Much current research in computer science is concerned with two questions: is a program correct? And how can we improve a correct program preserving correctness? This latter question is known as the refinement of programs and the purpose of this book is to consider these questions in a formal setting. In fact, correctness turns out to be a special case of refinement and so the focus is on refinement. Although a reasonable background knowledge is assumed from mathematics and CS, the book is a self-contained introduction suitable for graduate students and researchers coming to this subject for...

Mathematics is based on proofs. The proof shows the logical reasoning behind a theorem, allows us to understand the meaning of it, its limitations and its consequences. Without a proof, a theorem is like magic; with a proof it is (sometimes more, sometimes less) self evident. But proofs are considered difficult in mathematics education of today, in particular at secondary level, and are therefore often avoided in teaching. When proofs are given, they are often informal and the underlying logic is not explicated. The purpose of this book is to put forward an alternative method for teaching...