On confluence of Constraint Handling Rules

Abdennadher, Slim; Frühwirth, Thom; Meuss, Holger

doi:10.1007/3-540-61551-2_62

Cited by 15 publications

(26 citation statements)

References 7 publications

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“…Previous results on confluence of CHR programs, e.g., [1,2,3], mainly refer to a logic-based semantics, which is well-suited for showing program properties, but it does not comply with typical implementations [20,28] and applies only for a small subset of CHR programs. Other works [6,7] suggest an alternative operational semantics that lifts these limitations, including the ability to handle Prolog-style built-in predicates such as var/1, etc.…”

Section: Related Workmentioning

confidence: 99%

Confluence of CHR Revisited: Invariants and Modulo Equivalence

Christiansen

Kirkeby

2019

Logic-Based Program Synthesis and Transformation

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simulation of one transition system by another is introduced as a means to simulate a potentially infinite class of similar transition sequences within a single transition sequence. This is useful for proving confluence under invariants of a given system, as it may reduce the number of proof cases to consider from infinity to a finite number. The classical confluence results for Constraint Handling Rules (CHR) can be explained in this way, using CHR as a simulation of itself. Using an abstract simulation based on a ground representation, we extend these results to include confluence under invariant and modulo equivalence, which have not been done in a satisfactory way before. IntroductionConfluence of a transition system means that any two alternative transition sequences from a given state can be extended to reach a common state. Proving confluence of nondeterministic systems may be important for correctness proofs and it anticipates parallel implementations and application order optimizations. Confluence modulo equivalence generalizes this so that these "common states" need not be identical, but only equivalent according to an equivalence relation. This allows for redundant data representations (e.g., sets as lists) and procedures that search for an optimal solution to a problem, when any of two equally good solutions can be accepted (e.g., the Viterbi algorithm analyzed for confluence modulo equivalence in [7]).We introduce a notion of abstract simulation of one system, the object system, by another, the meta level system, and show how proofs of confluence (under invariant, modulo equivalence) for an object system may be expressed within a meta level system. This may reduce the number of proof cases to be considered, often from infinity to a finite number. We apply this to the programming language of Constraint Handling Rules, CHR [14,15,16], giving a clearer exposition of existing results and extending them for invariants and modulo equivalence.

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Section: Related Workmentioning

confidence: 99%

Confluence of CHR Revisited: Invariants and Modulo Equivalence

Christiansen

Kirkeby

2019

Logic-Based Program Synthesis and Transformation

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“…Most earlier approaches worked only for an idealized set of logical built-ins managed by a "magic" constraint solver that has no counterpart in standard CHR implementations, e.g., [1,2,3,4,7]. It was suggested by [7] to take invariants into account (under the name of observable confluence), staying within the first-order framework.…”

Section: Related Workmentioning

confidence: 99%

Towards a Constraint Solver for Proving Confluence with Invariant and Equivalence of Realistic CHR Programs

Christiansen

Kirkeby

2019

Functional and Constraint Logic Programming

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Confluence of a nondeterministic program ensures a functional input-output relation, freeing the programmer from considering the actual scheduling strategy, and allowing optimized and perhaps parallel implementations. The more general property of confluence modulo equivalence ensures that equivalent inputs are related to equivalent outputs, that need not be identical. Confluence under invariants is also considered. Constraint Handling Rules (CHR) is an important example of a rewrite based logic programming language, and we aim at a mechanizable method for proving confluence modulo equivalence of terminating programs. While earlier approaches to confluence for CHR programs concern an idealized logic subset, we refer to a semantics compatible with standard Prolog-based implementations. We specify a meta-level constraint language in which invariants and equivalences can be expressed and manipulated, extending our previous theoretical results towards a practical implementation.

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“…Here back ± tracking is prohibitive anyway, since it would usually mean to revoke previously given feedback. Con uence analysis of CHR systems was investigated in (Abdennadher, Fru È hwirth, and Meuss, 1996) and a completion procedure was introduced in (Abdennadher and Fru È hwirth, 1998). These results immediately carry over to our parsers, because they are de ned as CHR systems.…”

Section: Parsing As Constraint Solvingmentioning

confidence: 99%

A constraint-based framework for diagrammatic reasoning

Meyer¹

2000

Applied Artificial Intelligence

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In the near future, visual and diagrammatic human ± computer interfaces, such as those of UML ± based CASE tools, will be required to o †er a much more intelligent behavior than just editing. Y et there is very little formal support and there are almost no tools available for the construction of intelligent diagrammatic environments. T he present paper introduces a constraint ± based formalism for the speciÐcation and implementation of complex diagrammatic environments. W e start from grammar ± based deÐnitions of diagrammatic languages and show how a constraint solver for diagram recognition and interpretation can automatically be constructed from such grammars. In a second step, the capabilities of these solvers are extended by allowing to axiomatise formal diagrammatic systems so that they can be regarded as a new constraint domain. T he ultimate aim of this schema is to establish a constraint logic language for diagrammatic reasoning applications.

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On confluence of Constraint Handling Rules

Cited by 15 publications

References 7 publications

Confluence of CHR Revisited: Invariants and Modulo Equivalence

Confluence of CHR Revisited: Invariants and Modulo Equivalence

Towards a Constraint Solver for Proving Confluence with Invariant and Equivalence of Realistic CHR Programs

A constraint-based framework for diagrammatic reasoning

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