Refinement Calculus A Systematic Introduction [Paperback]

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 the first time. There are numerous exercises provided of varying degrees of challenge.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 the first time. There are numerous exercises provided of varying degrees of challenge.1 Introduction.- 1.1 Contracts.- 1.2 Using Contracts.- 1.3 Computers as Agents.- 1.4 Algebra of Contracts.- 1.5 Programming Constructs.- 1.6 Specification Constructs.- 1.7 Correctness.- 1.8 Refinement of Programs.- 1.9 Background.- 1.10 Overview of the Book.- I Foundations.- 2 Posets, Lattices, and Categories.- 2.1 Partially Ordered Sets.- 2.2 Lattices.- 2.3 Product and Function Spaces.- 2.4 Lattice Homomorphisms.- 2.5 Categories.- 2.6 Summary and Discussion.- 2.7 Exercises.- 3 Higher-Order Logic.- 3.1 Types and Terms.- 3.2 Semantics.- 3.3 Deductive Systems.- 3.4 Theories.- 3.5 Summary and Discussion.- 3.6 Exercises.- 4 Fulƒ-