2022-03-23 18:39:43 +03:00
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module Control.Function.FunExt
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%default total
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||| This interface contains a proposition for the function extensionality.
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||| It is not meant to be ever implemented.
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||| It can be used to mark properties as requiring function extensionality to hold,
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||| i.e. its main objective is to provide a universal way to formulate a conditional property
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||| that holds only in the presence of function extensionality.
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2022-04-01 14:13:17 +03:00
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public export
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2022-03-23 18:39:43 +03:00
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interface FunExt where
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2022-04-28 22:40:57 +03:00
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funExt : {0 b : a -> Type} -> {0 f, g : (x : a) -> b x} -> ((x : a) -> f x = g x) -> f = g
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2024-05-16 20:37:37 +03:00
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export
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funExt0 : FunExt => {0 b : a -> Type} -> {0 f, g : (0 x : a) -> b x} -> ((x : a) -> f x = g x) -> f = g
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funExt0 prf = rewrite funExt {f = \x => f x} {g = \y => g y} prf in Refl
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export
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funExt1 : FunExt => {0 b : a -> Type} -> {0 f, g : (1 x : a) -> b x} -> ((x : a) -> f x = g x) -> f = g
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funExt1 prf = rewrite funExt {f = \x => f x} {g = \y => g y} prf in Refl
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