Proving pointer programs in higher-order logic

Building on the work of Burstall, this paper develops sound modelling and reasoning methods for imperative programs with pointers: heaps are modelled as mappings from addresses to values, and pointer structures are mapped to higher-level data types for verification. The programming language is embedded in higher-order logic. Its Hoare logic is derived. The whole development is purely definitional and thus sound. Apart from some smaller examples, the viability of this approach is demonstrated with a non-trivial case study. We show the correctness of the Schorr–Waite graph marking algorithm and present part of its readable proof in Isabelle/HOL.

Authors

• Farhad Mehta
• Tobias Nipkow

Keywords

• Pointer programs
• Verification
• Hoare logic
• Higher-order logic
• Schorr–Waite algorithm