Proof assistants based on dependent type theory provide expressive languages for both
programming and proving within the same system. However, all of the major …

The implementation and semantics of dependent type theories can be studied in a syntax-
independent way: the objective metatheory of dependent type theories exploits the universal …

In their usual form, representation independence metatheorems provide an external
guarantee that two implementations of an abstract interface are interchangeable when they …

Proof assistants based on dependent type theory provide expressive languages for both
programming and proving within the same system. However, all of the major …

This paper discusses the formalization of synthetic cohomology theory in a cubical extension
of Agda which natively supports univalence and higher inductive types. This enables …

We present a cubical type theory based on the Cartesian cube category (faces,
degeneracies, symmetries, diagonals, but no connections or reversal) with univalent …

Context: Gradually-typed languages allow typed and untyped code to interoperate, but
typically come with significant drawbacks. In some languages, the types are unreliable; in …

Brunerie's 2016 PhD thesis contains the first synthetic proof in Homotopy Type Theory
(HoTT) of the classical result that the fourth homotopy group of the 3-sphere is ℤ/2ℤ. The …

Programs are rarely implemented in a single language, and thus questions of type
soundness should address not only the semantics of a single language, but how it interacts …

We investigate gradual variations on the Calculus of Inductive Construction (CIC) for swifter
prototyping with imprecise types and terms. We observe, with a no-go theorem, a crucial …