Abstracting Refinements for Transformation

ING REFINEMENTS FOR TRANSFORMATION EINAR BROCH JOHNSEN University of Oslo, Department of Informatics P.O. Box 1080 Blindern, N-0316 Oslo, Norway [email protected] CHRISTOPH LÜTH Universität Bremen, FB 3 — Mathematik und Informatik P.O. Box 330 440, D-28334 Bremen, Germany [email protected] Abstract. Formal program development by stepwise refinement involves a lot of work discharging proof obligations. Transformational techniques can reduce this work: applying correct transformation rules removes the need for verifying the correctness of each refinement step individually. However, a crucial problem is how to identify appropriate transformation rules. In this paper, a method is proposed to incrementally construct a set of correctness preserving transformation rules for refinement relations in arbitrary specification formalisms. Transformational developments are considered as proofs, which are generalised. This results in a framework where specific example refinements can be systematically generalised to more applicable transformation rules. The method is implemented in the Isabelle theorem prover and demonstrated on an example of data refinement. Formal program development by stepwise refinement involves a lot of work discharging proof obligations. Transformational techniques can reduce this work: applying correct transformation rules removes the need for verifying the correctness of each refinement step individually. However, a crucial problem is how to identify appropriate transformation rules. In this paper, a method is proposed to incrementally construct a set of correctness preserving transformation rules for refinement relations in arbitrary specification formalisms. Transformational developments are considered as proofs, which are generalised. This results in a framework where specific example refinements can be systematically generalised to more applicable transformation rules. The method is implemented in the Isabelle theorem prover and demonstrated on an example of data refinement. ACM CCS