A domain-theoretic model construction for Coquand/Huet's calcu-lus of constructions
Résumé
Software is produced by humans and thus errorprone. To guarantee that a software product works correctly, that is, according to the given specification, it is normally tested against a variety of possible scenarios. As follows from daily experience not all errors will be found this way, leading to back-up cycles. For applications in safety-critical situations such as autonomous mobile robots or car driving systems this approach is thus inefficient: the correctness has to be mathematically proven. Given the size of such software packages, proving its correctness by hand is a tedious task. To this end interactive proof assistants have been developed that automatically generate large parts of the proof. A popular such assistant is the Coq package. It is based on the Calculus of Constructions (CC) introduced by T. Coquand and G. Huet (1988), still one of the most powerful systems of constructive logic.
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