3 papers
cs.LO2026
Impredicativity in Linear Dependent Type Theory
Sam Speight, Niels van der Weide
We construct a realizability model of linear dependent type theory from a linear combinatory algebra. Our model motivates a number of additions to the type theory. In particular, w…
math.CT2025
A Structural Account of Combinatory Completeness
Ivan Kuzmin, Chad Nester, Ülo Reimaa +1
We give a general notion of combinatory completeness with respect to a faithful cartesian club and use it systematically to obtain characterisations of a number of different kinds…
cs.LO2024
Groupoidal Realizability for Intensional Type Theory
Sam Speight
We develop realizability models of intensional type theory, based on groupoids, wherein realizers themselves carry non-trivial (non-discrete) homotopical structure. In the spirit o…