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17 lines
783 B
Idris
17 lines
783 B
Idris
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||| Additional data types related to ordering notions
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module Data.Order
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%default total
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||| Trichotomous formalises the fact that three relations are mutually exclusive.
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||| It is meant to be used with relations that complement each other so that the
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||| `Trichotomous lt eq gt` relation is the total relation.
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public export
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data Trichotomous : (lt, eq, gt : a -> a -> Type) -> (a -> a -> Type) where
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MkLT : {0 lt, eq, gt : a -> a -> Type} ->
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lt v w -> Not (eq v w) -> Not (gt v w) -> Trichotomous lt eq gt v w
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MkEQ : {0 lt, eq, gt : a -> a -> Type} ->
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Not (lt v w) -> eq v w -> Not (gt v w) -> Trichotomous lt eq gt v w
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MkGT : {0 lt, eq, gt : a -> a -> Type} ->
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Not (lt v w) -> Not (eq v w) -> gt v w -> Trichotomous lt eq gt v w
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