A meta-programming approach to realizing dependently typed logic programming

  • Authors:

  • Zachary Snow;David Baelde;Gopalan Nadathur

  • Affiliations:

  • University of Minnesota, Minneapolis, MN, USA;University of Minnesota, Minneapolis, MN, USA;University of Minnesota, Minneapolis, MN, USA

  • Venue:
  • Proceedings of the 12th international ACM SIGPLAN symposium on Principles and practice of declarative programming
  • Year:
  • 2010

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Abstract

Dependently typed λ-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 proof-and-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 specifications to be viewed as hohh meta-programs. Using the Teyjus implementation of λ Prolog, we show that our translation provides an efficient means for executing LF specifications, complementing the ability that the Twelf system provides for reasoning about them.