A syntactic approach to inferring the life-time of data-regions

Structured operational semantics is widely recognized as a conceptually simple and practically expressive framework to formally design type systems in programming languages. Being easy to reason with, the type-theoretical setting of operational semantics is used increasingly to formulate program analysis techniques, called effect systems. Effect systems distinguish between the specification of a program analysis problem, defined as a logic, and its implementation, by using resolution and inference techniques. However, specifying precise program analysis, by considering expressive type systems, requires addressing difficult type-theoretical issues. Giving polymorphic types to recursive functions or using subtyping in the presence of type polymorphism are such issues. We present a new program analysis technique which is first to correctly integrate these type-theoretical features within a decidable setting. Our analysis statically determines the life-time of aliased data regions. It uses subtyping to statically approximate alias properties of data. It employs region polymorphism to denote the generic usage of data within value definitions and recursive function definitions. A key ingredient to correctly and intuitively integrating these typing features are a syntactic representation of dynamic locations and of their static abstractions using regions. We present an inference algorithm which precisely determines these abstractions by using fixed-point iteration. It reconstructs the principal solution of the analysis logic and takes the contextual use of (recursive) function definitions into account. We prove its termination soundness and completeness with respect to the analysis logic. As a result, our technique shares with previous effect systems a conceptual simplicity, yet providing more precise information.