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A Convex Powerdomain over Lattices: its Logic and λCalculus
, 1997
"... To model at the same time parallel and nondeterministic 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 fro ..."
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To model at the same time parallel and nondeterministic 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 preorder of the λcalculus.
IOS Press AConvex Powerdomain over Lattices: its Logic andCalculus
"... Abstract. To model at the same time parallel and nondeterministic functional calculi we de ne 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 ..."
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Abstract. To model at the same time parallel and nondeterministic functional calculi we de ne 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 de ne acalculus and a type assignment system using the logic of D 1 as the related type theory. Weprove that the lter model of this calculus, which is isomorphic to D 1,is fully abstract with respect to the observational Preorder of thecalculus.