Formalized, Effective Domain Theory in Coq

I present highlights from a formalized development of domain theory in the theorem prover Coq. This is the first development of domain theory that is effective, formalized and that supports all the usual constructions on domains. In particular, I develop constructive models of both the unpointed profinite and the pointed profinite domains. Standard constructions (e.g., products, sums, the function space, and powerdomains) are all developed. In addition, I build the machinery necessary to compute solutions to recursive domain equations.