Data.Functor.Compose

Copyright (c) Ross Paterson 2010
License BSD-style (see the file LICENSE)
Maintainer libraries@haskell.org
Stability stable
Portability portable
Safe Haskell Trustworthy
Language Haskell2010

Description

Composition of functors.

Since: base-4.9.0.0

newtype Compose (f :: k -> Type) (g :: k1 -> k) (a :: k1) infixr 9 Source

Right-to-left composition of functors. The composition of applicative functors is always applicative, but the composition of monads is not always a monad.

Examples
Expand
>>> fmap (subtract 1) (Compose (Just [1, 2, 3]))
Compose (Just [0,1,2])

>>> Compose (Just [1, 2, 3]) <> Compose Nothing
Compose (Just [1,2,3])

>>> Compose (Just [(++ "World"), (++ "Haskell")]) <*> Compose (Just ["Hello, "])
Compose (Just ["Hello, World","Hello, Haskell"])

Constructors

Compose infixr 9

Fields

Instances
Instances details
TestEquality f => TestEquality (Compose f g :: k2 -> Type) Source

The deduction (via generativity) that if g x :~: g y then x :~: y.

Since: base-4.14.0.0
Instance details

Defined in Data.Functor.Compose

Methods

testEquality :: forall (a :: k2) (b :: k2). Compose f g a -> Compose f g b -> Maybe (a :~: b) Source

Functor f => Generic1 (Compose f g :: k -> Type) Source
Instance details

Defined in Data.Functor.Compose

Associated Types

type Rep1 (Compose f g :: k -> Type)

Since: base-4.9.0.0
Instance details

Defined in Data.Functor.Compose

type Rep1 (Compose f g :: k -> Type) = D1 ('MetaData "Compose" "Data.Functor.Compose" "base-4.21.0.0-8e62" 'True) (C1 ('MetaCons "Compose" 'PrefixI 'True) (S1 ('MetaSel ('Just "getCompose") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (f :.: Rec1 g)))

Methods

from1 :: forall (a :: k). Compose f g a -> Rep1 (Compose f g) a Source

to1 :: forall (a :: k). Rep1 (Compose f g) a -> Compose f g a Source

(Foldable1 f, Foldable1 g) => Foldable1 (Compose f g) Source

Since: base-4.18.0.0
Instance details

Defined in Data.Foldable1

Methods

fold1 :: Semigroup m => Compose f g m -> m Source

foldMap1 :: Semigroup m => (a -> m) -> Compose f g a -> m Source

foldMap1' :: Semigroup m => (a -> m) -> Compose f g a -> m Source

toNonEmpty :: Compose f g a -> NonEmpty a Source

maximum :: Ord a => Compose f g a -> a Source

minimum :: Ord a => Compose f g a -> a Source

head :: Compose f g a -> a Source

last :: Compose f g a -> a Source

foldrMap1 :: (a -> b) -> (a -> b -> b) -> Compose f g a -> b Source

foldlMap1' :: (a -> b) -> (b -> a -> b) -> Compose f g a -> b Source

foldlMap1 :: (a -> b) -> (b -> a -> b) -> Compose f g a -> b Source

foldrMap1' :: (a -> b) -> (a -> b -> b) -> Compose f g a -> b Source

(Eq1 f, Eq1 g) => Eq1 (Compose f g) Source

Since: base-4.9.0.0
Instance details

Defined in Data.Functor.Compose

Methods

liftEq :: (a -> b -> Bool) -> Compose f g a -> Compose f g b -> Bool Source

(Ord1 f, Ord1 g) => Ord1 (Compose f g) Source

Since: base-4.9.0.0
Instance details

Defined in Data.Functor.Compose

Methods

liftCompare :: (a -> b -> Ordering) -> Compose f g a -> Compose f g b -> Ordering Source

(Read1 f, Read1 g) => Read1 (Compose f g) Source

Since: base-4.9.0.0
Instance details

Defined in Data.Functor.Compose

Methods

liftReadsPrec :: (Int -> ReadS a) -> ReadS [a] -> Int -> ReadS (Compose f g a) Source

liftReadList :: (Int -> ReadS a) -> ReadS [a] -> ReadS [Compose f g a] Source

liftReadPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec (Compose f g a) Source

liftReadListPrec :: ReadPrec a -> ReadPrec [a] -> ReadPrec [Compose f g a] Source

(Show1 f, Show1 g) => Show1 (Compose f g) Source

Since: base-4.9.0.0
Instance details

Defined in Data.Functor.Compose

Methods

liftShowsPrec :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> Int -> Compose f g a -> ShowS Source

liftShowList :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> [Compose f g a] -> ShowS Source

(Functor f, Contravariant g) => Contravariant (Compose f g) Source
Instance details

