A Meta-Programming Approach to Realizing Dependently Typed Logic Programming

Dependently typed lambda calculi such as the Logical Framework (LF) can encode relationships between terms in types and can naturally capture correspondences between formulas and their proofs. Such calculi can also be given a logic programming interpretation: the Twelf system is based on such an interpretation of LF. We consider here whether a conventional logic programming language can provide the benefits of a Twelf-like system for encoding type and proofand-formula dependencies. In particular, we present a simple mapping from LF specifications to a set of formulas in the higher-order hereditary Harrop (hohh) language, that relates derivations and proof-search between the two frameworks. We then show that this encoding can be improved by exploiting knowledge of the well-formedness of the original LF specifications to elide much redundant type-checking information. The resulting logic program has a structure that closely resembles the original specification, thereby allowing LF speci...

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Zachary Snow, David Baelde, Gopalan Nadathur
• Keywords: CORR 2010, Education, Lambda Calculi, LF Specifications, Typed Lambda Calculi