A Type System for CHR

The language of Constraint Handling Rules (CHR) of T. Frühwirth [1] is a successful rule-based language for implementing constraint solvers in a wide variety of domains. It is an extension of a host language, such as Prolog [2], Java or Haskell [3], allowing the introduction of new constraints in a declarative way. One peculiarity of CHR is that it allows multiple heads in rules. For the sake of simplicity, we consider only simpli.cation rules, since the distinction of propagation and simpagation rules [1] is not needed for typing purposes. A simpli.cation rule is of the form \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$H_{1},...,H_{i} \Leftrightarrow G_{1},...,G_{j}|B_{1},...,B_{k}$\end{document}, where H1,...,Hi is a nonempty sequence of CHR constraints, the guard G1,...,Gj is a sequence of native constraints and the body B1,...,Bk is a sequence of CHR and native constraints.