Proof checking

Universe

A level used to organize types without placing every type inside itself.

Definition

Universe

A universe is a level in the type hierarchy used to classify types and avoid inconsistent self-reference.

A polymorphic declaration can refer to a universe variable rather than one fixed level. The kernel checks constraints among these levels.

01

Example

A generic identity function can work for a type α in any permitted universe.

02

Important distinction

Universe polymorphism does not mean one universe contains itself.

After reading this article, you should be able to

  • Define Universe in the sense used on this site.
  • Explain why type systems use a hierarchy of universes.