Defined in Data.Functor.Contravariant

Methods

contramap :: (a' -> a) -> Compose f g a -> Compose f g a' Source

(>$) :: b -> Compose f g b -> Compose f g a Source

(Alternative f, Applicative g) => Alternative (Compose f g) Source

Since: base-4.9.0.0
Instance details

Defined in Data.Functor.Compose

Methods

empty :: Compose f g a Source

(<|>) :: Compose f g a -> Compose f g a -> Compose f g a Source

some :: Compose f g a -> Compose f g [a] Source

many :: Compose f g a -> Compose f g [a] Source

(Applicative f, Applicative g) => Applicative (Compose f g) Source

Since: base-4.9.0.0
Instance details

Defined in Data.Functor.Compose

Methods

pure :: a -> Compose f g a Source

(<*>) :: Compose f g (a -> b) -> Compose f g a -> Compose f g b Source

liftA2 :: (a -> b -> c) -> Compose f g a -> Compose f g b -> Compose f g c Source

(*>) :: Compose f g a -> Compose f g b -> Compose f g b Source

(<*) :: Compose f g a -> Compose f g b -> Compose f g a Source

(Functor f, Functor g) => Functor (Compose f g) Source

Since: base-4.9.0.0
Instance details

Defined in Data.Functor.Compose

Methods

fmap :: (a -> b) -> Compose f g a -> Compose f g b Source

(<$) :: a -> Compose f g b -> Compose f g a Source

(Foldable f, Foldable g) => Foldable (Compose f g) Source

Since: base-4.9.0.0
Instance details

Defined in Data.Functor.Compose

Methods

fold :: Monoid m => Compose f g m -> m Source

foldMap :: Monoid m => (a -> m) -> Compose f g a -> m Source

foldMap' :: Monoid m => (a -> m) -> Compose f g a -> m Source

foldr :: (a -> b -> b) -> b -> Compose f g a -> b Source

foldr' :: (a -> b -> b) -> b -> Compose f g a -> b Source

foldl :: (b -> a -> b) -> b -> Compose f g a -> b Source

foldl' :: (b -> a -> b) -> b -> Compose f g a -> b Source

foldr1 :: (a -> a -> a) -> Compose f g a -> a Source

foldl1 :: (a -> a -> a) -> Compose f g a -> a Source

toList :: Compose f g a -> [a] Source

null :: Compose f g a -> Bool Source

length :: Compose f g a -> Int Source

elem :: Eq a => a -> Compose f g a -> Bool Source

maximum :: Ord a => Compose f g a -> a Source

minimum :: Ord a => Compose f g a -> a Source

sum :: Num a => Compose f g a -> a Source

product :: Num a => Compose f g a -> a Source

(Traversable f, Traversable g) => Traversable (Compose f g) Source

Since: base-4.9.0.0
Instance details

Defined in Data.Functor.Compose

Methods

traverse :: Applicative f0 => (a -> f0 b) -> Compose f g a -> f0 (Compose f g b) Source

sequenceA :: Applicative f0 => Compose f g (f0 a) -> f0 (Compose f g a) Source

mapM :: Monad m => (a -> m b) -> Compose f g a -> m (Compose f g b) Source

sequence :: Monad m => Compose f g (m a) -> m (Compose f g a) Source

Monoid (f (g a)) => Monoid (Compose f g a) Source

Since: base-4.16.0.0
Instance details

Defined in Data.Functor.Compose

Methods

mempty :: Compose f g a Source

mappend :: Compose f g a -> Compose f g a -> Compose f g a Source

mconcat :: [Compose f g a] -> Compose f g a Source

Semigroup (f (g a)) => Semigroup (Compose f g a) Source

Since: base-4.16.0.0
Instance details

Defined in Data.Functor.Compose

Methods

(<>) :: Compose f g a -> Compose f g a -> Compose f g a Source

sconcat :: NonEmpty (Compose f g a) -> Compose f g a Source

stimes :: Integral b => b -> Compose f g a -> Compose f g a Source

(Typeable a, Typeable f, Typeable g, Typeable k1, Typeable k2, Data (f (g a))) => Data (Compose f g a) Source

Since: base-4.9.0.0
Instance details

Defined in Data.Functor.Compose

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g0. g0 -> c g0) -> Compose f g a -> c (Compose f g a) Source

