Inference of polymorphic and conditional strictness propertiesThomas

We deene an inference system for modular strictness analysis of functional programs by extending a conjunctive strictness logic with polymorphic and conditional properties. This extended set of properties is used to deene a syntax-directed, polymorphic strictness analysis based on polymorphic recur-sion whose soundness is established via a translation from the polymorphic system into the conjunctive system. From the polymorphic analysis, an inference algorithm based on constraint resolution is derived and shown complete for variant of the polymorphic analysis. The algorithm deduces at the same time a property and a set of hypotheses on the free variables of an expression which makes it suitable for analysis of program with module structure. 1 Introduction Static analysis of program fragments with free variables usually either requires an environment associating a property with each free variable or assumes that only trivial properties hold of the free variables. For programs structured into modules the latter approach is often the only one feasible and leads to poor analysis results. This paper suggests an improvement to this by proposing a modular program analysis framework where analysis of a program fragment results in a property and and environment that together describes the relation between the properties of the free variables and the result of the program. The presentation of program analyses via a set of logical inference rules (also called \non-standard type systems") is now a commonly used tool and has been applied to strictness , binding-time and control-ow analysis amongst others. Our approach consists in extending existing monomorphic analyses with polymorphic and conditional program properties (deened below). We focus on strictness analysis in this paper but a similar analysis for binding-time could be obtained from the analysis described in 10] and recently Banerjee 3] has presented a control-ow analysis for the pure lambda calculus, engineered using similar methods. Strictness types were considered by Kuo and Mishra 21]. With f standing for the property \undeened", a function is