Control.Isomorphic

Documentation

class Isomorphic b a => Isomorphic a b where

Methods

to' :: a -> b

This type class provides a single method to', which is a bijective function from a to b. We leverage UndecidableSuperClasses to demand that every instance of Isomorphic have an inverse. The sister instance (which may be the same instance) must have the follwing property when used with the to'

    to' . to' = id
  

Note, this class documents type isomorphisms specifically, where two types are isomorphic to one another. It does not document endoisomorphisms.

Instances

Isomorphic Bool All

Defined in Control.Isomorphic

Methods

to' :: Bool -> All

Isomorphic Bool Any

Defined in Control.Isomorphic

Methods

to' :: Bool -> Any

Isomorphic Bool IsNothing

Defined in Control.Isomorphic

Methods

to' :: Bool -> IsNothing

Isomorphic Bool IsJust

Defined in Control.Isomorphic

Methods

to' :: Bool -> IsJust

Isomorphic Bool IsLeft

Defined in Control.Isomorphic

Methods

to' :: Bool -> IsLeft

Isomorphic Bool IsRight

Defined in Control.Isomorphic

Methods

to' :: Bool -> IsRight

Enum a => Isomorphic Int a

Defined in Control.Isomorphic

Methods

to' :: Int -> a

Coercible a b => Isomorphic a b

Defined in Control.Isomorphic

Methods

to' :: a -> b

Enum a => Isomorphic a Int

Defined in Control.Isomorphic

Methods

to' :: a -> Int

Isomorphic a a

Defined in Control.Isomorphic

Methods

to' :: a -> a

Isomorphic All Bool

Defined in Control.Isomorphic

Methods

to' :: All -> Bool

Isomorphic Any Bool

Defined in Control.Isomorphic

Methods

to' :: Any -> Bool

Isomorphic String ByteString

Defined in Control.Isomorphic

Methods

to' :: String -> ByteString

Isomorphic String ByteString

Defined in Control.Isomorphic

Methods

to' :: String -> ByteString

Isomorphic String Text

Defined in Control.Isomorphic

Methods

to' :: String -> Text

Isomorphic String Text

Defined in Control.Isomorphic

Methods

to' :: String -> Text

Isomorphic ByteString String

Defined in Control.Isomorphic

Methods

to' :: ByteString -> String

Isomorphic ByteString ByteString

Defined in Control.Isomorphic

Methods

to' :: ByteString0 -> ByteString

Isomorphic ByteString Text

Defined in Control.Isomorphic

Methods

to' :: ByteString -> Text

Isomorphic ByteString Text

Defined in Control.Isomorphic

Methods

to' :: ByteString -> Text

Isomorphic ByteString String

Defined in Control.Isomorphic

Methods

to' :: ByteString -> String

Isomorphic ByteString ByteString

Defined in Control.Isomorphic

Methods

to' :: ByteString -> ByteString0

Isomorphic ByteString Text

Defined in Control.Isomorphic

Methods

to' :: ByteString -> Text

Isomorphic ByteString Text

Defined in Control.Isomorphic

Methods

to' :: ByteString -> Text

Isomorphic Text String

Defined in Control.Isomorphic

Methods

to' :: Text -> String

Isomorphic Text ByteString

Defined in Control.Isomorphic

Methods

to' :: Text -> ByteString

Isomorphic Text ByteString

Defined in Control.Isomorphic

Methods

to' :: Text -> ByteString

Isomorphic Text Text

Defined in Control.Isomorphic

Methods

to' :: Text0 -> Text

Isomorphic Text String

Defined in Control.Isomorphic

Methods

to' :: Text -> String

Isomorphic Text ByteString

Defined in Control.Isomorphic

Methods

to' :: Text -> ByteString

Isomorphic Text ByteString

Defined in Control.Isomorphic

Methods

to' :: Text -> ByteString

Isomorphic Text Text

Defined in Control.Isomorphic

Methods

to' :: Text -> Text0

Isomorphic IsNothing Bool

Defined in Control.Isomorphic

Methods

to' :: IsNothing -> Bool

Isomorphic IsJust Bool

Defined in Control.Isomorphic

Methods

to' :: IsJust -> Bool

Isomorphic IsLeft Bool

Defined in Control.Isomorphic

Methods

to' :: IsLeft -> Bool

Isomorphic IsRight Bool

Defined in Control.Isomorphic

Methods

to' :: IsRight -> Bool

Isomorphic Integer (Fixed a)

Defined in Control.Isomorphic

Methods

to' :: Integer -> Fixed a

Isomorphic a (Product a)

Defined in Control.Isomorphic

Methods

to' :: a -> Product a

Isomorphic a (Sum a)

Defined in Control.Isomorphic

Methods

to' :: a -> Sum a

Isomorphic a (Dual a)

