This is the third in a series of papers extending Martin-LÃ¶fâ€™s meaning explanations of dependent type theory to a Cartesian cubical realizability framework that accounts for higherdimensional types.â€¦ (More)

This paper contributes to recent investigations of the use of homotopy type theory to give machine-checked proofs of constructions from homotopy theory. We present a mechanized proof of a resultâ€¦ (More)

Mechanized reasoning has proved effective in avoiding serious mistakes in software and hardware, and yet remains unpopular in the practice ofmathematics. My thesis is aimed at making mechanizationâ€¦ (More)

Bezem, Coquand, and Huber have recently given a constructively valid model of higher type theory in a category of nominal cubical sets satisfying a novel condition, called the uniform Kan conditionâ€¦ (More)

We present a development of cellular cohomology in homotopy type theory. Cohomology associates to each space a sequence of abelian groups capturing part of its structure, and has the advantage overâ€¦ (More)

RedPRL is an experimental proof assistant based on Cartesian cubical computational type theory, a new type theory for higher-dimensional constructions inspired by homotopy type theory. In the styleâ€¦ (More)

Type refinements, introduced by Freeman and Pfenning and explored by Davies and Dunfield, unify the ontological and epistemic views of typing. Types tell us what programming language constructsâ€¦ (More)

Covering spaces play an important role in classical homotopy theory, whose algebraic characteristics have deep connections with fundamental groups of underlying spaces. It is natural to ask whetherâ€¦ (More)