Dependent types ensure partial correctness of theorem provers

Authors:
Andrew W. Appel;Amy P. Felty
Affiliations:
Princeton University, 35 Olden Street, Princeton, NJ 08544, USA (e-mail: appel@princeton.edu);University of Ottawa, 800 King Edward Ave., Ottawa, Ontario K1N 6N5, Canada (e-mail: afelty@site.uottawa.ca)
Venue:
Journal of Functional Programming
Year:
2004

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Abstract

Static type systems in programming languages allow many errors to be detected at compile time that wouldn't be detected until runtime otherwise. Dependent types are more expressive than the type systems in most programming languages, so languages that have them should allow programmers to detect more errors earlier. In this paper, using the Twelf system, we show that dependent types in the logic programming setting can be used to ensure partial correctness of programs which implement theorem provers, and thus avoid runtime errors in proof search and proof construction. We present two examples: a tactic-style interactive theorem prover and a union-find decision procedure.