We present Voevodsky's construction of a model of univalent type theory in the category of
simplicial sets. To this end, we first give a general technique for constructing categorical …

We present a categorical theory of'well-behaved'operational semantics which aims at
complementing the established theory of domains and denotational semantics to form a …

In this chapter we fix a particular syntax for a dependently typed calculus and define an
abstract notion of model as well as a general interpretation function mapping syntactical …

We introduce categories with families as a new notion of model for a basic framework of
dependent types. This notion is close to ordinary syntax and yet has a clean categorical …

This paper formalises within first-order logic some common practices in computer science to
do with representing and reasoning about syntactical structures involving lexically scoped …

We study the semantic foundation of expressive probabilistic programming languages, that
support higher-order functions, continuous distributions, and soft constraints (such as …

This is a monograph about logic. Specifically, it presents the mathe matical theory of the
logic of bunched implications, BI: I consider Bl's proof theory, model theory and computation …

Theories of dependent types have been proposed as a foundation of constructive
mathematics and as a framework in which to construct certified programs. In these …

In this paper we consider an intuitionistic variant of the modal logic S4 (which we call IS4).
The novelty of this paper is that we place particular importance on the natural deduction …

The homotopical approach to intensional type theory views proofs of equality as paths. We
explore what is required of an object I in a topos to give such a path-based model of type …