A Practical Approach to Verification of Recursive Programs in Theorema extended abstract

We report work in progress concerning the theoretical basis and the implementation in the Theorema system of a methodology for the generation of verification conditions for recursive procedures, with the aim of practical verification of recursive programs. Proving total correctness is achieved by proving separately partial correctness and then termination. We develop a pattern for proving partial correctness properties of programs which have simple functional recursive definitions, and we discuss how this can be extended to recursive programs having multiple recursive calls. The method for proving partial correctness is based on Scott Induction, from which we extract the essential features. Furthermore we develop a pattern for proving termination of simple recursive functional programs, uder the assumption that total correctness of all the auxiliary functions used in the program definition is provided. Combining the verification conditions from the two parts (partial correctness and termination) we construct verification conditions for proving total correctness. While proving [partial] correctness of non-recursive procedural programs is quite well understood, for instance by using Hoare Logic [3], [5], there are relatively few approaches to recursive procedures (see e.g. [7] Chap. 2). ∗The program verification project in the frame of e-Austria Timişoara is supported by BMBWK (Austrian Ministry of Education, Science and Culture), BMWA (Austrian Ministry of Economy and Work) and MEC (Romanian Ministry of Education and Research). The Theorema project is supported by FWF (Austrian National Science Foundation) – SFB project P1302.