Program extraction from nested definitions

Authors:
Kenji Miyamoto;Fredrik Nordvall Forsberg;Helmut Schwichtenberg
Affiliations:
Ludwig-Maximilians-Universität München, Germany;Swansea University, UK;Ludwig-Maximilians-Universität München, Germany
Venue:
ITP'13 Proceedings of the 4th international conference on Interactive Theorem Proving
Year:
2013

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Abstract

Minlog is a proof assistant which automatically extracts computational content in an extension of Gödel's T from formalized proofs. We report on extending Minlog to deal with predicates defined using a particular combination of induction and coinduction, via so-called nested definitions. In order to increase the efficiency of the extracted programs, we have also implemented a feature to translate terms into Haskell programs. To illustrate our theory and implementation, a formalisation of a theory of uniformly continuous functions due to Berger is presented.