Section: New Results

Constraint Handling Rules and Linear Logic

Participants : François Fages, Thierry Martinez, Sylvain Soliman.

Implementations of Constraint Handling Rules (CHR) follow a committed-choice forward chaining execution model: the non-determinism of the abstract semantics is partly refined with extra-logical syntactic convention on the program order and possibly notations for weighted semantics (with priorities or probabilities), and partly left unspecified in the underlying compiler. In [13] , we propose an alternative execution model which explores all the possible choices, by opposition to the committed-choice strategy. This execution model is angelic in the sense that if there exists a successful execution strategy (with respect to a given observable), then this strategy will be found. Formally, the set of computed goals is complete with respect to the set of the logical consequences of the interpretation of the initial goal in linear logic. In practice, this paper introduces a new data representation for sets of goals, the derivation nets. Sharing strategies between computation paths can be defined for derivation nets to make execution algorithmically tracktable in some cases where a naive exploration would be exponential. Control for refined execution is recovered with the introduction of user constraints to encode sequencing, fully captured in the linear-logic interpretation. As a consequence of angelic execution, CHR rules become decomposable while preserving accessibility properties. This decomposability makes natural the definition in angelic CHR of meta-interpreters to change the execution strategy. More generally, arbitrary computation can be interleaved during head matching, for custom user constraint indexation and deep guard definition.