Program extraction from nested definitions

Miyamoto, Kenji and Nordvall Forsberg, Fredrik and Schwichtenberg, Helmut; Blazy, Sandrine and Paulin-Mohring, Christine and Pichardie, David, eds. (2013) Program extraction from nested definitions. In: Interactive Theorem Proving. Lecture Notes in Computer Science . Springer Berlin/Heidelberg, FRA, pp. 370-385. ISBN 9783642396335 (https://doi.org/10.1007/978-3-642-39634-2_27)

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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.

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