A Convex Powerdomain over Lattices: its Logic and λ-Calculus (1997)
| Citations: | 1 - 1 self |
BibTeX
@MISC{Alessi97aconvex,
author = {Fabio Alessi and Mariangiola Dezani-Ciancaglini and Ugo de' Liguoro},
title = {A Convex Powerdomain over Lattices: its Logic and λ-Calculus},
year = {1997}
}
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Abstract
To model at the same time parallel and non-deterministic functional calculi we define a powerdomain functor P such that it is an endofunctor over the category of algebraic lattices. P is locally continuous and we study the initial solution D 1 of the domain equation D = P([D ! D]? ). We derive from the algebras of P the logic of D 1 , that is the axiomatic description of its compact elements. We then define a -calculus and a type assignment system using the logic of D 1 as the related type theory. We prove that the filter model of this calculus, which is isomorphic to D 1 , is fully abstract with respect to the observational pre-order of the λ-calculus.
