Practical Program Verification by Forward Symbolic Execution: Correctness and Examples

We present the theoretical aspects and a prototype implementation in the Theorema system of a method for the verification of recursive imperative programs. The method is based on forward symbolic execution and functional semantics and generates first order verification conditions for the total correctness which use only the underlying theory of the program. All verification conditions are generated automatically by our prototype implementation in the frame of the Theorema system based on Mathematica. The termination property is expressed as an induction principle depending on the structure of the program with respect to recursion. It turns out that part of the verification conditions (notably the termination condition) are crucial for the existence of the function defined by the program, without which the total correctness formula is trivial due to inconsistency of the assumptions. The formal description of the method is the basis for the implementation and also for the proof of its correctness.