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40 lines
830 B
Idris
40 lines
830 B
Idris
module Prelude.Uninhabited
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import Builtin
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import Prelude.Basics
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%default total
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||| A canonical proof that some type is empty.
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public export
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interface Uninhabited t where
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constructor MkUninhabited
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||| If I have a t, I've had a contradiction.
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||| @ t the uninhabited type
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uninhabited : t -> Void
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||| The eliminator for the `Void` type.
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%extern
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public export
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void : (0 x : Void) -> a
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export
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Uninhabited Void where
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uninhabited = id
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||| Use an absurd assumption to discharge a proof obligation.
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||| @ t some empty type
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||| @ a the goal type
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||| @ h the contradictory hypothesis
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public export
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absurd : Uninhabited t => (h : t) -> a
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absurd h = void (uninhabited h)
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public export
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Uninhabited (True = False) where
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uninhabited Refl impossible
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public export
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Uninhabited (False = True) where
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uninhabited Refl impossible
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