Combinations of abstract domains for logic programming

Abstract interpretation [7] is a systematic methodology to designstatic program analysis which has been studied extensively in the logicprogramming community, because of the potential for optimizations inlogic programming compilers and the sophistication of the analyses whichrequire conceptual support. With the emergence of efficient genericabstract interpretation algorithms for logic programming, the mainburden in building an analysis is the abstract domain which gives a safeapproximation of the concrete domain of computation. However, accurateabstract domains for logic programming are often complex because of thevariety of analyses to perform their interdependence, and the need tomaintain structural information. The purpose of this paper is to proposeconceptual and software support for the design of abstract domains. Itcontains two main contributions: the notion of open product and ageneric pattern domain. The <?Pub Fmt italic>openproduct<?Pub Fmt /italic> is a new way of combining abstract domainsallowing each combined domain to benefit from information from the othercomponents through the notions of queries and open operations. The openproduct is general-purpose and can be used for other programmingparadigms as well. <?Pub Fmt italic>The generic patterndomain<?Pub Fmt /italic> Pat (<inline-equation><f><ge>R</ge></f> </inline-equation>)automatically upgrades a domain D with structuralinformation yielding a more accurate domain Pat (D) without additionaldesign or implementation cost. The two contributions are orthogonal andcan be combined in various ways to obtain sophisticated domains whileimposing minimal requirements on the designer. Both contributions arecharacterized theoretically and experimentally and were used to designvery complex abstract domains such as PAT(OProp<inline-equation><f>⊗</f></inline-equation>OMode<inline-equation><f>⊗</f><?Pub Caret></inline-equation>OPS) which would be very difficult todesign otherwise. On this last domain, designers need only contributeabout 20% (about 3,400 lines) of the complete system (about 17,700lines).