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155 lines
4.7 KiB
Idris
155 lines
4.7 KiB
Idris
module Data.Either
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import public Control.Function
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import Data.List1
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%default total
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--------------------------------------------------------------------------------
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-- Checking for a specific constructor
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||| Extract the Left value, if possible
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public export
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getLeft : Either a b -> Maybe a
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getLeft (Left a) = Just a
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getLeft _ = Nothing
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||| Extract the Right value, if possible
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public export
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getRight : Either a b -> Maybe b
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getRight (Right b) = Just b
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getRight _ = Nothing
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||| True if the argument is Left, False otherwise
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public export
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isLeft : Either a b -> Bool
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isLeft (Left _) = True
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isLeft (Right _) = False
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||| True if the argument is Right, False otherwise
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public export
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isRight : Either a b -> Bool
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isRight (Left _) = False
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isRight (Right _) = True
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||| Proof that an `Either` is actually a Right value
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public export
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data IsRight : Either a b -> Type where
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ItIsRight : IsRight (Right x)
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export
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Uninhabited (IsRight (Left x)) where
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uninhabited ItIsRight impossible
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||| Proof that an `Either` is actually a Left value
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public export
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data IsLeft : Either a b -> Type where
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ItIsLeft : IsLeft (Left x)
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export
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Uninhabited (IsLeft (Right x)) where
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uninhabited ItIsLeft impossible
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--------------------------------------------------------------------------------
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-- Grouping values
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||| Compress the list of Lefts and Rights by accumulating
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||| all of the lefts and rights into non-empty blocks.
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export
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compress : List (Either a b) -> List (Either (List1 a) (List1 b))
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compress [] = []
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compress (Left x :: abs) = compressLefts (singleton x) abs where
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compressLefts : List1 a -> List (Either a b) -> List (Either (List1 a) (List1 b))
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compressLefts acc (Left a :: abs) = compressLefts (cons a acc) abs
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compressLefts acc abs = Left (reverse acc) :: compress abs
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compress (Right y :: abs) = compressRights (singleton y) abs where
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compressRights : List1 b -> List (Either a b) -> List (Either (List1 a) (List1 b))
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compressRights acc (Right b :: abs) = compressRights (cons b acc) abs
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compressRights acc abs = Right (reverse acc) :: compress abs
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||| Decompress a compressed list. This is the left inverse of `compress` but not its
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||| right inverse because nothing forces the input to be maximally compressed!
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export
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decompress : List (Either (List1 a) (List1 b)) -> List (Either a b)
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decompress = concatMap $ \case
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Left as => map Left $ forget as
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Right bs => map Right $ forget bs
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||| Keep the payloads of all Left constructors in a list of Eithers
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public export
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lefts : List (Either a b) -> List a
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lefts [] = []
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lefts (Left l :: xs) = l :: lefts xs
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lefts (Right _ :: xs) = lefts xs
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||| Keep the payloads of all Right constructors in a list of Eithers
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public export
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rights : List (Either a b) -> List b
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rights [] = []
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rights (Left _ :: xs) = rights xs
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rights (Right r :: xs) = r :: rights xs
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||| Split a list of Eithers into a list of the left elements and a list of the right elements
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public export
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partitionEithers : List (Either a b) -> (List a, List b)
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partitionEithers l = (lefts l, rights l)
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||| Remove a "useless" Either by collapsing the case distinction
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public export
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fromEither : Either a a -> a
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fromEither (Left l) = l
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fromEither (Right r) = r
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||| Right becomes left and left becomes right
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public export
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mirror : Either a b -> Either b a
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mirror (Left x) = Right x
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mirror (Right x) = Left x
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--------------------------------------------------------------------------------
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-- Bifunctor
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export
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pushInto : c -> Either a b -> Either (c, a) (c, b)
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pushInto c = bimap (\ a => (c, a)) (\ b => (c, b))
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-- ^ not using sections to keep it backwards compatible
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--------------------------------------------------------------------------------
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-- Conversions
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--------------------------------------------------------------------------------
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||| Convert a Maybe to an Either by using a default value in case of Nothing
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||| @ e the default value
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public export
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maybeToEither : (def : Lazy e) -> Maybe a -> Either e a
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maybeToEither def (Just j) = Right j
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maybeToEither def Nothing = Left def
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||| Convert an Either to a Maybe from Right injection
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public export
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eitherToMaybe : Either e a -> Maybe a
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eitherToMaybe (Left _) = Nothing
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eitherToMaybe (Right x) = Just x
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export
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eitherMapFusion : (f : _) -> (g : _) -> (p : _) -> (e : Either a b) -> either f g (map p e) = either f (g . p) e
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eitherMapFusion f g p $ Left x = Refl
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eitherMapFusion f g p $ Right x = Refl
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export
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eitherBimapFusion : (f : _) -> (g : _) -> (p : _) -> (q : _) -> (e : _) -> either f g (bimap p q e) = either (f . p) (g . q) e
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eitherBimapFusion f g p q $ Left z = Refl
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eitherBimapFusion f g p q $ Right z = Refl
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-- Injectivity of constructors
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||| Left is injective
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export
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Injective Left where
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injective Refl = Refl
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||| Right is injective
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export
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Injective Right where
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injective Refl = Refl
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