Verification of Imperative Programs in Theorema

We present the design and the implementation of a prototype verification condition generator for imperative programs. The generator is part of the Theorema system, a computer aided mathematical assistant which offers automated reasoning and computer algebra facilities. We use Hoare Logic and the weakest precondition strategy, but in addition we propose a novel method for analyzing loop constructs by aid of algebraic computations: combinatorial summation and equational elimination. The verification conditions and the termination term for programs containing loops and procedure calls are generated fully automatically, in a form which can be immediately used by the automatic provers of Theorema in order to check whether they hold.