Mathematical Methods in Program Development

Modern information processing systems show such complex properties as distribution, parallelism, interaction, time dependency, and nondeterminism. For critical applications, mathematical methods are needed to model the systems and to support their development and validation. Impressive progress in mathematical methods for programming software systems makes it possible to think about unifying the different approaches. This book gives a comprehensive overview of existing methods and presents some of the most recent results in applying them. The main topics are: advanced programming techniques, foundations of systems engineering, mathematical support methods, and application of the methods. The approaches presented are illustrated by examples and related to other approaches.

Eliminating the Chaff—Again: Banquet Speech at Marktoberdorf 1996.- Envoi at Marktoberdorf 1996.- 0. Designing Proofs and Programs.- Heuristics for a Very Simple Euclidean Proof (EWD1180).- Complete DAGs (EWD1204).- A Result of Rabbit Removal (EWD1208).- For the Record: Painting the Squared Plane (EWD1212).- The Marriage Agency (EWD1214).- Courtesy Dr. Birgit Schieder (EWD1215).- WLOG, or the Misery of the Unordered Pair (EWD1223).- My Simplest Theorem (EWD1232).- The Transitive Closure of a Wellfounded Relation (EWD1241).- The Formula for sin. (a + /?) (EWD1244a).- A Kind of Converse of Leibniz’s Principle (EWD1245).- The Strengths of the Academic Enterprise (EWD1175).- On a Method for the Formal Design of Multiprograms.- Foundations for Calculational Logic.- 1. Examples of Protocol Design.- Specification and Design of a Transmission Protocol by Successive Refinements Using B.- Formal Derivation of a Protocol in CSP.- 2. Languages and Models for Program Design.- Genesis of Algorithmic Languages.- Mathematical Methods in System and Software Engineering.- Unified Theories of Programming.- 3. Programming Paradigms.- On the Relationship Between Classes, Objects and Data Abstraction.- The Oz Programming Model.- A Foundation for Higher-order Concurrent Constraint Programming.- 4. Mechanical Proof Assistance.- Tool Support for Logics of Programs.- Machine-Assisted Verification Using Theorem Proving and Model Checking.