A meta-programming approach to realizing dependently typed logic programming

Zachary Snow, David Baelde, Gopalan Nadathur

Research output: Chapter in Book/Report/Conference proceedingConference contribution

13 Scopus citations

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 λProlog, 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.

Original languageEnglish (US)
Title of host publicationPPDP'10 - Proceedings of the 2010 Symposium on Principles and Practice of Declarative Programming
Pages187-198
Number of pages12
DOIs
StatePublished - 2010
Event12th International ACM SIGPLAN Symposium on Principles and Practice of Declarative Programming, PPDP 2010 - Hagenberg, Austria
Duration: Jul 26 2010Jul 28 2010

Publication series

NamePPDP'10 - Proceedings of the 2010 Symposium on Principles and Practice of Declarative Programming

Other

Other12th International ACM SIGPLAN Symposium on Principles and Practice of Declarative Programming, PPDP 2010
CountryAustria
CityHagenberg
Period7/26/107/28/10

Keywords

  • Dependently typed lambda calculi
  • Higher-order logic programming
  • Logical frameworks
  • Translation

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