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Full Description
Deductive program design aims at methods that guide and support the development of programs by techniques of deduction. Deduction is a well-known subject of study in logical theories. However, the application of deductive techniques in program design needs methods, heuristics, and understanding of the required forms and formats of the development result that go far beyond those found in logical theories. The summer school presents a very broad spectrum of approaches to these issues. Edsger W. Dijkstra gives a number of beautiful examples that show how to design proofs. Samson Abramsky, Simon Gay, and Rajagopal Nagarajan contribute a fundamental study founding concurrent programming on interaction categories and foundations of type theory. Tony Hoare presents unifying views on mathematical models for computing science. Unifying theories are especially important if the whole development process of programs is to be supported by deductive techniques. The rest of the contributions address applications of deductive program design methods. They are directed to different areas of application; for example Richard Bird's and Oege de Moor's algebra of programming is mainly intended for classical functional programming, and the contribution on data refinement and their transformation by David Gries considers sequential procedural programs.
Contents
On Traditions in Marktoberdorf (Banquet Speech).- 0. Examples of Proof Design.- Fibonacci and the Greatest Common Divisor (EWD1077).- The Balance and the Coins (EWD1083).- Bulterman's Theorem on Shortest Trees (EWD1131).- A Prime is in at Most 1 Way the Sum of 2 Squares (EWD1155a).- A Bagatelle on Euclid's Algorithm (EWD1158).- On Two Equations that Have the Same Extreme Solution (EWD1168).- An Alternative of the ETAC to EWD1163 (EWD1169).- The Argument about the Arithmetic Mean and the Geometric Mean, Heuristics Included (EWD1171).- 1. Mathematical Models of Programming.- Interaction Categories and the Foundations of Typed Concurrent Programming.- Mathematical Models for Computing Science.- 2. Techniques of Program Derivation.- The Algebra of Programming.- Data Refinement and the Transform.- 3. Logic of Concurrency.- On TLA as a Logic.- Specification and Refinement of a Buffer of Length One.- Model Checking.- Notes on Proof Outline Logic.- 4. Method of Hardware Design.- Proof and Design.- A Program Transformation Approach to Asynchronous VLSI Design.
