portada Semantics of Type Theory: Correctness, Completeness and Independence Results (en Inglés)

Semantics of Type Theory: Correctness, Completeness and Independence Results (en Inglés)

Formato

Libro Físico

Autor

T. Streicher

Editorial

Birkhauser

Idioma

Inglés

N° páginas

299

Encuadernación

Tapa Blanda

Dimensiones

23.4x15.6x1.7 cm

Peso

0.44 kg.

ISBN13

9781461267577

Categorías

Ciencia y análisis de datos: generalidades
Fundamentos matemáticos
Análisis y captura de datos
Ciencias de la computación

Semantics of Type Theory: Correctness, Completeness and Independence Results (en Inglés)

T. Streicher (Autor) · Birkhauser · Tapa Blanda

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Reseña del libro "Semantics of Type Theory: Correctness, Completeness and Independence Results (en Inglés)"

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.