The Warshall Algorithm and Dickson's Lemma: Two Examples of Realistic Program Extraction

Authors:
Ulrich Berger;Helmut Schwichtenberg;Monika Seisenberger
Affiliations:
Department of Computer Science, University of Wales Swansea, Singleton Park, Swansea SA2 8PP, U.K.;Mathematisches Institut der Ludwig-Maximilians-Universität München, Theresienstraße 39, 80333 München, Germany;Mathematisches Institut der Ludwig-Maximilians-Universität München, Theresienstraße 39, 80333 München, Germany
Venue:
Journal of Automated Reasoning
Year:
2001

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Abstract

By means of two well-known examples it is demonstrated that the method of extracting programs from proofs is manageable in practice and may yield efficient programs. The Warshall algorithm computing the transitive closure of a relation is extracted from a constructive proof that repetitions in a path can always be avoided. Second, we extract a program from a classical (i.e., nonconstructive) proof of a special case of Dickson's lemma, by transforming the classical proof into a constructive one. These techniques (as well as the examples) are implemented in the interactive theorem prover MINLOG developed at the University of Munich.