Interprocedural Abstract Interpretation

Abstract

In this chapter we extend the theory of abstract interpretation interprocedurally. The point of this extension, which proceeds essentially along the lines of [KS1], is to mimic the operational behaviour of run-time systems of Algollike programming languages. Central is the introduction of data flow analysis stacks (DFA-stacks) and return functions. DFA-stacks can be considered the compile-time equivalent of run-time stacks of run-time systems. While the DFA-information of interest is encoded as intraprocedurally by the elements of a lattice, the local semantic functions defining the abstract semantics of elementary statements are enhanced. Interprocedurally, they work on DFA-stacks composed of lattice elements instead of lattice elements only. Return functions, finally, mimic the effect of a return from a (recursive) procedure call on the run-time stack. In comparison to the presentation of [KS1], the development is enhanced in order to handle formal procedure calls and external procedures.