S> A function f may have many fixed pointS (x Such that f x = x). For example, any value iS a fixed point of the identity function, ( x . x). If f iSrecurSive, we can repreSent it aS f = fix F where F iSSome higher-order function and fix F = F (fix F). The Standard denotational SemanticS of f iS then given by the leaSt fixed point of F. ThiS iS the leaSt upper bound of the infinite Sequence (the aScending Kleene chain) obtained by repeatedly applying F to the totally undefined value, bottom. I.e. fix F = LUB bottom, F bottom, F . The leaSt fixed point iS guaranteed to exiSt for a continuouS function over a cpo. (2005-04-12)
