Semantics of Type Theory: Correctness, Completeness and Independence Results (Progress in Theoretical Computer Science) - Softcover

Streicher, T.

 
9781461267577: Semantics of Type Theory: Correctness, Completeness and Independence Results (Progress in Theoretical Computer Science)
Softcover
ISBN 10: 1461267579 ISBN 13: 9781461267577
Verlag: Birkhäuser, 2012

Inhaltsangabe

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 further: 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.

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Reseña del editor

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 further: 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.

„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.

Verlag
Birkhäuser
Erscheinungsdatum
2012
Sprache
Englisch
ISBN 10 
1461267579
ISBN 13 
9781461267577
Einband
Tapa blanda
Anzahl der Seiten
316
Kontakt zum Hersteller
Nicht verfügbar
Verantwortliche Person
Nicht verfügbar

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9780817635947: Semantics of Type Theory: Correctness, Completeness and Independence Results (Progress in Theoretical Computer Science)

Vorgestellte Ausgabe

ISBN 10:  0817635947 ISBN 13:  9780817635947
Verlag: Birkhauser Boston Inc, 1991
Hardcover