Data.Functor.Linear

The data functor hierarchy

This module defines the data functor library. Unlike in the case of non-linear, unrestricted, functors, there is a split between data functors, which represent containers, and control functors which represent effects. Please read this blog post. For more details, see Control.Functor.Linear.

• Linear data functors should be thought of as containers of data.
• Linear data applicative functors should be thought of as containers that can be zipped.
• Linear data traversible functors should be thought of as containers which store a finite number of values.

Data Functor Hierarchy

class Functor f where

Linear Data Functors should be thought of as containers holding values of type a over which you are able to apply a linear function of type a %1-> b on each value of type a in the functor and consume a given functor of type f a.

Methods

fmap :: (a %1 -> b) -> f a %1 -> f b

Instances

Functor []

Defined in Data.Functor.Linear.Internal.Functor

Methods

fmap :: (a %1 -> b) -> [a] %1 -> [b]

Functor Maybe

Defined in Data.Functor.Linear.Internal.Functor

Methods

fmap :: (a %1 -> b) -> Maybe a %1 -> Maybe b

Functor Identity

Defined in Data.Functor.Linear.Internal.Functor

Methods

fmap :: (a %1 -> b) -> Identity a %1 -> Identity b

Functor Ur

Defined in Data.Unrestricted.Internal.Instances

Methods

fmap :: (a %1 -> b) -> Ur a %1 -> Ur b

Functor IO

Defined in System.IO.Linear

Methods

fmap :: (a %1 -> b) -> IO a %1 -> IO b

Functor RIO

Defined in System.IO.Resource

Methods

fmap :: (a %1 -> b) -> RIO a %1 -> RIO b

Functor Array

Defined in Data.Array.Polarized.Pull.Internal

Methods

fmap :: (a %1 -> b) -> Array a %1 -> Array b

Functor Array

Defined in Data.Array.Mutable.Linear

Methods

fmap :: (a %1 -> b) -> Array a %1 -> Array b

Functor Vector

Defined in Data.Vector.Mutable.Linear

Methods

fmap :: (a %1 -> b) -> Vector a %1 -> Vector b

Functor Array

Defined in Data.Array.Polarized.Push

Methods

fmap :: (a %1 -> b) -> Array a %1 -> Array b

Functor (Either e)

Defined in Data.Functor.Linear.Internal.Functor

Methods

fmap :: (a %1 -> b) -> Either e a %1 -> Either e b

Functor ((,) a)

Defined in Data.Functor.Linear.Internal.Functor

Methods

fmap :: (a0 %1 -> b) -> (a, a0) %1 -> (a, b)

Functor m => Functor (MaybeT m)

Defined in Data.Functor.Linear.Internal.Functor

Methods

fmap :: (a %1 -> b) -> MaybeT m a %1 -> MaybeT m b

Functor f => Functor (Data f)

Defined in Control.Functor.Linear.Internal.Instances

Methods

fmap :: (a %1 -> b) -> Data f a %1 -> Data f b

Functor (V n)

Defined in Data.V.Linear.Internal.Instances

Methods

fmap :: (a %1 -> b) -> V n a %1 -> V n b

Functor (Of a)

Defined in Streaming.Internal.Type

Methods

fmap :: (a0 %1 -> b) -> Of a a0 %1 -> Of a b

Functor (HashMap k)

Defined in Data.HashMap.Mutable.Linear

Methods

fmap :: (a %1 -> b) -> HashMap k a %1 -> HashMap k b

Functor (Const x :: Type -> Type)

Defined in Data.Functor.Linear.Internal.Functor

Methods

fmap :: (a %1 -> b) -> Const x a %1 -> Const x b

Functor m => Functor (StateT s m)

Defined in Data.Functor.Linear.Internal.Functor

Methods

fmap :: (a %1 -> b) -> StateT s m a %1 -> StateT s m b

Functor m => Functor (ReaderT r m)

Defined in Data.Functor.Linear.Internal.Functor

Methods

fmap :: (a %1 -> b) -> ReaderT r m a %1 -> ReaderT r m b

Functor m => Functor (ExceptT e m)

Defined in Data.Functor.Linear.Internal.Functor

Methods

fmap :: (a %1 -> b) -> ExceptT e m a %1 -> ExceptT e m b

Functor m => Functor (StateT s m)

Defined in Control.Functor.Linear.Internal.State

Methods

fmap :: (a %1 -> b) -> StateT s m a %1 -> StateT s m b

Functor m => Functor (ReaderT r m)

