On the Combination of Symbolic Constraints, Solution Domains, and Constraint Solvers

When combining languages for symbolic constraints, one is typically faced with the problem of how to treat \mixed" constraints. The two main problems are (1) how to deene a combined solution structure over which these constraints are to be solved, and (2) how to combine the constraint solving methods for pure constraints into one for mixed constraints. The paper introduces the notion of a \free amalgamated product" as a possible solution to the rst problem. Subsequently, we deene so-called simply-combinable structures (SC-structures). For SC-structures over disjoint signatures, a canonical amalgamation construction exists, which for the subclass of strong SC-structures yields the free amalgamated product. The combination technique of BS92, BaS94a] can be used to combine constraint sol-vers for (strong) SC-structures over disjoint signatures into a solver for their (free) amalgamated product. In addition to term algebras mo-dulo equational theories, the class of SC-structures contains many solution structures that have been used in constraint logic programming, such as the algebra of rational trees, feature structures, and domains consisting of hereditarily nite (wellfounded or non-wellfounded) nested sets and lists.