Correctness and Completeness (Progress in Theoretical Computer Science) - Hardcover

T. Streicher

Hardcover

ISBN 10: 0817635947 ISBN 13: 9780817635947

Publisher: Birkhäuser Boston, 1991

Synopsis

Typing plays an important role in software development. Types can be consid­ ered as weak specifications of programs and checking that a program is of a certain type provides a verification that a program satisfies such a weak speci­ fication. By translating a problem specification into a proposition in constructive logic, one can go one step the effectiveness and unifonnity of a con­ structive proof allows us to extract a program from a proof of this proposition. Thus by the "proposition-as-types" paradigm one obtains types whose elements are considered as proofs. Each of these proofs contains a program correct w.r.t. the given problem specification. This opens the way for a coherent approach to the derivation of provably correct programs. These features have led to a "typeful" programming style where the classi­ cal typing concepts such as records or (static) arrays are enhanced by polymor­ phic and dependent types in such a way that the types themselves get a complex mathematical structure. Systems such as Coquand and Huet's Calculus of Con­ structions are calculi for computing within extended type systems and provide a basis for a deduction oriented mathematical foundation of programming. On the other hand, the computational power and the expressive (impred­ icativity !) of these systems makes it difficult to define appropriate semantics.

Edition details

• Publisher: Birkhäuser Boston
• Publication date: 1991
• Language: English
• ISBN 10: 0817635947
• ISBN 13: 9780817635947
• Binding: Hardcover
• Edition number: 1
• Number of pages: 298