{-# LANGUAGE DeriveDataTypeable #-} {-# LANGUAGE DeriveGeneric #-} {-# LANGUAGE GADTs #-} {-# LANGUAGE GeneralizedNewtypeDeriving #-} {-# LANGUAGE PolyKinds #-} {-# LANGUAGE ScopedTypeVariables #-} {-# LANGUAGE Trustworthy #-} {-# LANGUAGE StandaloneDeriving #-} ----------------------------------------------------------------------------- -- | -- Module : Data.Functor.Compose -- Copyright : (c) Ross Paterson 2010 -- License : BSD-style (see the file LICENSE) -- -- Maintainer : libraries@haskell.org -- Stability : stable -- Portability : portable -- -- Composition of functors. -- -- @since 4.9.0.0 ----------------------------------------------------------------------------- module Data.Functor.Compose ( Compose(..), ) where import Data.Functor.Classes import Control.Applicative import Data.Coerce (coerce) import Data.Data (Data) import Data.Type.Equality (TestEquality(..), (:~:)(..)) import GHC.Generics (Generic, Generic1) import Text.Read () infixr 9 `Compose` -- | Right-to-left composition of functors. -- The composition of applicative functors is always applicative, -- but the composition of monads is not always a monad. newtype Compose f g a = Compose { forall {k} {k} (f :: k -> *) (g :: k -> k) (a :: k). Compose f g a -> f (g a) getCompose :: f (g a) } deriving ( Typeable (Compose f g a) Typeable (Compose f g a) -> (forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Compose f g a -> c (Compose f g a)) -> (forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Compose f g a)) -> (Compose f g a -> Constr) -> (Compose f g a -> DataType) -> (forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Compose f g a))) -> (forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Compose f g a))) -> ((forall b. Data b => b -> b) -> Compose f g a -> Compose f g a) -> (forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Compose f g a -> r) -> (forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Compose f g a -> r) -> (forall u. (forall d. Data d => d -> u) -> Compose f g a -> [u]) -> (forall u. Int -> (forall d. Data d => d -> u) -> Compose f g a -> u) -> (forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> Compose f g a -> m (Compose f g a)) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> Compose f g a -> m (Compose f g a)) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> Compose f g a -> m (Compose f g a)) -> Data (Compose f g a) Compose f g a -> Constr Compose f g a -> DataType (forall b. Data b => b -> b) -> Compose f g a -> Compose f g a forall a. Typeable a -> (forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> a -> c a) -> (forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c a) -> (a -> Constr) -> (a -> DataType) -> (forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c a)) -> (forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c a)) -> ((forall b. Data b => b -> b) -> a -> a) -> (forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> a -> r) -> (forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> a -> r) -> (forall u. (forall d. Data d => d -> u) -> a -> [u]) -> (forall u. Int -> (forall d. Data d => d -> u) -> a -> u) -> (forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> a -> m a) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> a -> m a) -> (forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> a -> m a) -> Data a forall u. Int -> (forall d. Data d => d -> u) -> Compose f g a -> u forall u. (forall d. Data d => d -> u) -> Compose f g a -> [u] forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Compose f g a -> r forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Compose f g a -> r forall {k} {f :: k -> *} {k} {g :: k -> k} {a :: k}. (Typeable a, Typeable f, Typeable g, Typeable k, Typeable k, Data (f (g a))) => Typeable (Compose f g a) forall k (f :: k -> *) k (g :: k -> k) (a :: k). (Typeable a, Typeable f, Typeable g, Typeable k, Typeable k, Data (f (g a))) => Compose f g a -> Constr forall k (f :: k -> *) k (g :: k -> k) (a :: k). (Typeable a, Typeable f, Typeable g, Typeable k, Typeable k, Data (f (g a))) => Compose f g a -> DataType forall k (f :: k -> *) k (g :: k -> k) (a :: k). (Typeable a, Typeable f, Typeable g, Typeable k, Typeable k, Data (f (g a))) => (forall b. Data b => b -> b) -> Compose f g a -> Compose f g a forall k (f :: k -> *) k (g :: k -> k) (a :: k) u. (Typeable a, Typeable f, Typeable g, Typeable k, Typeable k, Data (f (g a))) => Int -> (forall d. Data d => d -> u) -> Compose f g a -> u forall k (f :: k -> *) k (g :: k -> k) (a :: k) u. (Typeable a, Typeable f, Typeable g, Typeable k, Typeable k, Data (f (g a))) => (forall d. Data d => d -> u) -> Compose f g a -> [u] forall k (f :: k -> *) k (g :: k -> k) (a :: k) r r'. (Typeable a, Typeable f, Typeable g, Typeable k, Typeable k, Data (f (g a))) => (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Compose f g a -> r forall k (f :: k -> *) k (g :: k -> k) (a :: k) r r'. (Typeable a, Typeable f, Typeable g, Typeable k, Typeable k, Data (f (g a))) => (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Compose f g a -> r forall k (f :: k -> *) k (g :: k -> k) (a :: k) (m :: * -> *). (Typeable a, Typeable f, Typeable g, Typeable k, Typeable k, Data (f (g a)), Monad m) => (forall d. Data d => d -> m d) -> Compose f g a -> m (Compose f g a) forall k (f :: k -> *) k (g :: k -> k) (a :: k) (m :: * -> *). (Typeable a, Typeable f, Typeable g, Typeable k, Typeable k, Data (f (g a)), MonadPlus m) => (forall d. Data d => d -> m d) -> Compose f g a -> m (Compose f g a) forall k (f :: k -> *) k (g :: k -> k) (a :: k) (c :: * -> *). (Typeable a, Typeable f, Typeable g, Typeable k, Typeable k, Data (f (g a))) => (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Compose f g a) forall k (f :: k -> *) k (g :: k -> k) (a :: k) (c :: * -> *). (Typeable a, Typeable f, Typeable g, Typeable k, Typeable k, Data (f (g a))) => (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Compose f g a -> c (Compose f g a) forall k (f :: k -> *) k (g :: k -> k) (a :: k) (t :: * -> *) (c :: * -> *). (Typeable a, Typeable f, Typeable g, Typeable k, Typeable k, Data (f (g a)), Typeable t) => (forall d. Data d => c (t d)) -> Maybe (c (Compose f g a)) forall k (f :: k -> *) k (g :: k -> k) (a :: k) (t :: * -> * -> *) (c :: * -> *). (Typeable a, Typeable f, Typeable g, Typeable k, Typeable k, Data (f (g a)), Typeable t) => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Compose f g a)) forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> Compose f g a -> m (Compose f g a) forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> Compose f g a -> m (Compose f g a) forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Compose f g a) forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Compose f g a -> c (Compose f g a) forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Compose f g a)) forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Compose f g a)) $cgfoldl :: forall k (f :: k -> *) k (g :: k -> k) (a :: k) (c :: * -> *). (Typeable a, Typeable f, Typeable g, Typeable k, Typeable k, Data (f (g a))) => (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Compose f g a -> c (Compose f g a) gfoldl :: forall (c :: * -> *). (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Compose f g a -> c (Compose f g a) $cgunfold :: forall k (f :: k -> *) k (g :: k -> k) (a :: k) (c :: * -> *). (Typeable a, Typeable f, Typeable g, Typeable k, Typeable k, Data (f (g a))) => (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Compose f g a) gunfold :: forall (c :: * -> *). (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Compose f g a) $ctoConstr :: forall k (f :: k -> *) k (g :: k -> k) (a :: k). (Typeable a, Typeable f, Typeable g, Typeable k, Typeable k, Data (f (g a))) => Compose f g a -> Constr toConstr :: Compose f g a -> Constr $cdataTypeOf :: forall k (f :: k -> *) k (g :: k -> k) (a :: k). (Typeable a, Typeable f, Typeable g, Typeable k, Typeable k, Data (f (g a))) => Compose f g a -> DataType dataTypeOf :: Compose f g a -> DataType $cdataCast1 :: forall k (f :: k -> *) k (g :: k -> k) (a :: k) (t :: * -> *) (c :: * -> *). (Typeable a, Typeable f, Typeable g, Typeable k, Typeable k, Data (f (g a)), Typeable t) => (forall d. Data d => c (t d)) -> Maybe (c (Compose f g a)) dataCast1 :: forall (t :: * -> *) (c :: * -> *). Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Compose f g a)) $cdataCast2 :: forall k (f :: k -> *) k (g :: k -> k) (a :: k) (t :: * -> * -> *) (c :: * -> *). (Typeable a, Typeable f, Typeable g, Typeable k, Typeable k, Data (f (g a)), Typeable t) => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Compose f g a)) dataCast2 :: forall (t :: * -> * -> *) (c :: * -> *). Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Compose f g a)) $cgmapT :: forall k (f :: k -> *) k (g :: k -> k) (a :: k). (Typeable a, Typeable f, Typeable g, Typeable k, Typeable k, Data (f (g a))) => (forall b. Data b => b -> b) -> Compose f g a -> Compose f g a gmapT :: (forall b. Data b => b -> b) -> Compose f g a -> Compose f g a $cgmapQl :: forall k (f :: k -> *) k (g :: k -> k) (a :: k) r r'. (Typeable a, Typeable f, Typeable g, Typeable k, Typeable k, Data (f (g a))) => (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Compose f g a -> r gmapQl :: forall r r'. (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Compose f g a -> r $cgmapQr :: forall k (f :: k -> *) k (g :: k -> k) (a :: k) r r'. (Typeable a, Typeable f, Typeable g, Typeable k, Typeable k, Data (f (g a))) => (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Compose f g a -> r gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Compose f g a -> r $cgmapQ :: forall k (f :: k -> *) k (g :: k -> k) (a :: k) u. (Typeable a, Typeable f, Typeable g, Typeable k, Typeable k, Data (f (g a))) => (forall d. Data d => d -> u) -> Compose f g a -> [u] gmapQ :: forall u. (forall d. Data d => d -> u) -> Compose f g a -> [u] $cgmapQi :: forall k (f :: k -> *) k (g :: k -> k) (a :: k) u. (Typeable a, Typeable f, Typeable g, Typeable k, Typeable k, Data (f (g a))) => Int -> (forall d. Data d => d -> u) -> Compose f g a -> u gmapQi :: forall u. Int -> (forall d. Data d => d -> u) -> Compose f g a -> u $cgmapM :: forall k (f :: k -> *) k (g :: k -> k) (a :: k) (m :: * -> *). (Typeable a, Typeable f, Typeable g, Typeable k, Typeable k, Data (f (g a)), Monad m) => (forall d. Data d => d -> m d) -> Compose f g a -> m (Compose f g a) gmapM :: forall (m :: * -> *). Monad m => (forall d. Data d => d -> m d) -> Compose f g a -> m (Compose f g a) $cgmapMp :: forall k (f :: k -> *) k (g :: k -> k) (a :: k) (m :: * -> *). (Typeable a, Typeable f, Typeable g, Typeable k, Typeable k, Data (f (g a)), MonadPlus m) => (forall d. Data d => d -> m d) -> Compose f g a -> m (Compose f g a) gmapMp :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> Compose f g a -> m (Compose f g a) $cgmapMo :: forall k (f :: k -> *) k (g :: k -> k) (a :: k) (m :: * -> *). (Typeable a, Typeable f, Typeable g, Typeable k, Typeable k, Data (f (g a)), MonadPlus m) => (forall d. Data d => d -> m d) -> Compose f g a -> m (Compose f g a) gmapMo :: forall (m :: * -> *). MonadPlus m => (forall d. Data d => d -> m d) -> Compose f g a -> m (Compose f g a) Data -- ^ @since 4.9.0.0 , (forall x. Compose f g a -> Rep (Compose f g a) x) -> (forall x. Rep (Compose f g a) x -> Compose f g a) -> Generic (Compose f g a) forall x. Rep (Compose f g a) x -> Compose f g a forall x. Compose f g a -> Rep (Compose f g a) x forall a. (forall x. a -> Rep a x) -> (forall x. Rep a x -> a) -> Generic a forall k (f :: k -> *) k (g :: k -> k) (a :: k) x. Rep (Compose f g a) x -> Compose f g a forall k (f :: k -> *) k (g :: k -> k) (a :: k) x. Compose f g a -> Rep (Compose f g a) x $cfrom :: forall k (f :: k -> *) k (g :: k -> k) (a :: k) x. Compose f g a -> Rep (Compose f g a) x from :: forall x. Compose f g a -> Rep (Compose f g a) x $cto :: forall k (f :: k -> *) k (g :: k -> k) (a :: k) x. Rep (Compose f g a) x -> Compose f g a to :: forall x. Rep (Compose f g a) x -> Compose f g a Generic -- ^ @since 4.9.0.0 , (forall (a :: k). Compose f g a -> Rep1 (Compose f g) a) -> (forall (a :: k). Rep1 (Compose f g) a -> Compose f g a) -> Generic1 (Compose f g) forall (a :: k). Rep1 (Compose f g) a -> Compose f g a forall (a :: k). Compose f g a -> Rep1 (Compose f g) a forall k (f :: k -> *). (forall (a :: k). f a -> Rep1 f a) -> (forall (a :: k). Rep1 f a -> f a) -> Generic1 f forall (f :: * -> *) k (g :: k -> *) (a :: k). Functor f => Rep1 (Compose f g) a -> Compose f g a forall (f :: * -> *) k (g :: k -> *) (a :: k). Functor f => Compose f g a -> Rep1 (Compose f g) a $cfrom1 :: forall (f :: * -> *) k (g :: k -> *) (a :: k). Functor f => Compose f g a -> Rep1 (Compose f g) a from1 :: forall (a :: k). Compose f g a -> Rep1 (Compose f g) a $cto1 :: forall (f :: * -> *) k (g :: k -> *) (a :: k). Functor f => Rep1 (Compose f g) a -> Compose f g a to1 :: forall (a :: k). Rep1 (Compose f g) a -> Compose f g a Generic1 -- ^ @since 4.9.0.0 , NonEmpty (Compose f g a) -> Compose f g a Compose f g a -> Compose f g a -> Compose f g a (Compose f g a -> Compose f g a -> Compose f g a) -> (NonEmpty (Compose f g a) -> Compose f g a) -> (forall