Say we have an arbitrary domain $D$ with a countable basis $B$. Now, how do i build a "language" whose "denotation" lives in the domain?
My understanding is that Dana Scott initially built domains to get a model of typed lambda calculus. Then, people bgan studing domains in their own right. So if I know that something forms a domain, can I "extract computation" / "extract a language" out of it?
Perhaps said differently, does every domain $D$ [with more conditions as necessary] always come equipped with the structure of a closed cartesian category?