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Compose f g a) Source

toConstr :: Compose f g a -> Constr Source

dataTypeOf :: Compose f g a -> DataType Source

dataCast1 :: Typeable t => (forall d. Data d => c (t d)) -> Maybe (c (Compose f g a)) Source

dataCast2 :: Typeable t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Compose f g a)) Source

gmapT :: (forall b. Data b => b -> b) -> Compose f g a -> Compose f g a Source

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Compose f g a -> r Source

gmapQr :: forall r r'. (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Compose f g a -> r Source

gmapQ :: (forall d. Data d => d -> u) -> Compose f g a -> [u] Source

gmapQi :: Int -> (forall d. Data d => d -> u) -> Compose f g a -> u Source

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Compose f g a -> m (Compose f g a) Source

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Compose f g a -> m (Compose f g a) Source

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Compose f g a -> m (Compose f g a) Source

Bounded (f (g a)) => Bounded (Compose f g a) Source

Since: base-4.19.0.0
Instance details

Defined in Data.Functor.Compose

Methods

minBound :: Compose f g a Source

maxBound :: Compose f g a Source

Enum (f (g a)) => Enum (Compose f g a) Source

Since: base-4.19.0.0
Instance details

Defined in Data.Functor.Compose

Methods

succ :: Compose f g a -> Compose f g a Source

pred :: Compose f g a -> Compose f g a Source

toEnum :: Int -> Compose f g a Source

fromEnum :: Compose f g a -> Int Source

enumFrom :: Compose f g a -> [Compose f g a] Source

enumFromThen :: Compose f g a -> Compose f g a -> [Compose f g a] Source

enumFromTo :: Compose f g a -> Compose f g a -> [Compose f g a] Source

enumFromThenTo :: Compose f g a -> Compose f g a -> Compose f g a -> [Compose f g a] Source

Floating (f (g a)) => Floating (Compose f g a) Source

Since: base-4.20.0.0
Instance details

Defined in Data.Functor.Compose

Methods

pi :: Compose f g a Source

exp :: Compose f g a -> Compose f g a Source

log :: Compose f g a -> Compose f g a Source

sqrt :: Compose f g a -> Compose f g a Source

(**) :: Compose f g a -> Compose f g a -> Compose f g a Source

logBase :: Compose f g a -> Compose f g a -> Compose f g a Source

sin :: Compose f g a -> Compose f g a Source

cos :: Compose f g a -> Compose f g a Source

tan :: Compose f g a -> Compose f g a Source

asin :: Compose f g a -> Compose f g a Source

acos :: Compose f g a -> Compose f g a Source

atan :: Compose f g a -> Compose f g a Source

sinh :: Compose f g a -> Compose f g a Source

cosh :: Compose f g a -> Compose f g a Source

tanh :: Compose f g a -> Compose f g a Source

asinh :: Compose f g a -> Compose f g a Source

acosh :: Compose f g a -> Compose f g a Source

atanh :: Compose f g a -> Compose f g a Source

log1p :: Compose f g a -> Compose f g a Source

expm1 :: Compose f g a -> Compose f g a Source

log1pexp :: Compose f g a -> Compose f g a Source

log1mexp :: Compose f g a -> Compose f g a Source

RealFloat (f (g a)) => RealFloat (Compose f g a) Source

Since: base-4.20.0.0
Instance details

Defined in Data.Functor.Compose

Methods

floatRadix :: Compose f g a -> Integer Source

floatDigits :: Compose f g a -> Int Source

floatRange :: Compose f g a -> (Int, Int) Source

decodeFloat :: Compose f g a -> (Integer, Int) Source

encodeFloat :: Integer -> Int -> Compose f g a Source

exponent :: Compose f g a -> Int Source

significand :: Compose f g a -> Compose f g a Source

scaleFloat :: Int -> Compose f g a -> Compose f g a Source

isNaN :: Compose f g a -> Bool Source

isInfinite :: Compose f g a -> Bool Source

isDenormalized :: Compose f g a -> Bool Source

isNegativeZero :: Compose f g a -> Bool Source

isIEEE :: Compose f g a -> Bool Source

atan2 :: Compose f g a -> Compose f g a -> Compose f g a Source

Generic (Compose f g a) Source
Instance details

Defined in Data.Functor.Compose

Associated Types

type Rep (Compose f g a)

Since: base-4.9.0.0
Instance details

Defined in Data.Functor.Compose

type Rep (Compose f g a) = D1 ('MetaData "Compose" "Data.Functor.Compose" "base-4.21.0.0-8e62" 'True) (C1 ('MetaCons "Compose" 'PrefixI 'True) (S1 ('MetaSel ('Just "getCompose") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (f (g a)))))