b. Integral b => b -> Compose f g a -> Compose f g a) -> Semigroup (Compose f g a) forall b. Integral b => b -> Compose f g a -> Compose f g a forall a. (a -> a -> a) -> (NonEmpty a -> a) -> (forall b. Integral b => b -> a -> a) -> Semigroup a forall k (f :: k -> *) k (g :: k -> k) (a :: k). Semigroup (f (g a)) => NonEmpty (Compose f g a) -> Compose f g a forall k (f :: k -> *) k (g :: k -> k) (a :: k). Semigroup (f (g a)) => Compose f g a -> Compose f g a -> Compose f g a forall k (f :: k -> *) k (g :: k -> k) (a :: k) b. (Semigroup (f (g a)), Integral b) => b -> Compose f g a -> Compose f g a $c<> :: forall k (f :: k -> *) k (g :: k -> k) (a :: k). Semigroup (f (g a)) => Compose f g a -> Compose f g a -> Compose f g a <> :: Compose f g a -> Compose f g a -> Compose f g a $csconcat :: forall k (f :: k -> *) k (g :: k -> k) (a :: k). Semigroup (f (g a)) => NonEmpty (Compose f g a) -> Compose f g a sconcat :: NonEmpty (Compose f g a) -> Compose f g a $cstimes :: forall k (f :: k -> *) k (g :: k -> k) (a :: k) b. (Semigroup (f (g a)), Integral b) => b -> Compose f g a -> Compose f g a stimes :: forall b. Integral b => b -> Compose f g a -> Compose f g a Semigroup -- ^ @since 4.16.0.0 , Semigroup (Compose f g a) Compose f g a Semigroup (Compose f g a) -> Compose f g a -> (Compose f g a -> Compose f g a -> Compose f g a) -> ([Compose f g a] -> Compose f g a) -> Monoid (Compose f g a) [Compose f g a] -> Compose f g a Compose f g a -> Compose f g a -> Compose f g a forall a. Semigroup a -> a -> (a -> a -> a) -> ([a] -> a) -> Monoid a forall {k} {f :: k -> *} {k} {g :: k -> k} {a :: k}. Monoid (f (g a)) => Semigroup (Compose f g a) forall k (f :: k -> *) k (g :: k -> k) (a :: k). Monoid (f (g a)) => Compose f g a forall k (f :: k -> *) k (g :: k -> k) (a :: k). Monoid (f (g a)) => [Compose f g a] -> Compose f g a forall k (f :: k -> *) k (g :: k -> k) (a :: k). Monoid (f (g a)) => Compose f g a -> Compose f g a -> Compose f g a $cmempty :: forall k (f :: k -> *) k (g :: k -> k) (a :: k). Monoid (f (g a)) => Compose f g a mempty :: Compose f g a $cmappend :: forall k (f :: k -> *) k (g :: k -> k) (a :: k). Monoid (f (g a)) => Compose f g a -> Compose f g a -> Compose f g a mappend :: Compose f g a -> Compose f g a -> Compose f g a $cmconcat :: forall k (f :: k -> *) k (g :: k -> k) (a :: k). Monoid (f (g a)) => [Compose f g a] -> Compose f g a mconcat :: [Compose f g a] -> Compose f g a Monoid -- ^ @since 4.16.0.0 ) -- Instances of Prelude classes -- | @since 4.18.0.0 deriving instance Eq (f (g a)) => Eq (Compose f g a) -- | @since 4.18.0.0 deriving instance Ord (f (g a)) => Ord (Compose f g a) -- | @since 4.18.0.0 deriving instance Read (f (g a)) => Read (Compose f g a) -- | @since 4.18.0.0 deriving instance Show (f (g a)) => Show (Compose f g a) -- Instances of lifted Prelude classes -- | @since 4.9.0.0 instance (Eq1 f, Eq1 g) => Eq1 (Compose f g) where liftEq :: forall a b. (a -> b -> Bool) -> Compose f g a -> Compose f g b -> Bool liftEq a -> b -> Bool eq (Compose f (g a) x) (Compose f (g b) y) = (g a -> g b -> Bool) -> f (g a) -> f (g b) -> Bool forall a b. (a -> b -> Bool) -> f a -> f b -> Bool forall (f :: * -> *) a b. Eq1 f => (a -> b -> Bool) -> f a -> f b -> Bool liftEq ((a -> b -> Bool) -> g a -> g b -> Bool forall a b. (a -> b -> Bool) -> g a -> g