We present the topos S of trees as a model of guarded recursion. We study the internal
dependently-typed higher-order logic of S and show that S models two modal operators, on …

We present an internal formalisation of a type heory with dependent types in Type Theory
using a special case of higher inductive types from Homotopy Type Theory which we call …

A family of syntactic models for the calculus of construction with universes (CC ω) is
described, all of them preserving conversion of the calculus definitionally, and thus giving …

There is a critical tension between substitution, dependent elimination and effects in type
theory. In this paper, we crystallize this tension in the form of a no-go theorem that …

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We present the guarded lambda-calculus, an extension of the simply typed lambda-calculus
with guarded recursive and coinductive types. The use of guarded recursive types ensures …

This paper studies forcing translations of proofs in dependent type theory, through the Curry-
Howard correspondence. Based on a call-by-push-value decomposition, we synthesize two …

Homotopy type theory may be seen as an internal language for the∞-category of weak∞-
groupoids. Moreover, weak∞-groupoids model the univalence axiom. Voevodsky proposes …

Heyting-Lewis Logic is the extension of intuitionistic propositional logic with a strict
implication connective that satisfies the constructive counterparts of axioms for strict …

In this thesis, we investigate several key results in the canon of metamathematics, applying
the contemporary perspective of formalisation in constructive type theory and mechanisation …