Provably Correct Graph Transformations with Small-tALC

We present a prototype for executing and verifying graph transformations. The transformations are written in a simple imperative programming language, and preand post-conditions as well as loop invariants are specified in the Description Logic ALC (whence the name of the tool). The programming language has a precisely defined operational semantics and a sound Hoare-style calculus. The tool consists of the following sub-components: a compiler to Java for executing the transformations; a verification condition generator; and a tableau prover for an extension of ALC capable of deciding the generated verification conditions. A description of these components and their interaction is the main purpose of this paper.