## Paper: Encoding the calculus of constructions in a higher-order logic (at LICS 1993)

**Amy Felty**

### Abstract

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

### BibTeX

@InProceedings{Felty-Encodingthecalculus, author = {Amy Felty}, title = {Encoding the calculus of constructions in a higher-order logic}, booktitle = {Proceedings of the Eighth Annual IEEE Symposium on Logic in Computer Science (LICS 1993)}, year = {1993}, month = {June}, pages = {233--244}, location = {Montreal, Canada}, publisher = {IEEE Computer Society Press} }