  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.
