Cs> 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 as f = fix F where F is some 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)
