CLP projection for constraint handling rules

Haemmerlé, Rémy; López-García, Pedro; Hermenegildo, Manuel V.

doi:10.1145/2003476.2003496

Cited by 5 publications

(12 citation statements)

References 33 publications

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“…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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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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“…As a corollary, we see that the logical reading of a confluent program is consistent. This idea can be traced back to the pioneering works about CHR confluence [2], but the constructive characterization of the least model for confluent programs is more recent [17]. The proof of this characterization is, however, more involved in the original settings of CHR because of the multiset nature of atoms.…”

Section: Theorem 36 (Least S-model)mentioning

confidence: 99%

On Combining Backward and Forward Chaining in Constraint Logic Programming

Haemmerlé

2014

Proceedings of the 16th International Symposium on Principles and Practice of Declarative Programming

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We address the problem of designing constraint logic languages that usefully combine backward and forward chaining in a sound and complete way. Following the approach of Constraint Logic Programming, we define a class of programming languages that generalize both Constraint Logic and Concurrent Constraint Programming. Syntactically, this class corresponds to Constraint Handling Rules with disjunctions, but differ operationally by featuring set-based semantics instead of multiset-based ones; i.e., conjunction and disjunction are idempotent. The assumption of program confluence is the crux on which both the committed choice strategy and the logical completeness of the languages rely.

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“…An alternative method for proving ground termination in our context is the notion of CLP projection as described in (Haemmerlé et al 2011). Formally, the projection of a simplification rule (h 1 , .…”

Section: Relaxed Conditions To Guarantee Soundness For Terminating Goalsmentioning

confidence: 99%

“…The projection of a CHR program is the union of the projections of its simplifications. If the projection of a set P of mono-headed simplifications is terminating then so is P (Haemmerlé et al 2011). Since purely built-in propagation rules either do not apply or fail on ground states, there exists a direct correspondence between the ground termination if P and its projection.…”

Section: Relaxed Conditions To Guarantee Soundness For Terminating Goalsmentioning

confidence: 99%

On Termination, Confluence and Consistent CHR-based Type Inference

Duck

Haemmerlé

Sulzmann³

2014

Theory and Practice of Logic Programming

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We consider the application of Constraint Handling Rules (CHR) for the specification of type inference systems, such as that used by Haskell. Confluence of CHR guarantees that the answer provided by type inference is correct and consistent. The standard method for establishing confluence relies on an assumption that the CHR program is terminating. However, many examples in practice give rise to non-terminating CHR programs, rendering this method inapplicable. Despite no guarantee of termination or confluence, the Glasgow Haskell Compiler (GHC) supports options that allow the user to proceed with type inference anyway, e.g. via the use of the UndecidableInstances flag. In this paper we formally identify and verify a set of relaxed criteria, namely range-restrictedness, local confluence, and ground termination, that ensure the consistency of CHR-based type inference that maps to potentially non-terminating CHR programs

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CLP projection for constraint handling rules

Cited by 5 publications

References 33 publications

Constraint Handling Rules - What Else?

Constraint Handling Rules - What Else?

On Combining Backward and Forward Chaining in Constraint Logic Programming

On Termination, Confluence and Consistent CHR-based Type Inference

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