A Convex Powerdomain over Lattices: its Logic and λ-Calculus

Abstract

To model at the same time parallel and nondeterministic functional calculi we define a powerdomain functor R such that it is an endofunctor over the category of algebraic lattices. R is locally continuous and we study the initial solution D ∞ of the domain equation D = R([D → D] ⊥). We derive from the algebras of R the logic of D ∞, that is the axiomatic description of its compact elements. We then define a λ-calculus and a type assignment system using the logic of D ∞ as the related type theory. We prove that the filter model of this calculus, which is isomorphic to D ∞, is fully abstract with respect to the observational Preorder of the λ-calculus.