Abstract
Models of the untyped λ-calculus may be defined either as applicative structures satisfying a bunch of first-order axioms (λ-models), or as reflexive objects in cartesian closed categories (categorical models). In this paper we show that any categorical model of λ-calculus can be presented as a λ-model, even when the underlying category does not have enough points. We provide an example of an extensional model of λ-calculus in a category of sets and relations which has not enough points. Finally, we present some of its algebraic properties which make it suitable for dealing with non-deterministic extensions of λ-calculus. © Springer-Verlag Berlin Heidelberg 2007.
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Bucciarelli, A., Ehrhard, T., & Manzonetto, G. (2007). Not enough points is enough. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4646 LNCS, pp. 298–312). Springer Verlag. https://doi.org/10.1007/978-3-540-74915-8_24
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