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.
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Berger, U., Schwichtenberg, H. & Seisenberger, M. The Warshall Algorithm and Dickson's Lemma: Two Examples of Realistic Program Extraction. Journal of Automated Reasoning 26, 205–221 (2001). https://doi.org/10.1023/A:1026748613865
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DOI: https://doi.org/10.1023/A:1026748613865