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Abstract | |||||||||||||||
| Stone dualities allow to describe special classes of topological spaces by means of (possibly finitary) partial orders. Typically, these partial orders are given by the topology, a basis for it, or a subbasis for it. The seminal result is the duality between the categories of Stone spaces and that of Boolean algebras (see [4]). Other very important examples are the descriptions of Scott domains as information systems [5] and the description of SFP domains as pre-locales [1]. Intersection types can be viewed also as a restriction of the domain theory in logical form, see [1], to the special case of modeling pure lambda calculus by means of ω-algebraic complete lattices. Intersection types have been used as a powerful tool both for the analysis and the synthesis of λ-models, see e.g. [2]. On the one hand, intersection type disciplines provide finitary inductive definitions of interpretation of λ-terms in models. On the other hand, they are suggestive for the shape the domain model has to have in order to exhibit certain properties [3]. | |||||||||||||||
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