Semantics of Type Theory: Correctness, Completeness and Independence Results

di T. Streicher (Autore)

Springer-Verlag New York Inc., 2012

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.

• Autore: T. Streicher
• Editore: Springer-Verlag New York Inc.
• Collana: Progress in Theoretical Computer Science
• Anno: 2012
• Rilegatura: Paperback / softback
• Pagine: 299 p.
• Dimensioni: 235 x 155 mm
• EAN: 9781461267577

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