Some Domain Theory and Denotational Semantics in Coq

We present a Coq formalization of constructive *** -cpos (extending earlier work by Paulin-Mohring) up to and including the inverse-limit construction of solutions to mixed-variance recursive domain equations, and the existence of invariant relations on those solutions. We then define operational and denotational semantics for both a simply-typed CBV language with recursion and an untyped CBV language, and establish soundness and adequacy results in each case.