Defined in Control.Functor.Linear.Internal.Reader

Methods

fmap :: (a %1 -> b) -> ReaderT r m a %1 -> ReaderT r m b

(Functor m, Functor f) => Functor (Stream f m)

Defined in Streaming.Internal.Type

Methods

fmap :: (a %1 -> b) -> Stream f m a %1 -> Stream f m b

(Functor f, Functor g) => Functor (Sum f g)

Defined in Data.Functor.Linear.Internal.Functor

Methods

fmap :: (a %1 -> b) -> Sum f g a %1 -> Sum f g b

Functor (ContT r m)

Defined in Data.Functor.Linear.Internal.Functor

Methods

fmap :: (a %1 -> b) -> ContT r m a %1 -> ContT r m b

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

Defined in Data.Functor.Linear.Internal.Functor

Methods

fmap :: (a %1 -> b) -> Compose f g a %1 -> Compose f g b

(<$>) :: Functor f => (a %1 -> b) -> f a %1 -> f b

(<$) :: (Functor f, Consumable b) => a -> f b %1 -> f a

Replace all occurances of b with the given a and consume the functor f b.

void :: (Functor f, Consumable a) => f a %1 -> f ()

Discard a consumable value stored in a data functor.

class Functor f => Applicative f where

Data Applicative-s can be seen as containers which can be zipped together. A prime example of data Applicative are vectors of known length (ZipLists would be, if it were not for the fact that zipping them together drops values, which we are not allowed to do in a linear container).

In fact, an applicative functor is precisely a functor equipped with (pure and) liftA2 :: (a %1-> b %1-> c) -> f a %1-> f b %1-> f c. In the case where f = [], the signature of liftA2 would specialise to that of zipWith.

Intuitively, the type of liftA2 means that Applicatives can be seen as containers whose "number" of elements is known at compile-time. This includes vectors of known length but excludes Maybe, since this may contain either zero or one value. Similarly, ((->) r) forms a Data Applicative, since this is a (possibly infinitary) container indexed by r, while lists do not, since they may contain any number of elements.

Remarks for the mathematically inclined

An Applicative is, as in the restricted case, a lax monoidal endofunctor of the category of linear types. That is, it is equipped with

• a (linear) function () %1-> f ()
• a (linear) natural transformation (f a, f b) %1-> f (a, b)

It is a simple exercise to verify that these are equivalent to the definition of Applicative. Hence that the choice of linearity of the various arrow is indeed natural.

Minimal complete definition

pure, (liftA2 | (<*>))

Methods

pure :: a -> f a

(<*>) :: f (a %1 -> b) %1 -> f a %1 -> f b

liftA2 :: (a %1 -> b %1 -> c) -> f a %1 -> f b %1 -> f c

Instances

Applicative Identity

Defined in Data.Functor.Linear.Internal.Applicative

Methods

pure :: a -> Identity a

(<*>) :: Identity (a %1 -> b) %1 -> Identity a %1 -> Identity b

liftA2 :: (a %1 -> b %1 -> c) -> Identity a %1 -> Identity b %1 -> Identity c

Applicative Ur

Defined in Data.Unrestricted.Internal.Instances

Methods

pure :: a -> Ur a

(<*>) :: Ur (a %1 -> b) %1 -> Ur a %1 -> Ur b

liftA2 :: (a %1 -> b %1 -> c) -> Ur a %1 -> Ur b %1 -> Ur c

Applicative IO

Defined in System.IO.Linear

Methods

pure :: a -> IO a

(<*>) :: IO (a %1 -> b) %1 -> IO a %1 -> IO b

liftA2 :: (a %1 -> b %1 -> c) -> IO a %1 -> IO b %1 -> IO c

Applicative RIO

Defined in System.IO.Resource

Methods

pure :: a -> RIO a

(<*>) :: RIO (a %1 -> b) %1 -> RIO a %1 -> RIO b

liftA2 :: (a %1 -> b %1 -> c) -> RIO a %1 -> RIO b %1 -> RIO c

Monoid a => Applicative ((,) a)

Defined in Data.Functor.Linear.Internal.Applicative

Methods

pure :: a0 -> (a, a0)

(<*>) :: (a, a0 %1 -> b) %1 -> (a, a0) %1 -> (a, b)

liftA2 :: (a0 %1 -> b %1 -> c) -> (a, a0) %1 -> (a, b) %1 -> (a, c)

Applicative f => Applicative (Data f)

Defined in Control.Functor.Linear.Internal.Instances

Methods

pure :: a -> Data f a

(<*>) :: Data f (a %1 -> b) %1 -> Data f a %1 -> Data f b

liftA2 :: (a %1 -> b %1 -> c) -> Data f a %1 -> Data f b %1 -> Data f c

KnownNat n => Applicative (V n)

