Safe Haskell	None
Language	Haskell2010

Control.Isomorphic

Synopsis

class Isomorphic b a => Isomorphic a b where
- to' :: a -> b
via :: forall b a c. (Isomorphic b c, Isomorphic a b) => a -> c
to :: forall b a. Isomorphic a b => a -> b
from :: forall a b. Isomorphic a b => a -> b
newtype IsRight = IsRight {
- unIsRight :: Either () ()
}
newtype IsLeft = IsLeft {
- unIsLeft :: Either () ()
}
newtype IsJust = IsJust {
- unIsJust :: Maybe ()
}
newtype IsNothing = IsNothing {
- unIsNothing :: Maybe ()
}
as :: (Isomorphic b d, Isomorphic c a) => (a -> b) -> c -> d
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)

Documentation

class Isomorphic b a => Isomorphic a b where Source #

Methods

to' :: a -> b Source #

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 Source #
Instance details Defined in Control.Isomorphic Methods to' :: Bool -> All Source #
Isomorphic Bool Any Source #
Instance details Defined in Control.Isomorphic Methods to' :: Bool -> Any Source #
Isomorphic Bool IsNothing Source #
Instance details Defined in Control.Isomorphic Methods to' :: Bool -> IsNothing Source #
Isomorphic Bool IsJust Source #
Instance details Defined in Control.Isomorphic Methods to' :: Bool -> IsJust Source #
Isomorphic Bool IsLeft Source #
Instance details Defined in Control.Isomorphic Methods to' :: Bool -> IsLeft Source #
Isomorphic Bool IsRight Source #
Instance details Defined in Control.Isomorphic Methods to' :: Bool -> IsRight Source #
Enum a => Isomorphic Int a Source #
Instance details Defined in Control.Isomorphic Methods to' :: Int -> a Source #
Coercible a b => Isomorphic a b Source #
Instance details Defined in Control.Isomorphic Methods to' :: a -> b Source #
Enum a => Isomorphic a Int Source #
Instance details Defined in Control.Isomorphic Methods to' :: a -> Int Source #
Isomorphic a a Source #
Instance details Defined in Control.Isomorphic Methods to' :: a -> a Source #
Isomorphic All Bool Source #
Instance details Defined in Control.Isomorphic Methods to' :: All -> Bool Source #
Isomorphic Any Bool Source #
Instance details Defined in Control.Isomorphic Methods to' :: Any -> Bool Source #
Isomorphic String ByteString Source #
Instance details Defined in Control.Isomorphic Methods to' :: String -> ByteString Source #
Isomorphic String ByteString Source #
Instance details Defined in Control.Isomorphic Methods to' :: String -> ByteString Source #
Isomorphic String Text Source #
Instance details Defined in Control.Isomorphic Methods to' :: String -> Text Source #
Isomorphic String Text Source #
Instance details Defined in Control.Isomorphic Methods to' :: String -> Text Source #
Isomorphic ByteString String Source #
Instance details Defined in Control.Isomorphic Methods to' :: ByteString -> String Source #
Isomorphic ByteString ByteString Source #
Instance details Defined in Control.Isomorphic Methods to' :: ByteString0 -> ByteString Source #
Isomorphic ByteString Text Source #
Instance details Defined in Control.Isomorphic Methods to' :: ByteString -> Text Source #
Isomorphic ByteString Text Source #
Instance details Defined in Control.Isomorphic Methods to' :: ByteString -> Text Source #
Isomorphic ByteString String Source #
Instance details Defined in Control.Isomorphic Methods to' :: ByteString -> String Source #
Isomorphic ByteString ByteString Source #
Instance details Defined in Control.Isomorphic Methods to' :: ByteString -> ByteString0 Source #
Isomorphic ByteString Text Source #
Instance details Defined in Control.Isomorphic Methods to' :: ByteString -> Text Source #
Isomorphic ByteString Text Source #
Instance details Defined in Control.Isomorphic Methods to' :: ByteString -> Text Source #
Isomorphic Text String Source #
Instance details Defined in Control.Isomorphic Methods to' :: Text -> String Source #
Isomorphic Text ByteString Source #
Instance details Defined in Control.Isomorphic Methods to' :: Text -> ByteString Source #
Isomorphic Text ByteString Source #
Instance details Defined in Control.Isomorphic Methods to' :: Text -> ByteString Source #
Isomorphic Text Text Source #
Instance details Defined in Control.Isomorphic Methods to' :: Text0 -> Text Source #
Isomorphic Text String Source #
Instance details Defined in Control.Isomorphic Methods to' :: Text -> String Source #
Isomorphic Text ByteString Source #
Instance details Defined in Control.Isomorphic Methods to' :: Text -> ByteString Source #
