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Home/ Semantics of Type Theory: Correctness, Completeness and Independence Results (Softcover Reprint of t
Semantics of Type Theory: Correctness, Completeness and Independence Results (Softcover Reprint of t

Semantics of Type Theory: Correctness, Completeness and Independence Results (Softcover Reprint of t

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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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Pub dateOct 29, 2012
ISBN-101461267579
ISBN-139781461267577
LanguageEnglish
Last updated 2026-01-28 09:01
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