We present a novel analysis of the fundamental Löb induction principle from guarded
recursion. Taking advantage of recent work in modal type theory and univalent foundations …

Simplicial type theory extends homotopy type theory with a directed path type which
internalizes the notion of a homomorphism within a type. This concept has significant …

In this book, we aim to introduce the reader to a modern research perspective on the design
of “full-spectrum” dependent type theories. After studying this book, readers should be …

Multimode Type Theory (MTT) is a generic type theory that can be instantiated with an
arbitrary mode theory to model features like parametricity, cohesion and guarded recursion …

Riehl and Shulman introduced simplicial type theory (STT), a variant of homotopy type
theory which aimed to study not just homotopy theory, but its fusion with category theory …

Effect handlers are a powerful abstraction for defining, customising, and composing
computational effects. Statically ensuring that all effect operations are handled requires …

The study of modal logic has witnessed tremendous development following the introduction
of Kripke semantics. However, recent developments in programming languages and type …

We walk through a few proofs of canonicity and normalization, each one with more aspects
dissected and re-expressed in category theory, so that readers can compare the difference …

Although the pure functional semantics of computer programs has been well-studied since
at least the seminal work of Scott and Strachey, it has remained challenging to integrate cost …

Directed univalence in simplicial homotopy type theory Page 1 Directed univalence in simplicial
homotopy type theory Jonathan Weinberger jww Daniel Gratzer and Ulrik Buchholtz …