Isomorphic Text ByteString Source #
Instance details Defined in Control.Isomorphic Methods to' :: Text -> ByteString Source #
Isomorphic Text Text Source #
Instance details Defined in Control.Isomorphic Methods to' :: Text -> Text0 Source #
Isomorphic IsNothing Bool Source #
Instance details Defined in Control.Isomorphic Methods to' :: IsNothing -> Bool Source #
Isomorphic IsJust Bool Source #
Instance details Defined in Control.Isomorphic Methods to' :: IsJust -> Bool Source #
Isomorphic IsLeft Bool Source #
Instance details Defined in Control.Isomorphic Methods to' :: IsLeft -> Bool Source #
Isomorphic IsRight Bool Source #
Instance details Defined in Control.Isomorphic Methods to' :: IsRight -> Bool Source #
Isomorphic Integer (Fixed a) Source #
Instance details Defined in Control.Isomorphic Methods to' :: Integer -> Fixed a Source #
Isomorphic a (Product a) Source #
Instance details Defined in Control.Isomorphic Methods to' :: a -> Product a Source #
Isomorphic a (Sum a) Source #
Instance details Defined in Control.Isomorphic Methods to' :: a -> Sum a Source #
Isomorphic a (Dual a) Source #
Instance details Defined in Control.Isomorphic Methods to' :: a -> Dual a Source #
Isomorphic a (Identity a) Source #
Instance details Defined in Control.Isomorphic Methods to' :: a -> Identity a Source #
Isomorphic IsNothing (Maybe ()) Source #
Instance details Defined in Control.Isomorphic Methods to' :: IsNothing -> Maybe () Source #
Isomorphic IsJust (Maybe ()) Source #
Instance details Defined in Control.Isomorphic Methods to' :: IsJust -> Maybe () Source #
Isomorphic IsLeft (Either () ()) Source #
Instance details Defined in Control.Isomorphic Methods to' :: IsLeft -> Either () () Source #
Isomorphic IsRight (Either () ()) Source #
Instance details Defined in Control.Isomorphic Methods to' :: IsRight -> Either () () Source #
Isomorphic a (Const a x) Source #
Instance details Defined in Control.Isomorphic Methods to' :: a -> Const a x Source #
Isomorphic a (D1 d (C1 c (S1 s (K1 i a :: Type -> Type))) a) Source #
Instance details Defined in Control.Isomorphic Methods to' :: a -> D1 d (C1 c (S1 s (K1 i a))) a Source #
Isomorphic (Maybe ()) IsNothing Source #
Instance details Defined in Control.Isomorphic Methods to' :: Maybe () -> IsNothing Source #
Isomorphic (Maybe ()) IsJust Source #
Instance details Defined in Control.Isomorphic Methods to' :: Maybe () -> IsJust Source #
Isomorphic (Fixed a) Integer Source #
Instance details Defined in Control.Isomorphic Methods to' :: Fixed a -> Integer Source #
Isomorphic (Identity a) a Source #
Instance details Defined in Control.Isomorphic Methods to' :: Identity a -> a Source #
Isomorphic (Dual a) a Source #
Instance details Defined in Control.Isomorphic Methods to' :: Dual a -> a Source #
Isomorphic (Sum a) a Source #
Instance details Defined in Control.Isomorphic Methods to' :: Sum a -> a Source #
Isomorphic (Product a) a Source #
Instance details Defined in Control.Isomorphic Methods to' :: Product a -> a Source #
Isomorphic [a] (ZipList a) Source #
Instance details Defined in Control.Isomorphic Methods to' :: [a] -> ZipList a Source #
Isomorphic (Maybe a) (Last a) Source #
Instance details Defined in Control.Isomorphic Methods to' :: Maybe a -> Last a Source #
Isomorphic (Maybe a) (First a) Source #
Instance details Defined in Control.Isomorphic Methods to' :: Maybe a -> First a Source #
(Functor f, Isomorphic a b) => Isomorphic (f a) (f b) Source #
Instance details Defined in Control.Isomorphic Methods to' :: f a -> f b Source #
Isomorphic (ZipList a) [a] Source #
Instance details Defined in Control.Isomorphic Methods to' :: ZipList a -> [a] Source #
Isomorphic (First a) (Maybe a) Source #
Instance details Defined in Control.Isomorphic Methods to' :: First a -> Maybe a Source #
Isomorphic (Last a) (Maybe a) Source #
Instance details Defined in Control.Isomorphic Methods to' :: Last a -> Maybe a Source #
Isomorphic (Maybe a) (Either a ()) Source #
Instance details Defined in Control.Isomorphic Methods to' :: Maybe a -> Either a () Source #
Isomorphic (Maybe a) (Either () a) Source #
Instance details Defined in Control.Isomorphic Methods to' :: Maybe a -> Either () a Source #
Isomorphic (m a) (WrappedMonad m a) Source #
Instance details Defined in Control.Isomorphic Methods to' :: m a -> WrappedMonad m a Source #
Isomorphic (Endo a) (a -> a) Source #
