Safe Modification of Pointer Programs in Refinement Calculus

This paper discusses stepwise refinement of pointer programs in the framework of refinement calculus. We augment the underlying logic with formulas of separation logic and then introduce a pair of new predicate transformers, called

separating assertion

and

separating assumption

. The new predicate transformers are derived from separating conjunction and separating implication, which are fundamental logical connectives in separation logic. They represent primitive forms of heap allocation/deallocation operators and the basic pointer statements can be specified by means of them. We derive several refinement laws that are useful for stepwise refinement and demonstrate the use of the laws in the context of correctness preserving transformations that are intended for improved memory usage.

The formal development is carried out in the framework of higher-order logic and is based on Back and Preoteasa’s axiomatization of state space and its extension to the heap storage [BP05, Pre06]. All the results have been implemented and verified in the theorem prover PVS.