Idris2/libs/base/Decidable/Equality/Core.idr
Denis Buzdalov 4364793484 Type definition from Decidable.Equality was moved to a separate module
This is done to make able for `Data.*` modules of datatypes declared in
prelude to import modules that have their own definitions of `DecEq`
inside them (i.e. modules of datatypes declared in the `base`).
2020-12-04 19:09:05 +00:00

30 lines
1.0 KiB
Idris

module Decidable.Equality.Core
%default total
--------------------------------------------------------------------------------
-- Decidable equality
--------------------------------------------------------------------------------
||| Decision procedures for propositional equality
public export
interface DecEq t where
||| Decide whether two elements of `t` are propositionally equal
decEq : (x1 : t) -> (x2 : t) -> Dec (x1 = x2)
--------------------------------------------------------------------------------
-- Utility lemmas
--------------------------------------------------------------------------------
||| The negation of equality is symmetric (follows from symmetry of equality)
export
negEqSym : forall a, b . (a = b -> Void) -> (b = a -> Void)
negEqSym p h = p (sym h)
||| Everything is decidably equal to itself
export
decEqSelfIsYes : DecEq a => {x : a} -> decEq x x = Yes Refl
decEqSelfIsYes {x} with (decEq x x)
decEqSelfIsYes {x} | Yes Refl = Refl
decEqSelfIsYes {x} | No contra = absurd $ contra Refl