Instance details Defined in Control.Isomorphic Methods to' :: Endo a -> a -> a Source #
Isomorphic (NonEmpty a) (a, [a]) Source #
Instance details Defined in Control.Isomorphic Methods to' :: NonEmpty a -> (a, [a]) Source #
Isomorphic (f (g a)) (Compose f g a) Source #
Instance details Defined in Control.Isomorphic Methods to' :: f (g a) -> Compose f g a Source #
Isomorphic (Either () ()) IsLeft Source #
Instance details Defined in Control.Isomorphic Methods to' :: Either () () -> IsLeft Source #
Isomorphic (Either () ()) IsRight Source #
Instance details Defined in Control.Isomorphic Methods to' :: Either () () -> IsRight Source #
Isomorphic (a -> a) (Endo a) Source #
Instance details Defined in Control.Isomorphic Methods to' :: (a -> a) -> Endo a Source #
Isomorphic (Either () a) (Maybe a) Source #
Instance details Defined in Control.Isomorphic Methods to' :: Either () a -> Maybe a Source #
Isomorphic (Either a ()) (Maybe a) Source #
Instance details Defined in Control.Isomorphic Methods to' :: Either a () -> Maybe a Source #
Isomorphic (a, [a]) (NonEmpty a) Source #
Instance details Defined in Control.Isomorphic Methods to' :: (a, [a]) -> NonEmpty a Source #
Isomorphic (WrappedMonad m a) (m a) Source #
Instance details Defined in Control.Isomorphic Methods to' :: WrappedMonad m a -> m a Source #
Isomorphic ((a, b) -> c) (a -> b -> c) Source #
Instance details Defined in Control.Isomorphic Methods to' :: ((a, b) -> c) -> a -> b -> c Source #
Isomorphic (a -> b -> c) (b -> a -> c) Source #
Instance details Defined in Control.Isomorphic Methods to' :: (a -> b -> c) -> b -> a -> c Source #
Isomorphic (a -> b -> c) ((a, b) -> c) Source #
Instance details Defined in Control.Isomorphic Methods to' :: (a -> b -> c) -> (a, b) -> c Source #
Isomorphic (Either a b) (Either b a) Source #
Instance details Defined in Control.Isomorphic Methods to' :: Either a b -> Either b a Source #
Isomorphic ((a, b), c) (a, (b, c)) Source #
Instance details Defined in Control.Isomorphic Methods to' :: ((a, b), c) -> (a, (b, c)) Source #
Isomorphic (a, (b, c)) ((a, b), c) Source #
Instance details Defined in Control.Isomorphic Methods to' :: (a, (b, c)) -> ((a, b), c) Source #
Isomorphic (a, b) (b, a) Source #
Instance details Defined in Control.Isomorphic Methods to' :: (a, b) -> (b, a) Source #
Isomorphic (a () b) (ArrowMonad a b) Source #
Instance details Defined in Control.Isomorphic Methods to' :: a () b -> ArrowMonad a b Source #
Isomorphic (ST s a) (ST s a) Source #
Instance details Defined in Control.Isomorphic Methods to' :: ST0 s a -> ST s a Source #
Isomorphic (ST s a) (ST s a) Source #
Instance details Defined in Control.Isomorphic Methods to' :: ST s a -> ST0 s a Source #
Isomorphic (ArrowMonad a b) (a () b) Source #
Instance details Defined in Control.Isomorphic Methods to' :: ArrowMonad a b -> a () b Source #
Isomorphic (a -> m b) (Kleisli m a b) Source #
Instance details Defined in Control.Isomorphic Methods to' :: (a -> m b) -> Kleisli m a b Source #
Isomorphic ((a, b), c) (a, b, c) Source #
Instance details Defined in Control.Isomorphic Methods to' :: ((a, b), c) -> (a, b, c) Source #
Isomorphic (a, (b, c)) (a, b, c) Source #
Instance details Defined in Control.Isomorphic Methods to' :: (a, (b, c)) -> (a, b, c) Source #
Isomorphic (a b c) (WrappedArrow a b c) Source #
Instance details Defined in Control.Isomorphic Methods to' :: a b c -> WrappedArrow a b c Source #
Isomorphic (Const a x) a Source #
Instance details Defined in Control.Isomorphic Methods to' :: Const a x -> a Source #
Isomorphic (a, b, c) ((a, b), c) Source #
Instance details Defined in Control.Isomorphic Methods to' :: (a, b, c) -> ((a, b), c) Source #
Isomorphic (a, b, c) (a, (b, c)) Source #
Instance details Defined in Control.Isomorphic Methods to' :: (a, b, c) -> (a, (b, c)) Source #
Isomorphic (WrappedArrow a b c) (a b c) Source #
Instance details Defined in Control.Isomorphic Methods to' :: WrappedArrow a b c -> a b c Source #
Isomorphic (Kleisli m a b) (a -> m b) Source #
Instance details Defined in Control.Isomorphic Methods to' :: Kleisli m a b -> a -> m b Source #
Isomorphic (D1 d (C1 c (S1 s (K1 i a :: Type -> Type))) a) a Source #
Instance details Defined in Control.Isomorphic Methods to' :: D1 d (C1 c (S1 s (K1 i a))) a -> a Source #
Isomorphic (Compose f g a) (f (g a)) Source #
Instance details Defined in Control.Isomorphic Methods to' :: Compose f g a -> f (g a) Source #

