Static Analysis of Multiparadigm Languages

We contribute to the state of the art in static analysis of declarative languages with multiparadigms. The language paradigms under consideration include normal order evaluation, higher-order functions, polymorphic typing, and logical variables. Our static analysis integrates strictness analysis, type inference, and mode analysis in a unified framework. Underlying the analysis in a unified framework. Underlying the analysis are various abstract domains and corresponding abstract semantics. The final semantic domain combines four notions: strictness subsets of operator occurrences, demand indicators, type indicators and instantiation indicator. The static analysis is defined by a set of abstract semantic functions expressing demand propagation, type and mode information through syntactic constructs of the interested language. Because of the formal semantics, the abstract properties of a program and the method itself may be reasoned formally. Under this semantics, all program expressions are given nontrivial annotation, it reflects that the expression is necessarily subject to evaluation corresponding to the indicated demand, and is expected to have the indicated type and instantiation mode. We start with a simple first-order language, and extend it with polymorphism, higherorder functions, and logical variables incrementally. The abstract domains and semantics are then modified correspondingly to reflect extensions of language paradigms. All the analysis methods are implemented. We also establish the relations between demands in our analysis and projections in context analysis and show that demands convey contextual strictness information through projections.