Proving and Disproving in Dynamic Logic for Java

Abstract: This thesis is about proving the functional correctness and incorrectness of imperative, object-oriented programs. One of the main approaches for the first item is deductive program verification, whereas the second item is traditionally handled by techniques like testing. In this thesis, we show how both correctness and incorrectness can be covered by dynamic logic for Java (a program logic) and be handled using similar techniques. The theorem prover KeY, which provides an implementation of dynamic logic for Java, was used for experiments and was extended for this purpose.

We introduce the concept of taclets, which is the rule language that is used to implement the calculus for Java dynamic logic in KeY. Apart from a detailed introduction of the language and complete definitions of the semantics of taclets, reasoning about the correctness of taclets is discussed. This part of the thesis is the most complete account on taclets so far.

The concept of updates is described, which is the central component for performing symbolic execution in Java dynamic logic. Updates are systematically developed as an imperative programming language that provides the following constructs: assignments, guards, sequential composition and bounded as well as unbounded parallel composition. The language is equipped both with a denotational semantics and a correct rewriting system for execution, whereby the latter is a generalisation of the syntactic application of substitutions. The normalisation of updates is discussed.