Modular CHR with ask and tell

In this paper, we introduce a modular version of the Constraint Handling Rules language CHR, called CHRat for modular CHR with ask and tell. Any constraint de ned in a CHRat component can be reused both in rules and guards in another CHRat component to de ne new constraint solvers. Unlike previous work on modular CHR, our approach is completely general as it does not rely on an automatic derivation of conditions for checking entailment in guards, but on a programming discipline for de ning both satis ability (tell) and entailment (ask) checks by CHRat rules for each constraint. We de ne the operational and declarative semantics of CHRat, provide a transformation of CHRat components to at CHR programs, and prove the preservation of the semantics. We then provide examples of the modularization of classical CHR constraint solvers and of the de nition of complex constraint solvers in a modular fashion.