Data Types as Lattices
Dana Scott · SIAM Journal on Computing · 1976
The meaning of many kinds of expressions in programming languages can be taken as elements of certain spaces of “partial” objects. In this report these spaces are modeled in one universal domain ${\bf P} \omega $, the set of all subsets of the integers. This domain renders the connection of this semantic theory with the ordinary theory of number theoretic (especially general recursive) functions clear and straightforward.