Invariant Relations: A Bridge from Programs to Equations

Great advances in program analysis would be enabled if it were possible to derive the function of a program from inputs to outputs (or from initial states to final states, depending on how we model program semantics). Efforts to do so have always stalled against the difficulty to derive the function of loops; the expedient solution to capture the function of loops by unrolling them an arbitrary number of iterations is clearly inadequate. In this paper, we propose a relations-based method to derive the function of a C-like program, including programs that have loops nested to an arbitrary level. To capture the semantics of loops, we use the concept of invariant relation.