b -> Bool forall (f :: * -> *) a b. Eq1 f => (a -> b -> Bool) -> f a -> f b -> Bool liftEq a -> b -> Bool eq) f (g a) x f (g b) y -- | @since 4.9.0.0 instance (Ord1 f, Ord1 g) => Ord1 (Compose f g) where liftCompare :: forall a b. (a -> b -> Ordering) -> Compose f g a -> Compose f g b -> Ordering liftCompare a -> b -> Ordering comp (Compose f (g a) x) (Compose f (g b) y) = (g a -> g b -> Ordering) -> f (g a) -> f (g b) -> Ordering forall a b. (a -> b -> Ordering) -> f a -> f b -> Ordering forall (f :: * -> *) a b. Ord1 f => (a -> b -> Ordering) -> f a -> f b -> Ordering liftCompare ((a -> b -> Ordering) -> g a -> g b -> Ordering forall a b. (a -> b -> Ordering) -> g a -> g b -> Ordering forall (f :: * -> *) a b. Ord1 f => (a -> b -> Ordering) -> f a -> f b -> Ordering liftCompare a -> b -> Ordering comp) f (g a) x f (g b) y -- | @since 4.9.0.0 instance (Read1 f, Read1 g) => Read1 (Compose f g) where liftReadPrec :: forall a. ReadPrec a -> ReadPrec [a] -> ReadPrec (Compose f g a) liftReadPrec ReadPrec a rp ReadPrec [a] rl = ReadPrec (Compose f g a) -> ReadPrec (Compose f g a) forall a. ReadPrec a -> ReadPrec a readData (ReadPrec (Compose f g a) -> ReadPrec (Compose f g a)) -> ReadPrec (Compose f g a) -> ReadPrec (Compose f g a) forall a b. (a -> b) -> a -> b $ ReadPrec (f (g a)) -> String -> (f (g a) -> Compose f g a) -> ReadPrec (Compose f g a) forall a t. ReadPrec a -> String -> (a -> t) -> ReadPrec t readUnaryWith (ReadPrec (g a) -> ReadPrec [g a] -> ReadPrec (f (g a)) forall a. ReadPrec a -> ReadPrec [a] -> ReadPrec (f a) forall (f :: * -> *) a. Read1 f => ReadPrec a -> ReadPrec [a] -> ReadPrec (f a) liftReadPrec ReadPrec (g a) rp' ReadPrec [g a] rl') String "Compose" f (g a) -> Compose f g a forall {k} {k} (f :: k -> *) (g :: k -> k) (a :: k). f (g a) -> Compose f g a Compose where rp' :: ReadPrec (g a) rp' = ReadPrec a -> ReadPrec [a] -> ReadPrec (g a) forall a. ReadPrec a -> ReadPrec [a] -> ReadPrec (g a) forall (f :: * -> *) a. Read1 f => ReadPrec a -> ReadPrec [a] -> ReadPrec (f a) liftReadPrec ReadPrec a rp ReadPrec [a] rl rl' :: ReadPrec [g a] rl' = ReadPrec a -> ReadPrec [a] -> ReadPrec [g a] forall a. ReadPrec a -> ReadPrec [a] -> ReadPrec [g a] forall (f :: * -> *) a. Read1 f => ReadPrec a -> ReadPrec [a] -> ReadPrec [f a] liftReadListPrec ReadPrec a rp ReadPrec [a] rl liftReadListPrec :: forall a. ReadPrec a -> ReadPrec [a] -> ReadPrec [Compose f g a] liftReadListPrec = ReadPrec a -> ReadPrec [a] -> ReadPrec [Compose f g a] forall (f :: * -> *) a. Read1 f => ReadPrec a -> ReadPrec [a] -> ReadPrec [f a] liftReadListPrecDefault liftReadList :: forall a. (Int -> ReadS a) -> ReadS [a] -> ReadS [Compose f g a] liftReadList = (Int -> ReadS a) -> ReadS [a] -> ReadS [Compose f g a] forall (f :: * -> *) a. Read1 f => (Int -> ReadS a) -> ReadS [a] -> ReadS [f a] liftReadListDefault -- | @since 4.9.0.0 instance (Show1 f, Show1 g) => Show1 (Compose f g) where liftShowsPrec :: forall a. (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Compose f g a -> ShowS liftShowsPrec Int -> a -> ShowS sp [a] -> ShowS sl Int d (Compose f (g a) x) = (Int -> f (g a) -> ShowS) -> String -> Int -> f (g a) -> ShowS forall a. (Int -> a -> ShowS) -> String -> Int -> a -> ShowS showsUnaryWith ((Int -> g a -> ShowS) -> ([g a] -> ShowS) -> Int -> f (g a) -> ShowS