Ebook: Programming and Mathematical Method: International Summer School

The Summer School in Marktoberdorf 1990 had as its overall theme the development of programs as an activity that can be carried out based on and supported by a mathematical method. In particular mathematical methods for the development of programs as parts of distributed systems were included. Mathematical programming methods are a very important topic for which a lot of research in recent years has been carried out. In the Marktoberdorf Summer School outstanding scientists lectured on mathematical programming methods. The lectures centred around logical and functional calculi for the • specification, • refinement, • verification of programs and program systems. Some extremely remarkable examples were given. Looking at these examples it becomes clear that proper research and teaching in the area of program methodology should always show its value by being applied at least to small examples or case studies. It is one of the problems of computing science that examples and case studies have to be short and small to be lJresentable in lectures and papers of moderate size. However, even small examples can tell a lot about the tractability and adequacy of methods and being able to treat small examples does at least prove that the method can be applied in modest ways. Furthermore it demonstrates to some extent the notational and calculational overhead of applying formal methods.

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The construction of a software system is a task that has to be structured toensure that the software product fulfills all expectations and the process of producing it remains manageable and reliable. Mathematical methods, including logic, algebra and functional calculus, are needed to support structuring and provide notations and basic formal concepts for the foundations of software engineering. Mathematical methods of programming reflect the need for modularization and abstraction and suggest appropriate goal-directed procedures for the construction of software programs. This volume contains the proceedings of an International Summer School held at Marktoberdorf in 1990, the 11th in a series on mathematical methods in programming. Outstanding scientists contributed papers centered around logical and functional calculi for the specification, refinement and verification of programs and program systems, and remarkable examples for the formal development of proofs and algorithms are given.

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The construction of a software system is a task that has to be structured toensure that the software product fulfills all expectations and the process of producing it remains manageable and reliable. Mathematical methods, including logic, algebra and functional calculus, are needed to support structuring and provide notations and basic formal concepts for the foundations of software engineering. Mathematical methods of programming reflect the need for modularization and abstraction and suggest appropriate goal-directed procedures for the construction of software programs. This volume contains the proceedings of an International Summer School held at Marktoberdorf in 1990, the 11th in a series on mathematical methods in programming. Outstanding scientists contributed papers centered around logical and functional calculi for the specification, refinement and verification of programs and program systems, and remarkable examples for the formal development of proofs and algorithms are given.
Content:
Front Matter....Pages I-VIII
Front Matter....Pages 1-2
On the design of a simple proof for Morley’s Theorem....Pages 3-9
Well-foundedness and the transitive closure....Pages 11-15
Designing the proof of Vizing’s Theorem....Pages 17-25
Phase Synchronization for two machines....Pages 27-31
The Lexicographic Minimum of a Cyclic Array....Pages 33-42
Front Matter....Pages 43-44
Metalevel Programming in Constructive Type Theory....Pages 45-93
Laws of Programming....Pages 95-122
Some Applications of Pointer Algebra....Pages 123-155
Some generalizations and applications of Dijkstra’s guarded commands....Pages 157-191
Front Matter....Pages 193-194
A Theory of Program Composition....Pages 195-212
Lectures on Data Refinement....Pages 213-244
Refinement algebra proves correctness of compilation....Pages 245-269
Front Matter....Pages 271-272
Process Algebra with Signals and Conditions....Pages 273-323
Functional Specification of Time Sensitive Communicating Systems....Pages 325-367
Systematic Derivation of Communicating Programs....Pages 369-407
Back Matter....Pages 409-412

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The construction of a software system is a task that has to be structured toensure that the software product fulfills all expectations and the process of producing it remains manageable and reliable. Mathematical methods, including logic, algebra and functional calculus, are needed to support structuring and provide notations and basic formal concepts for the foundations of software engineering. Mathematical methods of programming reflect the need for modularization and abstraction and suggest appropriate goal-directed procedures for the construction of software programs. This volume contains the proceedings of an International Summer School held at Marktoberdorf in 1990, the 11th in a series on mathematical methods in programming. Outstanding scientists contributed papers centered around logical and functional calculi for the specification, refinement and verification of programs and program systems, and remarkable examples for the formal development of proofs and algorithms are given.
Content:
Front Matter....Pages I-VIII
Front Matter....Pages 1-2
On the design of a simple proof for Morley’s Theorem....Pages 3-9
Well-foundedness and the transitive closure....Pages 11-15
Designing the proof of Vizing’s Theorem....Pages 17-25
Phase Synchronization for two machines....Pages 27-31
The Lexicographic Minimum of a Cyclic Array....Pages 33-42
Front Matter....Pages 43-44
Metalevel Programming in Constructive Type Theory....Pages 45-93
Laws of Programming....Pages 95-122
Some Applications of Pointer Algebra....Pages 123-155
Some generalizations and applications of Dijkstra’s guarded commands....Pages 157-191
Front Matter....Pages 193-194
A Theory of Program Composition....Pages 195-212
Lectures on Data Refinement....Pages 213-244
Refinement algebra proves correctness of compilation....Pages 245-269
Front Matter....Pages 271-272
Process Algebra with Signals and Conditions....Pages 273-323
Functional Specification of Time Sensitive Communicating Systems....Pages 325-367
Systematic Derivation of Communicating Programs....Pages 369-407
Back Matter....Pages 409-412
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