Defined in Control.Isomorphic

Methods

to' :: a -> Dual a

Isomorphic a (Identity a)

Defined in Control.Isomorphic

Methods

to' :: a -> Identity a

Isomorphic IsNothing (Maybe ())

Defined in Control.Isomorphic

Methods

to' :: IsNothing -> Maybe ()

Isomorphic IsJust (Maybe ())

Defined in Control.Isomorphic

Methods

to' :: IsJust -> Maybe ()

Isomorphic IsLeft (Either () ())

Defined in Control.Isomorphic

Methods

to' :: IsLeft -> Either () ()

Isomorphic IsRight (Either () ())

Defined in Control.Isomorphic

Methods

to' :: IsRight -> Either () ()

Isomorphic a (Const a x)

Defined in Control.Isomorphic

Methods

to' :: a -> Const a x

Isomorphic a (D1 d (C1 c (S1 s (K1 i a :: Type -> Type))) a)

Defined in Control.Isomorphic

Methods

to' :: a -> D1 d (C1 c (S1 s (K1 i a))) a

Isomorphic (Maybe ()) IsNothing

Defined in Control.Isomorphic

Methods

to' :: Maybe () -> IsNothing

Isomorphic (Maybe ()) IsJust

Defined in Control.Isomorphic

Methods

to' :: Maybe () -> IsJust

Isomorphic (Fixed a) Integer

Defined in Control.Isomorphic

Methods

to' :: Fixed a -> Integer

Isomorphic (Identity a) a

Defined in Control.Isomorphic

Methods

to' :: Identity a -> a

Isomorphic (Dual a) a

Defined in Control.Isomorphic

Methods

to' :: Dual a -> a

Isomorphic (Sum a) a

Defined in Control.Isomorphic

Methods

to' :: Sum a -> a

Isomorphic (Product a) a

Defined in Control.Isomorphic

Methods

to' :: Product a -> a

Isomorphic [a] (ZipList a)

Defined in Control.Isomorphic

Methods

to' :: [a] -> ZipList a

Isomorphic (Maybe a) (Last a)

Defined in Control.Isomorphic

Methods

to' :: Maybe a -> Last a

Isomorphic (Maybe a) (First a)

Defined in Control.Isomorphic

Methods

to' :: Maybe a -> First a

(Functor f, Isomorphic a b) => Isomorphic (f a) (f b)

Defined in Control.Isomorphic

Methods

to' :: f a -> f b

Isomorphic (ZipList a) [a]

Defined in Control.Isomorphic

Methods

to' :: ZipList a -> [a]

Isomorphic (First a) (Maybe a)

Defined in Control.Isomorphic

Methods

to' :: First a -> Maybe a

Isomorphic (Last a) (Maybe a)

Defined in Control.Isomorphic

Methods

to' :: Last a -> Maybe a

Isomorphic (Maybe a) (Either a ())

Defined in Control.Isomorphic

Methods

to' :: Maybe a -> Either a ()

Isomorphic (Maybe a) (Either () a)

Defined in Control.Isomorphic

Methods

to' :: Maybe a -> Either () a

Isomorphic (m a) (WrappedMonad m a)

Defined in Control.Isomorphic

Methods

to' :: m a -> WrappedMonad m a

Isomorphic (Endo a) (a -> a)

Defined in Control.Isomorphic

Methods

to' :: Endo a -> a -> a

Isomorphic (NonEmpty a) (a, [a])

Defined in Control.Isomorphic

Methods

to' :: NonEmpty a -> (a, [a])

Isomorphic (f (g a)) (Compose f g a)

Defined in Control.Isomorphic

Methods

to' :: f (g a) -> Compose f g a

Isomorphic (Either () ()) IsLeft

Defined in Control.Isomorphic

Methods

to' :: Either () () -> IsLeft

Isomorphic (Either () ()) IsRight

Defined in Control.Isomorphic

Methods

to' :: Either () () -> IsRight

Isomorphic (a -> a) (Endo a)

Defined in Control.Isomorphic

Methods

to' :: (a -> a) -> Endo a

Isomorphic (Either () a) (Maybe a)

Defined in Control.Isomorphic

Methods

to' :: Either () a -> Maybe a

Isomorphic (Either a ()) (Maybe a)

Defined in Control.Isomorphic

Methods

to' :: Either a () -> Maybe a

Isomorphic (a, [a]) (NonEmpty a)

Defined in Control.Isomorphic

Methods

to' :: (a, [a]) -> NonEmpty a

Isomorphic (WrappedMonad m a) (m a)

Defined in Control.Isomorphic

Methods

to' :: WrappedMonad m a -> m a

Isomorphic ((a, b) -> c) (a -> b -> c)

