We deal with a relational model for the demonic semantics of programs. The demonic semantics of a while loop is given as a fixed point of a function involving the demonic operators. This motivates us to investigate the fixed points of these functions. We give the expression of the greatest fixed point with respect to the demonic ordering (demonic inclusion) of the semantic function. We prove th...

A universal schema for diagonalization was popularized by N. S. Yanofsky (2003) in which the existence of a (diagonolized-out and contradictory) object implies the existence of a fixed-point for a certain function. It was shown that many self-referential paradoxes and diagonally proved theorems can fit in that schema. Here, we fit more theorems in the universal schema of diagonalization, such a...

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...

Some fixed point theorems based on an asymptotic regularity condition have been obtained, which generalize the previously well-known results. 2000 Mathematics Subject Classification: 47H10, 54H25.

Functional programmers happily use equational reasoning and induction to prove properties of recursive programs. To show properties of corecursive programs they employ coinduction, per perhaps less enthusiastically. Coinduction is often considered as a rather low-level proof method, especially, as it seems to depart rather radically from equational reasoning. In this talk we introduce an altern...

Several investigators have claimed that the retinal coordinates of corresponding points shift with vergence eye movements. Two kinds of shifts have been reported. First, global shifts that increase with retinal eccentricity; such shifts would cause a flattening of the horopter at all viewing distances and would facilitate fusion of flat surfaces. Second, local shifts that are centered on the fo...

In this article, we study the notion of virtually repelling fixed point. We first give a definition and an interpretation of it. We then prove that most proper holomorphic mappings f : U → V with U contained in V have at least one virtually repelling fixed point. 1. Preliminaries Let f : (C, α) → (C, α) be a holomorphic germ fixing α. Definition 1. The multiplicity m of α as a fixed point of f ...