SMCHR: satisfiability modulo constraint handling rules. Constraint handling rules (CHRs) are a high-level rule-based programming language for specification and implementation of constraint solvers. CHR manipulates a global store representing a flat conjunction of constraints. By default, CHR does not support goals with a more complex propositional structure including disjunction, negation, etc., or CHR relies on the host system to provide such features. In this paper we introduce satisfiability modulo constraint handling rules (SMCHR): a tight integration of CHR with a modern Boolean satisfiability (SAT) solver for quantifier-free formulae with an arbitrary propositional structure. SMCHR is essentially a satisfiability modulo theories (SMT) solver where the theory T is implemented in CHR. The execution algorithm of SMCHR is based on lazy clause generation, where a new clause for the SAT solver is generated whenever a rule is applied. We shall also explore the practical aspects of building an SMCHR system, including extending a “built-in” constraint solver supporting equality with unification and justifications.

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