Situated Simplification

Testing satisfaction of guards is the essential operation of concurrent constraint programming (CCP) systems. We present and prove correct, for the first time, an incremental algorithm for the simultaneous tests of entailment and disentailment of rational tree constraints to be used in CCP systems with deep guards (e.g., in AKL or in Oz). The algorithm is presented as the simplz+ztion of the constraints which form the (possibly deep) guards and which are situated at different nodes in a tree (of arbitrary depth). The nodes correspond to local computation spaces. In this algorithm, a variable may have multiple bindings (which each represent a constraint on that same variable in a different node). These may be realized in various ways. We give a simple fixed-point algorithm and use it for proving that the tests implemented by another, practical algorithm are correct and complete for entailment and disentailment. We formulate the results in this paper for rational tree constraints; they can be adapted to finite and feature trees.