2 Dec 2005 12:57
Re: Semantics of Intersection Type
[The Types Forum, http://lists.seas.upenn.edu/mailman/listinfo/types-list] Hongseok Yang wrote: >[The Types Forum, http://lists.seas.upenn.edu/mailman/listinfo/types-list] > >Would anyone point out the literature on the semantics of >intersection types? > > as far as I can see, the answers you got on the TYPES list all interpret your question as "what is the use of intersection types in semantics?" And the obvious answer is that they provide, by means of the "filter models", a concrete presentation of some well-know domains for interpreting lambda-calculi, where the types determine the compact elements (I myself wrote a paper on this topic, published in Information and Computation, Vol. 108, No. 1, 1994). But one could understand your question in another way, namely : "what can be a semantical interpretation of (intersection) types". Then an obvious answer is: a set of expressions of some calculus (the "realizability" interpretation of types), or more generally a set of elements in some model of the calculus. Generalizing this to predicates indexed by types, one gets the notion of a "logical relation". Some good references from this point of view are Krivine's book on "Lambda-Calculus, Types and Models" (Ellis Horwood, 1993), Mitchell's "Foundations for Programming Languages" (MIT Press, 1996), and Amadio and Curien's "Domains and Lambda-Calculi" (Cambridge University Press, 1998), which also contains a chapter on filter models.(Continue reading)
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