Constraints

, Volume 4, Issue 2, pp 133–165 | Cite as

Confluence and Semantics of Constraint Simplification Rules

  • Slim Abdennadher
  • Thom Frühwirth
  • Holger Meuss

Abstract

Constraint Simplification Rules (CSR) is a subset of the Constraint Handling Rules (CHR) language. CHR is a powerful special-purpose declarative programming language for writing constraint solvers. The CSR subset of CHR forms essentially a committed-choice language consisting of guarded rules with multiple heads that replace constraints by simpler ones until they are solved. This paper gives declarative and operational semantics as well as soundness and completeness results for CSR programs.

We also introduce a notion of confluence for CSR programs. Confluence is an essential syntactical property of any constraint solver. It ensures that the solver will always compute the same result for a given set of constraints independent of which rules are applied. It also means that it does not matter for the result in which order the constraints arrive at the constraint solver.

We give a decidable, sufficient and necessary syntactic condition for confluence of terminating CSR programs. Moreover, as shown in this paper, confluence of a program implies consistency of its logical meaning (under a mild restriction).

constraint reasoning semantics of programming languages committed-choice languages confluence determinism program analysis 

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Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Slim Abdennadher
    • 1
  • Thom Frühwirth
    • 1
  • Holger Meuss
    • 2
  1. 1.Computer Science DepartmentLudwig-Maximilians-UniversityMunichGermany
  2. 2.Center for Information and Language ProcessingLudwig-Maximilians-UniversityMunichGermany

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