Encoding the calculus of constructions in a higher-order logic

The author presents an encoding of the calculus of constructions (CC) in a higher-order intuitionistic logic (I) in a direct way, so that correct typing in CC corresponds to intuitionistic provability in a sequent calculus for I. In addition, she demonstrates a direct correspondence between proofs in these two systems. The logic I is an extension of hereditary Harrop formulas (hh), which serve as the logical foundation of the logic programming language λProlog. Like hh, I has the uniform proof property, which allows a complete nondeterministic search procedure to be described in a straightforward manner. Via the encoding, this search procedure provides a goal directed description of proof checking and proof search in CC