Dependently typed programming based on automated theorem proving

Authors:
Alasdair Armstrong;Simon Foster;Georg Struth
Affiliations:
Department of Computer Science, University of Sheffield, UK;Department of Computer Science, University of Sheffield, UK;Department of Computer Science, University of Sheffield, UK
Venue:
MPC'12 Proceedings of the 11th international conference on Mathematics of Program Construction
Year:
2012

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Abstract

Mella is a minimalistic dependently typed programming language and interactive theorem prover implemented in Haskell. Its main purpose is to investigate the effective integration of automated theorem provers in this pure and simple setting. Such integrations are essential for supporting program development in dependently typed languages. We integrate the equational theorem prover Waldmeister and test it on more than 800 proof goals from the TPTP library. In contrast to previous approaches, the reconstruction of Waldmeister proofs within Mella is quite robust and does not generate a significant overhead to proof search. Mella thus yields a template for integrating more expressive theorem provers in more sophisticated languages.