Methods

from :: Compose f g a -> Rep (Compose f g a) x Source

to :: Rep (Compose f g a) x -> Compose f g a Source

Num (f (g a)) => Num (Compose f g a) Source

Since: base-4.19.0.0
Instance details

Defined in Data.Functor.Compose

Methods

(+) :: Compose f g a -> Compose f g a -> Compose f g a Source

(-) :: Compose f g a -> Compose f g a -> Compose f g a Source

(*) :: Compose f g a -> Compose f g a -> Compose f g a Source

negate :: Compose f g a -> Compose f g a Source

abs :: Compose f g a -> Compose f g a Source

signum :: Compose f g a -> Compose f g a Source

fromInteger :: Integer -> Compose f g a Source

Read (f (g a)) => Read (Compose f g a) Source

Since: base-4.18.0.0
Instance details

Defined in Data.Functor.Compose

Methods

readsPrec :: Int -> ReadS (Compose f g a) Source

readList :: ReadS [Compose f g a] Source

readPrec :: ReadPrec (Compose f g a) Source

readListPrec :: ReadPrec [Compose f g a] Source

Fractional (f (g a)) => Fractional (Compose f g a) Source

Since: base-4.20.0.0
Instance details

Defined in Data.Functor.Compose

Methods

(/) :: Compose f g a -> Compose f g a -> Compose f g a Source

recip :: Compose f g a -> Compose f g a Source

fromRational :: Rational -> Compose f g a Source

Integral (f (g a)) => Integral (Compose f g a) Source

Since: base-4.19.0.0
Instance details

Defined in Data.Functor.Compose

Methods

quot :: Compose f g a -> Compose f g a -> Compose f g a Source

rem :: Compose f g a -> Compose f g a -> Compose f g a Source

div :: Compose f g a -> Compose f g a -> Compose f g a Source

mod :: Compose f g a -> Compose f g a -> Compose f g a Source

quotRem :: Compose f g a -> Compose f g a -> (Compose f g a, Compose f g a) Source

divMod :: Compose f g a -> Compose f g a -> (Compose f g a, Compose f g a) Source

toInteger :: Compose f g a -> Integer Source

Real (f (g a)) => Real (Compose f g a) Source

Since: base-4.19.0.0
Instance details

Defined in Data.Functor.Compose

Methods

toRational :: Compose f g a -> Rational Source

RealFrac (f (g a)) => RealFrac (Compose f g a) Source

Since: base-4.20.0.0
Instance details

Defined in Data.Functor.Compose

Methods

properFraction :: Integral b => Compose f g a -> (b, Compose f g a) Source

truncate :: Integral b => Compose f g a -> b Source

round :: Integral b => Compose f g a -> b Source

ceiling :: Integral b => Compose f g a -> b Source

floor :: Integral b => Compose f g a -> b Source

Show (f (g a)) => Show (Compose f g a) Source

Since: base-4.18.0.0
Instance details

Defined in Data.Functor.Compose

Methods

showsPrec :: Int -> Compose f g a -> ShowS Source

show :: Compose f g a -> String Source

showList :: [Compose f g a] -> ShowS Source

Eq (f (g a)) => Eq (Compose f g a) Source

Since: base-4.18.0.0
Instance details

Defined in Data.Functor.Compose

Methods

(==) :: Compose f g a -> Compose f g a -> Bool Source

(/=) :: Compose f g a -> Compose f g a -> Bool Source

Ord (f (g a)) => Ord (Compose f g a) Source

Since: base-4.18.0.0
Instance details

Defined in Data.Functor.Compose

Methods

compare :: Compose f g a -> Compose f g a -> Ordering Source

(<) :: Compose f g a -> Compose f g a -> Bool Source

(<=) :: Compose f g a -> Compose f g a -> Bool Source

(>) :: Compose f g a -> Compose f g a -> Bool Source

(>=) :: Compose f g a -> Compose f g a -> Bool Source

max :: Compose f g a -> Compose f g a -> Compose f g a Source

min :: Compose f g a -> Compose f g a -> Compose f g a Source

type Rep1 (Compose f g :: k -> Type) Source

Since: base-4.9.0.0
Instance details

Defined in Data.Functor.Compose

type Rep1 (Compose f g :: k -> Type) = D1 ('MetaData "Compose" "Data.Functor.Compose" "base-4.21.0.0-8e62" 'True) (C1 ('MetaCons "Compose" 'PrefixI 'True) (S1 ('MetaSel ('Just "getCompose") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (f :.: Rec1 g)))
type Rep (Compose f g a) Source

Since: base-4.9.0.0
Instance details

Defined in Data.Functor.Compose

type Rep (Compose f g a) = D1 ('MetaData "Compose" "Data.Functor.Compose" "base-4.21.0.0-8e62" 'True) (C1 ('MetaCons "Compose" 'PrefixI 'True) (S1 ('MetaSel ('Just "getCompose") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 (f (g a)))))

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Licensed under a BSD-style license (see top of the page).
https://downloads.haskell.org/~ghc/9.12.1/docs/libraries/base-4.21.0.0-8e62/Data-Functor-Compose.html