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

Streicher, T.

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

Sinopsis

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.

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Editorial
Birkhäuser
Año de publicación
2012
Idioma
Inglés
ISBN 10 
1461267579
ISBN 13 
9781461267577
Encuadernación
Tapa blanda
Número de páginas
316
Contacto del fabricante
no disponible
Persona responsable
no disponible

Otras ediciones populares con el mismo título

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

Edición Destacada

ISBN 10:  0817635947 ISBN 13:  9780817635947
Editorial: Birkhauser Boston Inc, 1991
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