Automating Termination Proofs for CHR

Pilozzi, Paolo; Schreye, Danny De

doi:10.1007/978-3-642-02846-5_43

Cited by 6 publications

(10 citation statements)

References 6 publications

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“…Instead of assuming termination, we proposed the weaker property observable termination and demonstrated it useful. Methods for proving termination of CHR programs have been studied, e.g., [11,19,20], but they still need to be adapted for observable termination. A constraint solver for the meta-level language is under development in CHR as the obvious implementation language.…”

Section: Resultsmentioning

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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Section: Resultsmentioning

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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“…Future work will therefore be directed towards a better understanding of this problem. We will also apply groundness and call type analysis on the result of the transformation and will, based on CHRTypes, develop a call type analyser for integration with CHRisTA [8], yielding the first fully automated termination analyser for the complete CHR(Prolog) language.…”

Section: Resultsmentioning

confidence: 99%

“…We plan to use CHRTypes as a source of information to obtain the call types of a CHR(Prolog) program. The computed call types can then be used as input to our termination analyser CHRisTA [8], instead of providing them ourselves, resulting in a fully automated termination analyser for CHR(Prolog).…”

Section: Introductionmentioning

confidence: 99%

A Transformational Approach for Proving Properties of the CHR Constraint Store

Pilozzi

Schrijvers

Bruynooghe

2010

Logic-Based Program Synthesis and Transformation

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Abstract. Proving termination of, or generating efficient control for Constraint Handling Rules (CHR) programs requires information about the kinds of constraints that can show up in the CHR constraint store. In contrast to Logic Programming (LP), there are not many tools available for deriving such information for CHR. Hence, instead of building analyses for CHR from scratch, we define a transformation from CHR to Prolog and reuse existing analysis tools for Prolog. The proposed transformation has been implemented and combined with PolyTypes 1.3, a type analyser for Prolog, resulting in an accurate description of the types of CHR programs. Moreover, the transformation is not limited to type analysis. It can also be used to prove other properties of the constraints showing up in constraint stores, using tools for Prolog.

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“…For CHR programs that mainly use simplification rules, simple rankings are often sufficient to prove termination [48,49]. More sophisticated methods are needed in the presence of propagation rules [97,98,57]. An approximation of CHR programs by constraint logic programs (CLP) has also been used to analyse the termination behavior of CHR [81].…”

Section: Termination and Time Complexity Analysismentioning

confidence: 99%

Constraint Handling Rules - What Else?

Frühwirth

2015

Rule Technologies: Foundations, Tools, and Applications

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Abstract. Constraint Handling Rules (CHR) is both an effective concurrent declarative constraint-based programming language and a versatile computational formalism. While conceptually simple, CHR is distinguished by a remarkable combination of desirable features:-a semantic foundation in classical and linear logic, -an effective and efficient sequential and parallel execution model -guaranteed properties like the anytime online algorithm properties -powerful analysis methods for deciding essential program properties. This overview of some CHR-related research and applications is by no means meant to be complete. Essential introductory reading for CHR provide the survey article [125] and the books [56,63]. Up-to-date information on CHR can be found online at the CHR web-page www. constraint-handling-rules.org, including the slides of the keynote talk associated with this article. In addition, the CHR website dtai. cs.kuleuven.be/CHR/ offers everything you want to know about CHR, including online demo versions and free downloads of the language. Executive SummaryConstraint Handling Rules (CHR) [56] tries to bridge the gap between theory and practice, between logical specification and executable program by abstraction through constraints and the concepts of computational logic. CHR has its roots in constraint logic programming and concurrent constraint programming, but also integrates ideas from multiset transformation and rewriting systems as well as automated reasoning and theorem proving. It seamlessly blends multi-headed rewriting and concurrent constraint logic programming into a compact userfriendly rule-based programming language. CHR consists of guarded reactive rules that transform multisets of relations called constraints until no more change occurs. By the notion of constraint, CHR does not need to distinguish between data and operations, and its rules are both descriptive and executable.In CHR, one distinguishes two main kinds of rules: Simplification rules replace constraints by simpler constraints while preserving logical equivalence, e.g., X≤Y∧Y≤X ⇔ X=Y. Propagation rules add new constraints that are logically redundant but may cause further simplification, e.g., X≤Y∧Y≤Z ⇒ X≤Z. Together with X≤X ⇔ true, these rules encode the axioms of a partial order relation. The rules compute its transitive closure and replace inequalities ≤ by equalities = whenever possible. For example, A≤B∧B≤C∧C≤A becomes A=B∧B=C. More program examples can be found in Section 2. Semantics of CHR are discussed in Section 3.

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Automating Termination Proofs for CHR

Cited by 6 publications

References 6 publications

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

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

A Transformational Approach for Proving Properties of the CHR Constraint Store

Constraint Handling Rules - What Else?

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