Thierry Coquand and Hendrik Persson. Grobner Bases in Type Theory. In T. Altenkirch, W. Naraschewski, and B. Reus, editors, Types for Proofs and Programs, volume 1657 of LNCS. Springer Verlag, Berlin, Heidelberg, New York, 1999.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....class of goal formulas defined in section 3. Furthermore we allow unproven lemmas D in the proof of 8x9yB, where D is a definite formula (also defined in section 3) Other interesting examples of program extraction from classical proofs have been studied by Murthy [16] Coquand s group (see e.g. [6]) in a type theoretic context and by Kohlenbach [13] using a Dialectica interpretation. There is also a different line of research aimed at giving an algorithmic interpretation to (specific instances of) the classical double negation rule. It essentially started with Griffin s observation [12] ....

Thierry Coquand and Hendrik Persson. Grobner Bases in Type Theory. In T. Altenkirch, W. Naraschewski, and B. Reus, editors, Types for Proofs and Programs, volume 1657 of LNCS. Springer Verlag, Berlin, Heidelberg, New York, 1999.

....standard transformation are necessary. In this paper we develop a refined method of extracting reasonable and sometimes unexpected programs from classical proofs. Other interesting examples of program extraction from classical proofs have been studied by Murthy [10] Coquand s group (see e.g. [4]) in a type theoretic context and by Kohlenbach [8] using a Dialectica interpretation. We now describe in more detail what the paper is about. In section 2 we fix our version of intuitionistic arithmetic for functionals, and recall how classical arithmetic can be seen as a subsystem. Then our ....

Thierry Coquand and Hendrik Persson. Grobner Bases in Type Theory. In T. Altenkirch, W. Naraschewski, and B. Reus, editors, Types for Proofs and Programs, volume 1657 of Lecture Notes in Computer Science. Springer Verlag, Berlin, Heidelberg, New York, 1999.

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