Theory and Applications of Type-Theoretic Universes

Application of universes: module systems

module type Group = sig
  type t
  val unit : t
  val mul : t -> t -> t
  val inv : t -> t
end

Group :\equiv (t : U) \times (u ni t : El t \to El t) \times (m u l : El t \to El t \to El t) \times (in v : El t \to El t)

One view on [Rossberg 2015Rossberg, A. 2015. 1ML – core and modules united (F-ing first-class modules). ACM SIGPLAN Notices 50, 35–47. http://dx.doi.org/10.1145/2858949.2784738.] is that it does module systems for 1ML via a universe of small types