Optimization Under the Perspective of Soundness, Completeness, and Reusability
Correct System Design, Recent Insight and Advances, (to Hans Langmaack on the occasion of his retirement from his professorship at the University of Kiel)
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Formal callability is the problem of determining for every formal procedure call of a program the set of procedures it may call at run-time. This information is the key for constructing the procedure call graph of a program, a common prerequisite of static analyses of programs with procedures. Moreover, under specific side-conditions it reduces in interprocedural data-flow analysis the analysis of programs with formal procedure calls to the analysis of programs without formal calls by treating formal calls as higher-order branch statements. We demonstrate that formal callability yields as a by-product the solution of the well-known formal reachability problem. This directly implies that formal callability is in general not decidable. However, we show that formal callability is decidable for programs, where formal procedure parameters do not occur in procedures, which are local to the procedure of their declaration (usually known as programs without global (formal) procedure parameters), but within a time bound which is exponential in the program size. Thus, we complement the new decidability result by introducing in addition a safe approximation of formal callability called potential passability, which can efficiently be computed. Moreover, for programs of mode depth 2 (i.e., formal procedures do not have procedures as parameters) without global procedure parameters, formal callability and potential passability coincide.