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

Composition of two bijections

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

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 Source #

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

newtype IsRight Source #

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

Constructors

IsRight
Fields unIsRight :: Either () ()

Instances

Show IsRight Source #
Instance details Defined in Control.Isomorphic Methods showsPrec :: Int -> IsRight -> ShowS # show :: IsRight -> String # showList :: [IsRight] -> ShowS #
Generic IsRight Source #
Instance details 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 Source #
Instance details Defined in Control.Isomorphic Methods to' :: Bool -> IsRight Source #
Isomorphic IsRight Bool Source #
Instance details Defined in Control.Isomorphic Methods to' :: IsRight -> Bool Source #
Isomorphic IsRight (Either () ()) Source #
Instance details Defined in Control.Isomorphic Methods to' :: IsRight -> Either () () Source #
Isomorphic (Either () ()) IsRight Source #
Instance details Defined in Control.Isomorphic Methods to' :: Either () () -> IsRight Source #
type Rep IsRight Source #
Instance details 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 Source #

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

Constructors

IsLeft
Fields unIsLeft :: Either () ()

Instances

Show IsLeft Source #
Instance details Defined in Control.Isomorphic Methods showsPrec :: Int -> IsLeft -> ShowS # show :: IsLeft -> String # showList :: [IsLeft] -> ShowS #
Generic IsLeft Source #
Instance details 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 Source #
Instance details Defined in Control.Isomorphic Methods to' :: Bool -> IsLeft Source #
Isomorphic IsLeft Bool Source #
Instance details Defined in Control.Isomorphic Methods to' :: IsLeft -> Bool Source #
Isomorphic IsLeft (Either () ()) Source #
Instance details Defined in Control.Isomorphic Methods to' :: IsLeft -> Either () () Source #
Isomorphic (Either () ()) IsLeft Source #
Instance details Defined in Control.Isomorphic Methods to' :: Either () () -> IsLeft Source #
type Rep IsLeft Source #
Instance details 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 Source #

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

Constructors

IsJust
Fields unIsJust :: Maybe ()

Instances

Show IsJust Source #
Instance details Defined in Control.Isomorphic Methods showsPrec :: Int -> IsJust -> ShowS # show :: IsJust -> String # showList :: [IsJust] -> ShowS #
Isomorphic Bool IsJust Source #
Instance details Defined in Control.Isomorphic Methods to' :: Bool -> IsJust Source #
Isomorphic IsJust Bool Source #
Instance details Defined in Control.Isomorphic Methods to' :: IsJust -> Bool Source #
Isomorphic IsJust (Maybe ()) Source #
Instance details Defined in Control.Isomorphic Methods to' :: IsJust -> Maybe () Source #
Isomorphic (Maybe ()) IsJust Source #
Instance details Defined in Control.Isomorphic Methods to' :: Maybe () -> IsJust Source #

newtype IsNothing Source #

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

Constructors

IsNothing
Fields unIsNothing :: Maybe ()

Instances

Show IsNothing Source #
Instance details Defined in Control.Isomorphic Methods showsPrec :: Int -> IsNothing -> ShowS # show :: IsNothing -> String # showList :: [IsNothing] -> ShowS #
Isomorphic Bool IsNothing Source #
Instance details Defined in Control.Isomorphic Methods to' :: Bool -> IsNothing Source #
Isomorphic IsNothing Bool Source #
Instance details Defined in Control.Isomorphic Methods to' :: IsNothing -> Bool Source #
Isomorphic IsNothing (Maybe ()) Source #
Instance details Defined in Control.Isomorphic Methods to' :: IsNothing -> Maybe () Source #
Isomorphic (Maybe ()) IsNothing Source #
Instance details Defined in Control.Isomorphic Methods to' :: Maybe () -> IsNothing Source #

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

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 Source #

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

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 Source #

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 Source #

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

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