Modeling Object Oriented Constraint Programs in Z

Abstract: Object oriented constraint programs (OOCPs) emerge as a leading evolution of constraint programming and artificial intelligence, first applied to a range of industrial applications called configuration problems. The rich variety of technical approaches to solving configuration problems (CLP(FD), CC(FD), DCSP, Terminological systems, constraint programs with set variables ...) is a source of difficulty. No universally accepted formal language exists for communicating about OOCPs, which makes the comparison of systems difficult. We present here a Z based specification of OOCPs which avoids the falltrap of hidden object semantics. The object system is part of the specification, and captures all of the most advanced notions from the object oriented modeling standard UML. The paper illustrates these issues and the conciseness and precision of Z by the specification of a working OOCP that solves an historical AI problem : parsing a context free grammar. Being written in Z, an OOCP specification also supports formal proofs. The whole builds the foundation of an adaptative and evolving framework for communicating about constrained object models and programs.