Section: Scientific Foundations

Concurrent constraint programming

The class of Concurrent Constraint programming languages (CC) was introduced a decade ago by Vijay Saraswat as a unifying framework for constraint logic programming and concurrent logic programming. The CC paradigm constitutes a representative abstraction of constraint programming languages, and thus allows a fine grained study of their fundamental properties.

CC generalizes the Constraint Logic Programming framework (CLP) by introducing a synchronization primitive, based on constraint entailment. It is a model of concurrent computation, where agents communicate through a shared store, represented by a constraint, which expresses some partial information on the values of the variables involved in the computation. The variables play the role of transmissible dynamically created communication channels.

One of the big successes of CC has been the simple and elegant reconstruction of finite domain constraint solvers, and the cooperation of several models to solve a single combinatorial problem. On the other hand, to use CC for programming reactive applications forces one to abandon the hypothesis of monotonic evolution of the constraint store; this is a strong motivation for new extensions of CC languages.

There are strong completeness theorems relating the execution of a CLP program and its translation in classical logic, which provide smooth reasoning techniques for such programs. However these theorems are broken by the synchronization operation of CC. Looking for a logical semantics of CC programs in the general paradigm of logic programming,

program = logical formula,

execution = proof search,

leads to a translation in Jean-Yves Girard's linear logic. This allows the recovery of some completeness results about successes and stores; even suspensions may be characterized with the non-commutative logic of Ruet and Abrusci.

It is thus possible to address important issues for Constraint Programming:

• verifying CC programs;

• combining CLP and state-based programming;

• dealing with local search inside a global constraint solving procedure.

The last two cases rely on a natural extension of CC languages, called Linear Concurrent Constraint languages (LCC), which simply replaces constraint systems built onto classical logic by constraint systems built onto linear logic. This allows us to represent state changes thanks to the consumption of resources during the synchronization action, modeled by the linear implication.