The worker-wrapper transformation: getting it right and making it better

A program optimisation must have two key properties: it must preserve the meaning of programs (correctness) while also making them more efficient (improvement). An optimisation's correctness can often be rigorously proven using formal mathematical methods, but improvement is generally considered harder to prove formally and is thus typically demonstrated with empirical techniques such as benchmarking. The result is a conspicuous ``reasoning gap'' between correctness and efficiency. In this thesis, we focus on a general-purpose optimisation: the worker\slash wrapper transformation. We develop a range of theories for establishing correctness and improvement properties of this transformation that all share a common structure. Our development culminates in a single theory that can be used to reason about both correctness and efficiency in a unified manner, thereby bridging the reasoning gap

Computer-Assisted Program Reasoning Based on a Relational Semantics of Programs

We present an approach to program reasoning which inserts between a program and its verification conditions an additional layer, the denotation of the program expressed in a declarative form. The program is first translated into its denotation from which subsequently the verification conditions are generated. However, even before (and independently of) any verification attempt, one may investigate the denotation itself to get insight into the "semantic essence" of the program, in particular to see whether the denotation indeed gives reason to believe that the program has the expected behavior. Errors in the program and in the meta-information may thus be detected and fixed prior to actually performing the formal verification. More concretely, following the relational approach to program semantics, we model the effect of a program as a binary relation on program states. A formal calculus is devised to derive from a program a logic formula that describes this relation and is subject for inspection and manipulation. We have implemented this idea in a comprehensive form in the RISC ProgramExplorer, a new program reasoning environment for educational purposes which encompasses the previously developed RISC ProofNavigator as an interactive proving assistant.Comment: In Proceedings THedu'11, arXiv:1202.453

Fifty years of Hoare's Logic

We present a history of Hoare's logic.Comment: 79 pages. To appear in Formal Aspects of Computin