Semantics of Type Theory (eBook, PDF)
T. Streicher
eBook, PDF

Semantics of Type Theory (eBook, PDF)

Correctness, Completeness and Independence Results

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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 c...

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