Refinement to Imperative HOL

Many algorithms can be implemented most efficiently with imperative data structures. This paper presents Sepref, a stepwise refinement based tool chain for the verification of imperative algorithms in Isabelle/HOL. As a back end we use imperative HOL, which allows to generate verified imperative code. On top of imperative HOL, we develop a separation logic framework with powerful proof tactics. We use this framework to verify basic imperative data structures and to define a refinement calculus between imperative and functional programs. We provide a tool to automatically synthesize a concrete imperative program and a refinement proof from an abstract functional program, selecting implementations of abstract data types according to a user-provided configuration. As a front end to describe the abstract programs, we use the Isabelle Refinement Framework, for which many algorithms have already been formalized. Our tool chain is complemented by a large selection of verified imperative data structures. We have used Sepref for several verification projects, resulting in efficient verified implementations that are competitive with unverified ones in Java or C ++ .