Confluence Modulo Equivalence in Constraint Handling Rules

Christiansen, Henning; Kirkeby, Maja Hanne

doi:10.1007/978-3-319-17822-6_3

Cited by 5 publications

(15 citation statements)

References 14 publications

(36 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For comparison with earlier work on confluence for CHR, we used here a logic-based CHR semantics, which has nice theoretical properties, but is incompatible with standard implementations of CHR and applies only for a limited set of programs. In [9], we have defined meta level constraints and a simulation for an alternative CHR semantics [6,7] that reflects CHR's Prolog based implementation, including a correct handling of Prolog's non-logical devices (e.g., var/1, nonvar/2, is/2) and runtime errors.…”

Section: Resultsmentioning

confidence: 99%

“…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. To compare with earlier work and for simplicity, the present paper refers to the logic-based semantics.…”

Section: Related Workmentioning

confidence: 99%

“…Example 1 ( [6,7]). The following CHR program, consisting of a single rule, collects a number of separate items into a set represented as a list of items.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Confluence of CHR Revisited: Invariants and Modulo Equivalence

Christiansen

Kirkeby

2019

Logic-Based Program Synthesis and Transformation

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Resultsmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Confluence of CHR Revisited: Invariants and Modulo Equivalence

Christiansen

Kirkeby

2019

Logic-Based Program Synthesis and Transformation

Self Cite

View full text Add to dashboard Cite

show abstract

“…Confluence modulo equivalence was introduced for CHR by [5], also arguing to use a Prolog-based semantics closer to current CHR implementations. An indepth theoretical analysis of these issues is given by [6], also suggesting to use a ground meta-level representation for invariants and equivalences.…”

Section: Related Workmentioning

confidence: 99%

“…The meaning of built-in predicates is given by a function Exe that maps them into substitutions. The set of built-in predicates may vary, see [5,6], but we assume always =/2 with Exe(t 1 =t 2 ) being a most general unifier of t 1 , t 2 if one exists, and failure otherwise. Exe is extended to sequences of built-ins as follows, which is not commutative.…”

Section: Prolog-based Chrmentioning

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

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Constraint Handling Rules - What Else?

Frühwirth

2015

Rule Technologies: Foundations, Tools, and Applications

View full text Add to dashboard Cite

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.

show abstract

Confluence Modulo Equivalence in Constraint Handling Rules

Cited by 5 publications

References 14 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

Constraint Handling Rules - What Else?

Contact Info

Product

Resources

About