Keywords: Calculus of Constructions, Higher Order Logic, Typed Lambda Calculus, Equational Logic, Rewriting Logic Rewriting logic together with it's membership equational sublogic favors the use of abstract specifications. It has a flexible computation system based on conditional rewriting modulo equations, and via its initial semsntics it supports a very liberal notion of inductive definitions. Pure type systems, on the other hand, in particular the calculus of constructions, provide higher-order (dependent) types, but they are based on a fixed notion of computation, namely beta-reduction. To close this gap we investigate (OCC) an equational variant of the calculus of constructions. The formal executable specification of OCC exploits the reflective capabilities of Maude, yielding an computational efficiency that brings us closer the the goal of a unified tool for programming, specification and verification integrating equational logic, higher-order logic and dependent types.