Defined in Data.V.Linear.Internal.Instances

Methods

pure :: a -> V n a

(<*>) :: V n (a %1 -> b) %1 -> V n a %1 -> V n b

liftA2 :: (a %1 -> b %1 -> c) -> V n a %1 -> V n b %1 -> V n c

Monoid x => Applicative (Const x :: Type -> Type)

Defined in Data.Functor.Linear.Internal.Applicative

Methods

pure :: a -> Const x a

(<*>) :: Const x (a %1 -> b) %1 -> Const x a %1 -> Const x b

liftA2 :: (a %1 -> b %1 -> c) -> Const x a %1 -> Const x b %1 -> Const x c

Applicative m => Applicative (ReaderT r m)

Defined in Data.Functor.Linear.Internal.Applicative

Methods

pure :: a -> ReaderT r m a

(<*>) :: ReaderT r m (a %1 -> b) %1 -> ReaderT r m a %1 -> ReaderT r m b

liftA2 :: (a %1 -> b %1 -> c) -> ReaderT r m a %1 -> ReaderT r m b %1 -> ReaderT r m c

Monad m => Applicative (StateT s m)

Defined in Control.Functor.Linear.Internal.State

Methods

pure :: a -> StateT s m a

(<*>) :: StateT s m (a %1 -> b) %1 -> StateT s m a %1 -> StateT s m b

liftA2 :: (a %1 -> b %1 -> c) -> StateT s m a %1 -> StateT s m b %1 -> StateT s m c

(Applicative m, Dupable r) => Applicative (ReaderT r m)

Defined in Control.Functor.Linear.Internal.Reader

Methods

pure :: a -> ReaderT r m a

(<*>) :: ReaderT r m (a %1 -> b) %1 -> ReaderT r m a %1 -> ReaderT r m b

liftA2 :: (a %1 -> b %1 -> c) -> ReaderT r m a %1 -> ReaderT r m b %1 -> ReaderT r m c

(Functor m, Functor f) => Applicative (Stream f m)

Defined in Streaming.Internal.Type

Methods

pure :: a -> Stream f m a

(<*>) :: Stream f m (a %1 -> b) %1 -> Stream f m a %1 -> Stream f m b

liftA2 :: (a %1 -> b %1 -> c) -> Stream f m a %1 -> Stream f m b %1 -> Stream f m c

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

Defined in Data.Functor.Linear.Internal.Applicative

Methods

pure :: a -> Compose f g a

(<*>) :: Compose f g (a %1 -> b) %1 -> Compose f g a %1 -> Compose f g b

liftA2 :: (a %1 -> b %1 -> c) -> Compose f g a %1 -> Compose f g b %1 -> Compose f g c

newtype Const a (b :: k)

The Const functor.

Constructors

Const

Fields

• getConst :: a

Instances

Strong Either Void (CoKleisli (Const x :: Type -> Type))

Defined in Data.Profunctor.Kleisli.Linear

Methods

first :: CoKleisli (Const x) a b -> CoKleisli (Const x) (Either a c) (Either b c)

second :: CoKleisli (Const x) b c -> CoKleisli (Const x) (Either a b) (Either a c)

Generic1 (Const a :: k -> Type)

Defined in Data.Functor.Const

Associated Types

type Rep1 (Const a) :: k -> Type

Methods

from1 :: forall (a0 :: k0). Const a a0 -> Rep1 (Const a) a0

to1 :: forall (a0 :: k0). Rep1 (Const a) a0 -> Const a a0

Show2 (Const :: Type -> Type -> Type)

Since: base-4.9.0.0

Defined in Data.Functor.Classes

Methods

liftShowsPrec2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> Int -> Const a b -> ShowS

liftShowList2 :: (Int -> a -> ShowS) -> ([a] -> ShowS) -> (Int -> b -> ShowS) -> ([b] -> ShowS) -> [Const a b] -> ShowS

Read2 (Const :: Type -> Type -> Type)

Since: base-4.9.0.0

Defined in Data.Functor.Classes

Methods

liftReadsPrec2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> Int -> ReadS (Const a b)

liftReadList2 :: (Int -> ReadS a) -> ReadS [a] -> (Int -> ReadS b) -> ReadS [b] -> ReadS [Const a b]

liftReadPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec (Const a b)

liftReadListPrec2 :: ReadPrec a -> ReadPrec [a] -> ReadPrec b -> ReadPrec [b] -> ReadPrec [Const a b]

