM84], we call:…”

Section: Lemma 19mentioning

confidence: 97%

Termination of rewrite relations on λ-terms based on Girard's notion of reducibility

Blanqui

2016

Theoretical Computer Science

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International audienceIn this paper, we show how to extend the notion of reducibility introduced by Girard for proving the termination of β-reduction in the polymorphic λ-calculus, to prove the termination of various kinds of rewrite relations on λ-terms, including rewriting modulo some equational theory and rewriting with matching modulo βη, by using the notion of computability closure. This provides a powerful termination criterion for various higher-order rewriting frameworks, including Klop's Combinatory Reductions Systems with simple types and Nipkow's Higher-order Rewrite Systems

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“…We cannot survey all such methods here: just for AC termination alone there is a substantial body of termination orderings and methods. However, we can mention sample references such as [19,18,3,29,12,23,26,13]. The paper closest in spirit to ours is probably the one by Giesl and Kapur [13], in that it also aims at developing proof methods modulo some generic class E of equational axioms.…”

Section: Related Work and Conclusionmentioning

confidence: 97%

Termination Modulo Combinations of Equational Theories

Durán

Lucas

Meseguer

2009

Lecture Notes in Computer Science

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Abstract. Rewriting with rules R modulo axioms E is a widely used technique in both rule-based programming languages and in automated deduction. Termination methods for rewriting systems modulo specific axioms E (e.g., associativity-commutativity) are known. However, much less seems to be known about termination methods that can be modular in the set E of axioms. In fact, current termination tools and proof methods cannot be applied to commonly occurring combinations of axioms that fall outside their scope. This work proposes a modular termination proof method based on semantics-and termination-preserving transformations that can reduce the proof of termination of rules R modulo E to an equivalent proof of termination of the transformed rules modulo a typically much simpler set B of axioms. Our method is based on the notion of variants of a term recently proposed by Comon and Delaune. We illustrate its practical usefulness by considering the very common case in which E is an arbitrary combination of associativity, commutativity, left-and right-identity axioms for various function symbols.

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Termination of a set of rules modulo a set of equations

Cited by 10 publications

References 0 publications

Commutation, transformation, and termination

Commutation, transformation, and termination

Termination of rewrite relations on λ-terms based on Girard's notion of reducibility

Termination Modulo Combinations of Equational Theories

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