Defined in Control.Isomorphic

Methods

to' :: ((a, b) -> c) -> a -> b -> c

Isomorphic (a -> b -> c) (b -> a -> c)

Defined in Control.Isomorphic

Methods

to' :: (a -> b -> c) -> b -> a -> c

Isomorphic (a -> b -> c) ((a, b) -> c)

Defined in Control.Isomorphic

Methods

to' :: (a -> b -> c) -> (a, b) -> c

Isomorphic (Either a b) (Either b a)

Defined in Control.Isomorphic

Methods

to' :: Either a b -> Either b a

Isomorphic ((a, b), c) (a, (b, c))

Defined in Control.Isomorphic

Methods

to' :: ((a, b), c) -> (a, (b, c))

Isomorphic (a, (b, c)) ((a, b), c)

Defined in Control.Isomorphic

Methods

to' :: (a, (b, c)) -> ((a, b), c)

Isomorphic (a, b) (b, a)

Defined in Control.Isomorphic

Methods

to' :: (a, b) -> (b, a)

Isomorphic (a () b) (ArrowMonad a b)

Defined in Control.Isomorphic

Methods

to' :: a () b -> ArrowMonad a b

Isomorphic (ST s a) (ST s a)

Defined in Control.Isomorphic

Methods

to' :: ST0 s a -> ST s a

Isomorphic (ST s a) (ST s a)

Defined in Control.Isomorphic

Methods

to' :: ST s a -> ST0 s a

Isomorphic (ArrowMonad a b) (a () b)

Defined in Control.Isomorphic

Methods

to' :: ArrowMonad a b -> a () b

Isomorphic (a -> m b) (Kleisli m a b)

Defined in Control.Isomorphic

Methods

to' :: (a -> m b) -> Kleisli m a b

Isomorphic ((a, b), c) (a, b, c)

Defined in Control.Isomorphic

Methods

to' :: ((a, b), c) -> (a, b, c)

Isomorphic (a, (b, c)) (a, b, c)

Defined in Control.Isomorphic

Methods

to' :: (a, (b, c)) -> (a, b, c)

Isomorphic (a b c) (WrappedArrow a b c)

Defined in Control.Isomorphic

Methods

to' :: a b c -> WrappedArrow a b c

Isomorphic (Const a x) a

Defined in Control.Isomorphic

Methods

to' :: Const a x -> a

Isomorphic (a, b, c) ((a, b), c)

Defined in Control.Isomorphic

Methods

to' :: (a, b, c) -> ((a, b), c)

Isomorphic (a, b, c) (a, (b, c))

Defined in Control.Isomorphic

Methods

to' :: (a, b, c) -> (a, (b, c))

Isomorphic (WrappedArrow a b c) (a b c)

Defined in Control.Isomorphic

Methods

to' :: WrappedArrow a b c -> a b c

Isomorphic (Kleisli m a b) (a -> m b)

Defined in Control.Isomorphic

Methods

to' :: Kleisli m a b -> a -> m b

Isomorphic (D1 d (C1 c (S1 s (K1 i a :: Type -> Type))) a) a

Defined in Control.Isomorphic

Methods

to' :: D1 d (C1 c (S1 s (K1 i a))) a -> a

Isomorphic (Compose f g a) (f (g a))

Defined in Control.Isomorphic

Methods

to' :: Compose f g a -> f (g a)

via :: forall b a c. (Isomorphic b c, Isomorphic a b) => a -> c

Composition of two bijections

to :: forall b a. Isomorphic a b => a -> b

This is the perfer version of the to' function. The order of arguments in forall has been set up so that the codomain is first. This is important to work with TypeApplications.

     to @Text "hi there"
   

For call sites where we need to annotate.

from :: forall a b. Isomorphic a b => a -> b

This is the same as to but has the forall arguments with a first.

newtype IsRight

A wrapper for Either () () that decides the isomorphism to Bool is Right biased

Constructors

IsRight

Fields

• unIsRight :: Either () ()

Instances

Show IsRight

Defined in Control.Isomorphic

Methods

showsPrec :: Int -> IsRight -> ShowS

show :: IsRight -> String

showList :: [IsRight] -> ShowS

Generic IsRight

Defined in Control.Isomorphic

Associated Types

type Rep IsRight :: Type -> Type

Methods

from :: IsRight -> Rep IsRight x

to :: Rep IsRight x -> IsRight

Isomorphic Bool IsRight

Defined in Control.Isomorphic

Methods

to' :: Bool -> IsRight

Isomorphic IsRight Bool

Defined in Control.Isomorphic

Methods

to' :: IsRight -> Bool

Isomorphic IsRight (Either () ())

Defined in Control.Isomorphic

Methods

to' :: IsRight -> Either () ()