Ord2 (Const :: Type -> Type -> Type)

Since: base-4.9.0.0

Defined in Data.Functor.Classes

Methods

liftCompare2 :: (a -> b -> Ordering) -> (c -> d -> Ordering) -> Const a c -> Const b d -> Ordering

Eq2 (Const :: Type -> Type -> Type)

Since: base-4.9.0.0

Defined in Data.Functor.Classes

Methods

liftEq2 :: (a -> b -> Bool) -> (c -> d -> Bool) -> Const a c -> Const b d -> Bool

Bifunctor (Const :: Type -> Type -> Type)

Since: base-4.8.0.0

Defined in Data.Bifunctor

Methods

bimap :: (a -> b) -> (c -> d) -> Const a c -> Const b d

first :: (a -> b) -> Const a c -> Const b c

second :: (b -> c) -> Const a b -> Const a c

Hashable2 (Const :: Type -> Type -> Type)

Defined in Data.Hashable.Class

Methods

liftHashWithSalt2 :: (Int -> a -> Int) -> (Int -> b -> Int) -> Int -> Const a b -> Int

Functor (Const m :: Type -> Type)

Since: base-2.1

Defined in Data.Functor.Const

Methods

fmap :: (a -> b) -> Const m a -> Const m b

(<$) :: a -> Const m b -> Const m a

Monoid m => Applicative (Const m :: Type -> Type)

Since: base-2.0.1

Defined in Data.Functor.Const

Methods

pure :: a -> Const m a

(<*>) :: Const m (a -> b) -> Const m a -> Const m b

liftA2 :: (a -> b -> c) -> Const m a -> Const m b -> Const m c

(*>) :: Const m a -> Const m b -> Const m b

(<*) :: Const m a -> Const m b -> Const m a

Foldable (Const m :: Type -> Type)

Since: base-4.7.0.0

Defined in Data.Functor.Const

Methods

fold :: Monoid m0 => Const m m0 -> m0

foldMap :: Monoid m0 => (a -> m0) -> Const m a -> m0

foldMap' :: Monoid m0 => (a -> m0) -> Const m a -> m0

foldr :: (a -> b -> b) -> b -> Const m a -> b

foldr' :: (a -> b -> b) -> b -> Const m a -> b

foldl :: (b -> a -> b) -> b -> Const m a -> b

foldl' :: (b -> a -> b) -> b -> Const m a -> b

foldr1 :: (a -> a -> a) -> Const m a -> a

foldl1 :: (a -> a -> a) -> Const m a -> a

toList :: Const m a -> [a]

null :: Const m a -> Bool

length :: Const m a -> Int

elem :: Eq a => a -> Const m a -> Bool

maximum :: Ord a => Const m a -> a

minimum :: Ord a => Const m a -> a

sum :: Num a => Const m a -> a

product :: Num a => Const m a -> a

Traversable (Const m :: Type -> Type)

Since: base-4.7.0.0

Defined in Data.Traversable

Methods

traverse :: Applicative f => (a -> f b) -> Const m a -> f (Const m b)

sequenceA :: Applicative f => Const m (f a) -> f (Const m a)

mapM :: Monad m0 => (a -> m0 b) -> Const m a -> m0 (Const m b)

sequence :: Monad m0 => Const m (m0 a) -> m0 (Const m a)

Show a => Show1 (Const a :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Functor.Classes

Methods

liftShowsPrec :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> Int -> Const a a0 -> ShowS

liftShowList :: (Int -> a0 -> ShowS) -> ([a0] -> ShowS) -> [Const a a0] -> ShowS

Read a => Read1 (Const a :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Functor.Classes

Methods

liftReadsPrec :: (Int -> ReadS a0) -> ReadS [a0] -> Int -> ReadS (Const a a0)

liftReadList :: (Int -> ReadS a0) -> ReadS [a0] -> ReadS [Const a a0]

liftReadPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec (Const a a0)

liftReadListPrec :: ReadPrec a0 -> ReadPrec [a0] -> ReadPrec [Const a a0]

Ord a => Ord1 (Const a :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Functor.Classes

Methods

liftCompare :: (a0 -> b -> Ordering) -> Const a a0 -> Const a b -> Ordering

Eq a => Eq1 (Const a :: Type -> Type)

Since: base-4.9.0.0

Defined in Data.Functor.Classes

Methods

liftEq :: (a0 -> b -> Bool) -> Const a a0 -> Const a b -> Bool

Hashable a => Hashable1 (Const a :: Type -> Type)

