Proving Fixed Points

Hervé Grall 1, 2
2 ASCOLA - Aspect and composition languages
Inria Rennes – Bretagne Atlantique , Département informatique - EMN, LINA - Laboratoire d'Informatique de Nantes Atlantique
Abstract : 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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Submitted on : Saturday, July 31, 2010 - 10:06:54 AM
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Hervé Grall. Proving Fixed Points. 2010. ⟨hal-00507775⟩

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