Normalized Rewriting: an Alternative to Rewriting modulo a Set of Equations

Marché, Claude

doi:10.1006/jsco.1996.0011

Cited by 57 publications

(37 citation statements)

References 29 publications

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“…The rewrite relation obtained from a CERS is based on the key idea of [26]. First, the subterm where a rule from R should be applied is normalized with >Λ −→ E\S .…”

Section: Definition 8 (Constrained Rewrite Rules)mentioning

confidence: 99%

Termination of Context-Sensitive Rewriting with Built-In Numbers and Collection Data Structures

Falke

Kapur

2010

Functional and Constraint Logic Programming

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Abstract. Context-sensitive rewriting is a restriction of rewriting that can be used to elegantly model declarative specification and programming languages such as Maude. Furthermore, it can be used to model lazy evaluation in functional languages such as Haskell. Building upon our previous work on an expressive and elegant class of rewrite systems (called CERSs) that contains built-in numbers and supports the use of collection data structures such as sets or multisets, we consider contextsensitive rewriting with CERSs in this paper. This integration results in a natural way for specifying algorithms in the rewriting framework. In order to prove termination of this kind of rewriting automatically, we develop a dependency pair framework for context-sensitive rewriting with CERSs, resulting in a flexible termination method that can be automated effectively. Several powerful termination techniques are developed within this framework. An implementation in the termination prover AProVE has been successfully evaluated on a large collection of examples.

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“…The rewrite relation obtained from a CERS is based on the key idea of [26]. First, the subterm where a rule from R should be applied is normalized with >Λ −→ E\S .…”

Section: Definition 8 (Constrained Rewrite Rules)mentioning

confidence: 99%

Termination of Context-Sensitive Rewriting with Built-In Numbers and Collection Data Structures

Falke

Kapur

2010

Functional and Constraint Logic Programming

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“…Thus, a natural way for integrating can in ground AC-completion is to extend normalized rewriting [17]. …”

Section: Canonized Rewritingmentioning

confidence: 99%

“…A generic framework for combining completion with a generic builtin equational theory E has been proposed in [10]. Normalized completion [17] is designed to use a modified rewriting relation when the theory E is equivalent to the union of the AC theory and a convergent rewriting system S. In this setting, rewriting steps are only performed on S-normalized terms. AC(X) can be seen as an adaptation of ground normalized completion to efficiently handle the theory E when it is equivalent to the union of the AC theory and a Shostak theory X.…”

Section: ∀X∀y∀z U(x U(y Z)) = U(u(x Y) Z) (A) ∀X∀y U(x Y) =mentioning

confidence: 99%

Canonized Rewriting and Ground AC Completion Modulo Shostak Theories

Conchon

Contejean

Iguernelala

2011

Tools and Algorithms for the Construction and Analysis of Systems

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Abstract. AC-completion efficiently handles equality modulo associative and commutative function symbols. When the input is ground, the procedure terminates and provides a decision algorithm for the word problem. In this paper, we present a modular extension of ground ACcompletion for deciding formulas in the combination of the theory of equality with user-defined AC symbols, uninterpreted symbols and an arbitrary signature disjoint Shostak theory X. Our algorithm, called AC(X), is obtained by augmenting in a modular way ground AC-completion with the canonizer and solver present for the theory X. This integration rests on canonized rewriting, a new relation reminiscent to normalized rewriting, which integrates canonizers in rewriting steps. AC(X) is proved sound, complete and terminating, and is implemented to extend the core of the Alt-Ergo theorem prover.

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“…2 The main application we have in mind, relying on minimal complete sets of AC-unifiers, is computing AC-critical pairs. This is for example useful for proving confluence of rewrite systems with and without AC-symbols [6,10,11] and required for normalized completion [8,14].…”

Section: Introductionmentioning

confidence: 99%

A Formally Verified Solver for Homogeneous Linear Diophantine Equations

Meßner

Parsert

Schöpf

et al. 2018

Interactive Theorem Proving

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Abstract. In this work we are interested in minimal complete sets of solutions for homogeneous linear diophantine equations. Such equations naturally arise during AC-unification-that is, unification in the presence of associative and commutative symbols. Minimal complete sets of solutions are for example required to compute AC-critical pairs. We present a verified solver for homogeneous linear diophantine equations that we formalized in Isabelle/HOL. Our work provides the basis for formalizing AC-unification and will eventually enable the certification of automated AC-confluence and AC-completion tools.

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Normalized Rewriting: an Alternative to Rewriting modulo a Set of Equations

Cited by 57 publications

References 29 publications

Termination of Context-Sensitive Rewriting with Built-In Numbers and Collection Data Structures

Termination of Context-Sensitive Rewriting with Built-In Numbers and Collection Data Structures

Canonized Rewriting and Ground AC Completion Modulo Shostak Theories

A Formally Verified Solver for Homogeneous Linear Diophantine Equations

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