A functional approach to worst-case execution time analysis

Abstract

Modern hard real-time systems demand safe determination of bounds on the execution times of programs. To this purpose, program execution for all possible combinations of input values is impracticable. In alternative, static analysis methods provide sound and efficient mechanisms for determining execution time bounds, regardless of input data. We present a calculation-based and compositional development of a functional static analyzer using the Abstract Interpretation framework. Meanings of programs are expressed in fixpoint form, using a two-level denotational meta-language. At the higher level, we devise a uniform fixpoint semantics with a relational-algebraic shape, defined as the reflexive transitive closure of the program binary relations. Fixpoints are calculated in the point-free style using functional composition and a proper recursive operator. At the lower level, state transformations are specified by semantic transformers designed as abstract interpretations of the transition semantics.