A compositional Semantics for CHR

TL;DR

This paper introduces a new fix-point, compositional semantics for Constraint Handling Rules (CHR), enabling modular analysis and verification of CHR programs by characterizing their input/output behavior.

Contribution

It presents the first compositional semantics for CHR, allowing the semantics of complex queries to be derived from their components.

Findings

Defines a fix-point semantics for CHR

Semantics is and-compositional, enabling modular analysis

Facilitates incremental and modular verification tools

Abstract

Constraint Handling Rules (CHR) are a committed-choice declarative language which has been designed for writing constraint solvers. A CHR program consists of multi-headed guarded rules which allow one to rewrite constraints into simpler ones until a solved form is reached. CHR has received a considerable attention, both from the practical and from the theoretical side. Nevertheless, due the use of multi-headed clauses, there are several aspects of the CHR semantics which have not been clarified yet. In particular, no compositional semantics for CHR has been defined so far. In this paper we introduce a fix-point semantics which characterizes the input/output behavior of a CHR program and which is and-compositional, that is, which allows to retrieve the semantics of a conjunctive query from the semantics of its components. Such a semantics can be used as a basis to define incremental and modular analysis and verification tools.