Online Computer Terms Dictionary - C

continuous function

A function f : D -> E, where D and E are cpos, is continuous if it is monotonic and

	f (lub Z) = lub { f z | z in Z }

All additive functions (functions which preserve all lubs) are continuous. A continuous function has a least fixed point if its domain has a least element, bottom (i.e. it is a cpo or a "pointed cpo" depending on your definition of a cpo). The least fixed point is

	fix f = lub {f^n bottom | n = 0..infinity}