Computational Reflection in the Calculus of Constructions and its Application to Theorem Proving

This paper describes a computational reflection mechanism for the calculus of constructions. In this framework it is possible to encode functions that operate on syntactic representations on the meta-level and to verify semantic relations between the object-level denotations of the source and the target of meta-functions. Moreover, it is shown how computational reflection can easily be integrated with existing proof development systems based on refinement methods in order to extend theorem proving capabilities in a sound way.

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