Quantitative Domains and Infinitary Algebras
Abstract We describe a class of models of the lambda calculus that generalize and simplify the quantitative domains of Girard (1988). Their salient feature is that these domains “do not have enough points”, in the sense that a map of domains is not entirely determined by its value on the points, i.e. the morphisms from the terminal object of the category. We construct a universal domain whose structure is particularly simple, and describe some of the features of the untyped lambda calculus associated to it. Finally, we show how linear logic can be interpreted in these domains, and construct another category of domains that supports linear logic.