Mathematics of Program Construction: 375th Anniversary of the Groningen University International Conference Groningen, The Netherlands, June 26–30, 1989 Proceedings

J. R. Abrial (auth.), J. L. A. van de Snepscheut (eds.)3540513051, 9783540513056

The papers included in this volume were presented at the Conference on Mathematics of Program Construction held from June 26 to 30, 1989. The conference was organized by the Department of Computing Science, Groningen University, The Netherlands, at the occasion of the University’s 375th anniversary. The creative inspiration of the modern computer has led to the development of new mathematics, the mathematics of program construction. Initially concerned with the posterior verification of computer programs, the mathematics have now matured to the point where they are actively being used for the discovery of elegant solutions to new programming problems. Initially concerned specifically with imperative programming, the application of mathematical methodologies is now established as an essential part of all programming paradigms – functional, logic and object-oriented programming, modularity and type structure etc. Initially concerned with software only, the mathematics are also finding fruit in hardware design so that the traditional boundaries between the two disciplines have become blurred. The varieties of mathematics of program construction are wide-ranging. They include calculi for the specification of sequential and concurrent programs, program transformation and analysis methodologies, and formal inference systems for the construction and analysis of programs. The mathematics of specification, implementation and analysis have become indispensable tools for practical programming.

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Table of contents :
A formal approach to large SOFTWARE CONSTRUCTION….Pages 1-20
Mathematics of program construction applied to analog neural networks….Pages 21-35
Termination is timing….Pages 36-47
Towards totally verified systems….Pages 48-65
Constructing a calculus of programs….Pages 66-90
Specifications of concurrently accessed data….Pages 91-114
Stepwise refinement of action systems….Pages 115-138
A lattice-theoretical basis for a specification language….Pages 139-156
Transformational programming and forests….Pages 157-173
Networks of communicating processes and their (De-)composition….Pages 174-196
Towards a calculus of data refinement….Pages 197-218
Stepwise refinement and concurrency: A small exercise….Pages 219-238
Deriving mixed evaluation from standard evaluation for a simple functional language….Pages 239-255
Realizability models for program construction….Pages 256-272
Initialisation with a final value, an exercise in program transformation….Pages 273-280
A derivation of a systolic rank order filter with constant response time….Pages 281-296
Searching by elimination….Pages 297-306
The projection of systolic programs….Pages 307-324
The formal construction of a parallel triangular system solver….Pages 325-334
Homomorphisms and promotability….Pages 335-347
Applicative assertions….Pages 348-362
Types and invariants in the refinement calculus….Pages 363-378
Algorithm theories and design tactics….Pages 379-398
A categorical approach to the theory of lists….Pages 399-408
Rabbitcounrt :=Rabbitcount — 1….Pages 409-420