Domains for Denotational Semantics
Proceedings of the 9th Colloquium on Automata, Languages and Programming
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The definitions of Conjunctive types and their subtype relation, as introduced by Coppo-Dezani, are extended to consider the conjunction as a partial mapping from pairs of types to types, and the subtype relation as a relation between finite sets of types and types. These extensions basically mean that only conjunctions of compatible types are allowed and that the subtype relation is more like, so to speak, the implication in propositional logic. We show that the basic properties of the typing system with conjunctive types are still true. The terms that have a type are exactly the terms that are convertible to a head normal form and it is possible to characterize the terms with normal form by means of the types that are derivable for them in the system. Furthermore, the type assignment defines the interpretation of terms in a very general class of models of the &lgr;-calculus: the models that are based on an information system, as defined by Scott.