forall a. (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> f a -> ShowS forall (f :: * -> *) a. Show1 f => (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> f a -> ShowS liftShowsPrec Int -> g a -> ShowS sp' [g a] -> ShowS sl') String "Compose" Int d f (g a) x where sp' :: Int -> g a -> ShowS sp' = (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> g a -> ShowS forall a. (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> g a -> ShowS forall (f :: * -> *) a. Show1 f => (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> f a -> ShowS liftShowsPrec Int -> a -> ShowS sp [a] -> ShowS sl sl' :: [g a] -> ShowS sl' = (Int -> a -> ShowS) -> ([a] -> ShowS) -> [g a] -> ShowS forall a. (Int -> a -> ShowS) -> ([a] -> ShowS) -> [g a] -> ShowS forall (f :: * -> *) a. Show1 f => (Int -> a -> ShowS) -> ([a] -> ShowS) -> [f a] -> ShowS liftShowList Int -> a -> ShowS sp [a] -> ShowS sl -- Functor instances -- | @since 4.9.0.0 instance (Functor f, Functor g) => Functor (Compose f g) where fmap :: forall a b. (a -> b) -> Compose f g a -> Compose f g b fmap a -> b f (Compose f (g a) x) = f (g b) -> Compose f g b forall {k} {k} (f :: k -> *) (g :: k -> k) (a :: k). f (g a) -> Compose f g a Compose ((g a -> g b) -> f (g a) -> f (g b) forall a b. (a -> b) -> f a -> f b forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b fmap ((a -> b) -> g a -> g b forall a b. (a -> b) -> g a -> g b forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b fmap a -> b f) f (g a) x) a a <$ :: forall a b. a -> Compose f g b -> Compose f g a <$ (Compose f (g b) x) = f (g a) -> Compose f g a forall {k} {k} (f :: k -> *) (g :: k -> k) (a :: k). f (g a) -> Compose f g a Compose ((g b -> g a) -> f (g b) -> f (g a) forall a b. (a -> b) -> f a -> f b forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b fmap (a a a -> g b -> g a forall a b. a -> g b -> g a forall (f :: * -> *) a b. Functor f => a -> f b -> f a <$) f (g b) x) -- | @since 4.9.0.0 instance (Foldable f, Foldable g) => Foldable (Compose f g) where foldMap :: forall m a. Monoid m => (a -> m) -> Compose f g a -> m foldMap a -> m f (Compose f (g a) t) = (g a -> m) -> f (g a) -> m forall m a. Monoid m => (a -> m) -> f a -> m forall (t :: * -> *) m a. (Foldable t, Monoid m) => (a -> m) -> t a -> m foldMap ((a -> m) -> g a -> m forall m a. Monoid m => (a -> m) -> g a -> m forall (t :: * -> *) m a. (Foldable t, Monoid m) => (a -> m) -> t a -> m foldMap a -> m f) f (g a) t -- | @since 4.9.0.0 instance (Traversable f, Traversable g) => Traversable (Compose f g) where traverse :: forall (f :: * -> *) a b. Applicative f => (a -> f b) -> Compose f g a -> f (Compose f g b) traverse a -> f b f (Compose f (g a) t) = f (g b) -> Compose f g b forall {k} {k} (f :: k -> *) (g :: k -> k) (a :: k). f (g a) -> Compose f g a Compose (f (g b) -> Compose f g b) -> f (f (g b)) -> f (Compose f g b) forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b <$> (g a -> f (g b)) -> f (g a) -> f (f (g b)) forall (t :: * -> *) (f :: * -> *) a b. (Traversable t, Applicative f) => (a -> f b) -> t a -> f (t b) forall (f :: * -> *) a b. Applicative f => (a -> f b) -> f a -> f (f b) traverse ((a -> f b) -> g a -> f (g b) forall (t :: * -> *) (f :: * -> *) a b. (Traversable t, Applicative f) => (a -> f b) -> t a -> f (t b) forall (f :: * -> *) a b. Applicative f => (a -> f b) -> g a -> f (g b) traverse a -> f b f) f (g a) t -- | @since 4.9.0.0 instance (Applicative f, Applicative g) => Applicative (Compose f g) where pure :: forall a. a -> Compose f g a pure a x = f (g a) -> Compose f g a forall {k} {k} (f :: k -> *) (g :: k -> k) (a :: k). f (g a) -> Compose f g a Compose (g a -> f (g a) forall a. a -> f a forall (f :: * -> *) a. Applicative f => a -> f a pure (a -> g a forall a. a -> g a forall (f :: * -> *) a. Applicative f => a -> f a pure a x)) Compose f (g (a -> b)) f <*> :: forall a b. Compose f g (a -> b) -> Compose f g a -> Compose f g b <*> Compose f (g a) x = f (g b) -> Compose f g b forall {k} {k} (f :: k -> *) (g :: k -> k) (a :: k). f (g a) -> Compose f g a Compose ((g (a -> b) -> g a -> g b) -> f (g (a -> b)) -> f (g a) -> f (g b) forall a b c. (a -> b -> c) -> f a -> f b -> f c forall (f :: * -> *) a b c. Applicative f => (a -> b -> c) -> f a -> f b -> f c liftA2 g (a -> b) -> g a -> g b forall a b. g (a -> b) -> g a -> g b forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b (<*>) f (g (a -> b)) f f (g a) x) liftA2 :: forall a b c. (a -> b -> c) -> Compose f g a -> Compose f g b -> Compose f g c liftA2 a -> b -> c f (Compose f (g a) x) (Compose f (g b) y) = f (g c) -> Compose f g c forall {k} {k} (f :: k -> *) (g :: k -> k) (a :: k). f (g a) -> Compose f g a Compose ((g a -> g b -> g c) -> f (g a) -> f (g b) -> f (g c) forall a b c. (a -> b -> c) -> f a -> f b -> f c forall (f :: * -> *) a b c. Applicative f => (a -> b -> c) -> f a -> f b -> f c liftA2 ((a -> b -> c) -> g a -> g b -> g c forall a b c. (a -> b -> c) -> g a -> g b -> g c forall (f :: * -> *) a b c. Applicative f => (a -> b -> c) -> f a -> f b -> f c liftA2 a -> b -> c f) f (g a) x f (g b) y) -- | @since 4.9.0.0 instance (Alternative f, Applicative g) => Alternative (Compose f g) where empty :: forall a. Compose f g a empty = f (g a) -> Compose f g a forall {k} {k} (f :: k -> *) (g :: k -> k) (a :: k). f (g a) -> Compose f g a Compose f (g a) forall a. f a forall (f :: * -> *) a. Alternative f => f a empty <|> :: forall a. Compose f g a -> Compose f g a -> Compose f g a (<|>) = (f (g a) -> f (g a) -> f (g a)) -> Compose f g a -> Compose f g a -> Compose f g a forall a b. Coercible a b => a -> b coerce (f (g a) -> f (g a) -> f (g a) forall a. f a -> f a -> f a forall (f :: * -> *) a. Alternative f => f a -> f a -> f a (<|>) :: f (g a) -> f (g a) -> f (g a)) :: forall a . Compose f g a -> Compose f g a -> Compose f g a -- | The deduction (via generativity) that if @g x :~: g y@ then @x :~: y@. -- -- @since 4.14.0.0 instance (TestEquality f) => TestEquality (Compose f g) where testEquality :: forall (a :: k) (b :: k). Compose f g a -> Compose f g b -> Maybe (a :~: b) testEquality (Compose f (g a) x) (Compose f (g b) y) = case f (g a) -> f (g b) -> Maybe (g a :~: g b) forall (a :: k) (b :: k). f a -> f b -> Maybe (a :~: b) forall {k} (f :: k -> *) (a :: k) (b :: k). TestEquality f => f a -> f b -> Maybe (a :~: b) testEquality f (g a) x f (g b) y of -- :: Maybe (g x :~: g y) Just g a :~: g b Refl -> (a :~: b) -> Maybe (a :~: b) forall a. a -> Maybe a Just a :~: a a :~: b forall {k} (a :: k). a :~: a Refl -- :: Maybe (x :~: y) Maybe (g a :~: g b) Nothing -> Maybe (a :~: b) forall a. Maybe a Nothing