Relational models of the lambda calculus

Abstract

In [7], Ehrhard et al. present a model of the untyped lambda calculus built from an object without enough points in a cartesian closed category MRel. This thesis presents the background needed to construct and understand this model. In particular we describe what it means for models to have enough points and exhibit connections between MRel with various categorical models of lambda calculus in the literature. In particular, we are able to relate the graph model to MRel. We also describe connections with various kinds of Kleisli categories arising from comonads and their associated theory.