The Interprocedural Coincidence Theorem

We present an interprocedural generalization of the well-known (intraprocedural) Coincidence Theorem of Kam and Ullman, which provides a sufficient condition for the equivalence of the meet over all paths (MOP) solution and the maximal fixed point (MFP) solution to a data flow analysis problem. This generalization covers arbitrary imperative programs with recursive procedures, global and local variables, and formal value parameters. In the absence of procedures, it reduces to the classical intraprocedural version. In particular, our stack-based approach generalizes the coincidence theorems of Barth and Sharir/Pnueli for the same setup, which do not properly deal with local variables of recursive procedures.