I present an analysis of the interpretation of anaphora that takes concepts from type-theoretic semantics, in particular the use of the Σ and Π dependent type constructors, and incorporates them into a model-theoretic framework. The analysis makes use of (parametrically) polymorphic lexical entries. The key ideas are that, in the simplest case, eventualities can play the role that proof objects do in type-theoretic semantics; that more complex, compositionally-defined, structures can play that role in other cases; and that pronouns can be modelled by context-dependent functions from proof objects of the preceding discourse (in this sense) to entities.
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