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 }
for all directed sets Z in D. In other words, the image of the lub is the
lub of any directed image.
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}
(19941130)
Nearby terms:
Continuation Passing Style « continuation passing
style « continuations « continuous function »
Continuous System Modeling Program » Continuous
System Simulation Language » continuous wave
