Linear-Logic Based Analysis of Constraint Handling Rules with Disjunction

Constraint Handling Rules (CHR) is a declarative committed-choice programming language with a strong relationship to linear logic. Its generalization CHR with Disjunction (CHRv) is a multi-paradigm declarative programming language that allows the embedding of horn programs. We analyse the assets and the limitations of the classical declarative semantics of CHR before we motivate and develop a linear-logic declarative semantics for CHR and CHRv. We show how to apply the linear-logic semantics to decide program properties and to prove operational equivalence of CHRv programs across the boundaries of language paradigms

Optimal Union-Find in Constraint Handling Rules

Constraint Handling Rules (CHR) is a committed-choice rule-based language that was originally intended for writing constraint solvers. In this paper we show that it is also possible to write the classic union-find algorithm and variants in CHR. The programs neither compromise in declarativeness nor efficiency. We study the time complexity of our programs: they match the almost-linear complexity of the best known imperative implementations. This fact is illustrated with experimental results.Comment: 12 pages, 3 figures, to appear in Theory and Practice of Logic Programming (TPLP

Observational equivalences for linear logic CC languages

Linear logic Concurrent Constraint programming (LCC) is an extension of concurrent constraint programming (CC) where the constraint system is based on Girard's linear logic instead of the classical logic. In this paper we address the problem of program equivalence for this programming framework. For this purpose, we present a structural operational semantics for LCC based on a label transition system and investigate different notions of observational equivalences inspired by the state of art of process algebras. Then, we demonstrate that the asynchronous \pi-calculus can be viewed as simple syntactical restrictions of LCC. Finally we show LCC observational equivalences can be transposed straightforwardly to classical Concurrent Constraint languages and Constraint Handling Rules, and investigate the resulting equivalences.Comment: 17 page

Unfolding in CHR

Program transformation is an appealing technique which allows to improve run-time efficiency, space-consumption and more generally to optimize a given program. Essentially it consists of a sequence of syntactic program manipulations which preserves some kind of semantic equivalence. One of the basic operations which is used by most program transformation systems is unfolding which consists in the replacement of a procedure call by its definition. While there is a large body of literature on transformation and unfolding of sequential programs, very few papers have addressed this issue for concurrent languages and, to the best of our knowledge, no other has considered unfolding of CHR programs. This paper defines a correct unfolding system for CHR programs. We define an unfolding rule, show its correctness and discuss some conditions which can be used to delete an unfolded rule while preserving the program meaning. We prove that confluence and termination properties are preserved by the above transformations