A Compositional Theory of Constraint

We propose a variant of the Hierarchical Constraint Logic Programming (HCLP) scheme of Borning, Wilson, and others. We consider compositionality and incre-mentality in Constraint Logic Programming, introduce HCLP, and present Wilson's proof 11] that it is non-compositional and non-monotonic. We deene a scheme for composing together solutions to individual hierarchies and show that hierarchy composition can be expressed very simply using bags (multisets). We have developed an alternative to bag intersection called guard, and we prove that it has various properties. First we use it to deene BCH, a scheme which calculates a superset of the solutions expected from HCLP. We prove that BCH is compositional. We then de-ne FGH, a non-compositional scheme which removes precisely those BCH solutions which are unacceptable to HCLP. FGH uses a class of functions we have deened, called lters; we give examples. We argue that the decomposition of HCLP into two parts, one compositional and one non-compositional, gives insight into HCLP's non-monotonicity and results in a more elegant semantics which is amenable to eecient implementation. A shorter version of this paper has been submitted to CP95.