On connections between CHR and LCC

Both CHR and LCC languages are based on the same model of concurrent computation, where agents communicate through a shared constraint store, with a synchronization mechanism based on constraint entailment. The Constraint Simplification Rules (CSR) subset of CHR and the flat subset of LCC, where agent nesting is restricted, are very close syntactically and semantically. The first contribution of this paper is to provide translations between CSR and flat-LCC and back. The second contribution is a transformation from the full LCC language to flat-LCC which preserves semantics. This transformation is similar to λ-lifting in functional languages. In conjunction with the equivalence between CHR and CSR with respect to naive operational semantics, these results lead to semantics-preserving translations from full LCC to CHR and conversely. Immediate consequences of this work include new proofs for CHR linear logic and phase semantics, relying on corresponding results for LCC, plus an encoding of the λ-calculus in CHR.