output of a function will contain more information when the information content of the input is increased. Formally, this means that we want a function to be monotonic.

When dealing with dcpos, one might also want computations to be compatible with the formation of limits of a directed set. Formally, this means that, for some function f, the image f(D) of a directed set D (i.e. the set of the images of each element of D) is again directed