Isomorphic (Either () ()) IsRight

Defined in Control.Isomorphic

Methods

to' :: Either () () -> IsRight

type Rep IsRight

Defined in Control.Isomorphic

type Rep IsRight = D1 (MetaData "IsRight" "Control.Isomorphic" "control-iso-0.1.0.2-EG67WcOEfRSL1q1q9OrCZc" True) (C1 (MetaCons "IsRight" PrefixI True) (S1 (MetaSel (Just "unIsRight") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Either () ()))))

newtype IsLeft

A wrapper for Either () () that decides the isomorphism to Bool is Left biased

Constructors

IsLeft

Fields

• unIsLeft :: Either () ()

Instances

Show IsLeft

Defined in Control.Isomorphic

Methods

showsPrec :: Int -> IsLeft -> ShowS

show :: IsLeft -> String

showList :: [IsLeft] -> ShowS

Generic IsLeft

Defined in Control.Isomorphic

Associated Types

type Rep IsLeft :: Type -> Type

Methods

from :: IsLeft -> Rep IsLeft x

to :: Rep IsLeft x -> IsLeft

Isomorphic Bool IsLeft

Defined in Control.Isomorphic

Methods

to' :: Bool -> IsLeft

Isomorphic IsLeft Bool

Defined in Control.Isomorphic

Methods

to' :: IsLeft -> Bool

Isomorphic IsLeft (Either () ())

Defined in Control.Isomorphic

Methods

to' :: IsLeft -> Either () ()

Isomorphic (Either () ()) IsLeft

Defined in Control.Isomorphic

Methods

to' :: Either () () -> IsLeft

type Rep IsLeft

Defined in Control.Isomorphic

type Rep IsLeft = D1 (MetaData "IsLeft" "Control.Isomorphic" "control-iso-0.1.0.2-EG67WcOEfRSL1q1q9OrCZc" True) (C1 (MetaCons "IsLeft" PrefixI True) (S1 (MetaSel (Just "unIsLeft") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (Either () ()))))

newtype IsJust

A wrapper for Maybe () that decides the isomorphism to Bool is Just biased

Constructors

IsJust

Fields

• unIsJust :: Maybe ()

Instances

Show IsJust

Defined in Control.Isomorphic

Methods

showsPrec :: Int -> IsJust -> ShowS

show :: IsJust -> String

showList :: [IsJust] -> ShowS

Isomorphic Bool IsJust

Defined in Control.Isomorphic

Methods

to' :: Bool -> IsJust

Isomorphic IsJust Bool

Defined in Control.Isomorphic

Methods

to' :: IsJust -> Bool

Isomorphic IsJust (Maybe ())

Defined in Control.Isomorphic

Methods

to' :: IsJust -> Maybe ()

Isomorphic (Maybe ()) IsJust

Defined in Control.Isomorphic

Methods

to' :: Maybe () -> IsJust

newtype IsNothing

A wrapper for Maybe () that decides the isomorphism to Bool is Nothing biased

Constructors

IsNothing

Fields

• unIsNothing :: Maybe ()

Instances

Show IsNothing

Defined in Control.Isomorphic

Methods

showsPrec :: Int -> IsNothing -> ShowS

show :: IsNothing -> String

showList :: [IsNothing] -> ShowS

Isomorphic Bool IsNothing

Defined in Control.Isomorphic

Methods

to' :: Bool -> IsNothing

Isomorphic IsNothing Bool

Defined in Control.Isomorphic

Methods

to' :: IsNothing -> Bool

Isomorphic IsNothing (Maybe ())

Defined in Control.Isomorphic

Methods

to' :: IsNothing -> Maybe ()

Isomorphic (Maybe ()) IsNothing

Defined in Control.Isomorphic

Methods

to' :: Maybe () -> IsNothing

as :: (Isomorphic b d, Isomorphic c a) => (a -> b) -> c -> d

lift a function to any types to which it is isomorphic

as2 :: (Isomorphic c f, Isomorphic d a, Isomorphic e b) => (a -> b -> c) -> d -> e -> f

as3 :: (Isomorphic d h, Isomorphic e a, Isomorphic f b, Isomorphic g c) => (a -> b -> c -> d) -> e -> f -> g -> h

as4 :: (Isomorphic e j, Isomorphic f a, Isomorphic g b, Isomorphic h c, Isomorphic i d) => (a -> b -> c -> d -> e) -> f -> g -> h -> i -> j

as5 :: (Isomorphic f l, Isomorphic g a, Isomorphic h b, Isomorphic i c, Isomorphic j d, Isomorphic k e) => (a -> b -> c -> d -> e -> f) -> g -> h -> i -> j -> k -> l

isoBi :: (Profunctor p, Isomorphic s a, Isomorphic b t, Functor f) => p a (f b) -> p s (f t)

A free lens Iso s t a b from the Isomorphic instances