Domain Theory

Short introduction to Domain Theory. To be written.

Why do we need Domains? Well, the thing is that there are a lot of functions between sets. We already know (thanks to Georg Cantor) exactly how many functions there are between two sets, and in fact we know that \(#(S \to \triangle S) > # S\).

\[S \to S\]

But why is that relevant? Well, since we want to evaluate our programs we basically want to connect our programs with some values with are the results of our program given by some specific evaluator. So an evaluator give us a way to relate (syntactic) programs with (semantic) values.

Definition:

\[\Sigma_{n \in Nats}\]