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| HAL : hal-00507775, version 1 |
| Fiche détaillée |  Récupérer au format |
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| Proving Fixed Points |
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| Hervé Grall 1, 2 |
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| (30/07/2010) |
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| We propose a method to characterize the fixed points described in Tarski's theorem for complete lattices. The method is deductive: the least and greatest fixed points are "proved" in some inference system defined from deduction rules. We also apply the method to two other fixed point theorems, a generalization of Tarski's theorem to chain-complete posets and Bourbaki-Witt's theorem. Finally, we compare the method with the traditional iterative method resorting to ordinals and the original impredicative method used by Tarski. |
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| 1 : | Laboratoire d'Informatique de Nantes Atlantique (LINA) |
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CNRS : UMR6241 – Université de Nantes – École Nationale Supérieure des Mines - Nantes |
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| 2 : | ASCOLA (INRIA - EMN) |
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INRIA – École Nationale Supérieure des Mines - Nantes |
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| Domaine | : | Informatique/Logique en informatique |
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| fixed points – partially ordered sets – inference systems – induction – coinduction |
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| Liste des fichiers attachés à ce document : | |||||
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| hal-00507775, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00507775 | |
| oai:hal.archives-ouvertes.fr:hal-00507775 | |
| Contributeur : Hervé Grall | |
| Soumis le : Samedi 31 Juillet 2010, 10:06:54 | |
| Dernière modification le : Dimanche 1 Août 2010, 19:37:11 | |
