Homotopy Type Theory
identity type (Rev #4)


The identity type has elements that are witnesses to the “sameness” of elements.


The identity type = A:AA𝒰=_A : A \to A \to \mathcal{U} can be defined as the inductive type? with the following constructor:

  • for any a:Aa:A, an element refl A:a= Aarefl_A: a=_A a

See also

higher inductive type


HoTT book

category: type theory

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