nLab typical ambiguity

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In (homotopy) type theory with type universes, by the typical universe ambiguity or just typical ambiguity, for short, one refers to the universe level remaining implicit, as long as a proof assistant is or would be able to deduce it from context.

Both Russell and Tarski style universes can be typically ambiguous or not.

Examples

  • Coq uses Russell style universes with typical ambiguity.

  • Agda uses Russell style universes without typical ambiguity: you always have to explicitly indicate the universe level.

  • The HoTT Book (first edition) uses Russell style universes with (except for a few places) typical ambiguity.

References

  • Solomon Feferman, Typical ambiguity: Trying to have your cake and eat it too

  • Blog Post

Last revised on June 16, 2022 at 12:21:17. See the history of this page for a list of all contributions to it.