2023-01-09 17:43:23 -05:00
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module Quox.Decidable
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2023-01-12 10:03:09 -05:00
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import public Data.Bool.Decidable
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2023-01-09 17:43:23 -05:00
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import public Decidable.Decidable
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import public Decidable.Equality
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import public Control.Relation
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public export
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0 REL : Type -> Type -> Type
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REL a b = a -> b -> Type
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public export
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0 Pred : Type -> Type
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Pred a = a -> Type
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public export
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0 Dec1 : Pred a -> Type
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Dec1 p = (x : a) -> Dec (p x)
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public export
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0 Dec2 : REL a b -> Type
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Dec2 p = (x : a) -> (y : b) -> Dec (p x y)
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2023-01-12 10:03:09 -05:00
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public export
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0 Reflects1 : Pred a -> (a -> Bool) -> Type
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p `Reflects1` f = (x : a) -> p x `Reflects` f x
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public export
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0 Reflects2 : REL a b -> (a -> b -> Bool) -> Type
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p `Reflects2` f = (x : a) -> (y : b) -> p x y `Reflects` f x y
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2023-01-09 17:43:23 -05:00
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public export
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(||) : Dec p -> Dec q -> Dec (Either p q)
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Yes y1 || _ = Yes $ Left y1
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No _ || Yes y2 = Yes $ Right y2
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No n1 || No n2 = No $ \case Left y1 => n1 y1; Right y2 => n2 y2
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public export
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(&&) : Dec p -> Dec q -> Dec (p, q)
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Yes y1 && Yes y2 = Yes (y1, y2)
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Yes _ && No n2 = No $ n2 . snd
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No n1 && _ = No $ n1 . fst
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2023-01-12 10:03:09 -05:00
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public export
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reflectToDec : p `Reflects` b -> Dec p
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reflectToDec (RTrue y) = Yes y
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reflectToDec (RFalse n) = No n
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