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 is recursive, we can represent it asf = fix Fwhere F is some higher-order function andfix 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)