Defined in Data.Hashable.Class

Methods

liftHashWithSalt :: (Int -> a0 -> Int) -> Int -> Const a a0 -> Int

Functor (Const x :: Type -> Type)

Defined in Data.Functor.Linear.Internal.Functor

Methods

fmap :: (a %1 -> b) -> Const x a %1 -> Const x b

Monoid x => Applicative (Const x :: Type -> Type)

Defined in Data.Functor.Linear.Internal.Applicative

Methods

pure :: a -> Const x a

(<*>) :: Const x (a %1 -> b) %1 -> Const x a %1 -> Const x b

liftA2 :: (a %1 -> b %1 -> c) -> Const x a %1 -> Const x b %1 -> Const x c

Traversable (Const a :: Type -> Type)

Defined in Data.Functor.Linear.Internal.Traversable

Methods

traverse :: Applicative f => (a0 %1 -> f b) -> Const a a0 %1 -> f (Const a b)

sequence :: Applicative f => Const a (f a0) %1 -> f (Const a a0)

Bounded a => Bounded (Const a b)

Since: base-4.9.0.0

Defined in Data.Functor.Const

Methods

minBound :: Const a b

maxBound :: Const a b

Enum a => Enum (Const a b)

Since: base-4.9.0.0

Defined in Data.Functor.Const

Methods

succ :: Const a b -> Const a b

pred :: Const a b -> Const a b

toEnum :: Int -> Const a b

fromEnum :: Const a b -> Int

enumFrom :: Const a b -> [Const a b]

enumFromThen :: Const a b -> Const a b -> [Const a b]

enumFromTo :: Const a b -> Const a b -> [Const a b]

enumFromThenTo :: Const a b -> Const a b -> Const a b -> [Const a b]

Eq a => Eq (Const a b)

Since: base-4.9.0.0

Defined in Data.Functor.Const

Methods

(==) :: Const a b -> Const a b -> Bool

(/=) :: Const a b -> Const a b -> Bool

Floating a => Floating (Const a b)

Since: base-4.9.0.0

Defined in Data.Functor.Const

Methods

pi :: Const a b

exp :: Const a b -> Const a b

log :: Const a b -> Const a b

sqrt :: Const a b -> Const a b

(**) :: Const a b -> Const a b -> Const a b

logBase :: Const a b -> Const a b -> Const a b

sin :: Const a b -> Const a b

cos :: Const a b -> Const a b

tan :: Const a b -> Const a b

asin :: Const a b -> Const a b

acos :: Const a b -> Const a b

atan :: Const a b -> Const a b

sinh :: Const a b -> Const a b

cosh :: Const a b -> Const a b

tanh :: Const a b -> Const a b

asinh :: Const a b -> Const a b

acosh :: Const a b -> Const a b

atanh :: Const a b -> Const a b

log1p :: Const a b -> Const a b

expm1 :: Const a b -> Const a b

log1pexp :: Const a b -> Const a b

log1mexp :: Const a b -> Const a b

Fractional a => Fractional (Const a b)

Since: base-4.9.0.0

Defined in Data.Functor.Const

Methods

(/) :: Const a b -> Const a b -> Const a b

recip :: Const a b -> Const a b

fromRational :: Rational -> Const a b

Integral a => Integral (Const a b)

Since: base-4.9.0.0

Defined in Data.Functor.Const

Methods

quot :: Const a b -> Const a b -> Const a b

rem :: Const a b -> Const a b -> Const a b

div :: Const a b -> Const a b -> Const a b

mod :: Const a b -> Const a b -> Const a b

quotRem :: Const a b -> Const a b -> (Const a b, Const a b)

divMod :: Const a b -> Const a b -> (Const a b, Const a b)

toInteger :: Const a b -> Integer

Num a => Num (Const a b)

Since: base-4.9.0.0

Defined in Data.Functor.Const

Methods

(+) :: Const a b -> Const a b -> Const a b

(-) :: Const a b -> Const a b -> Const a b

(*) :: Const a b -> Const a b -> Const a b

negate :: Const a b -> Const a b

abs :: Const a b -> Const a b

signum :: Const a b -> Const a b

fromInteger :: Integer -> Const a b

Ord a => Ord (Const a b)

Since: base-4.9.0.0

Defined in Data.Functor.Const

Methods

compare :: Const a b -> Const a b -> Ordering

(<) :: Const a b -> Const a b -> Bool

(<=) :: Const a b -> Const a b -> Bool

(>) :: Const a b -> Const a b -> Bool

(>=) :: Const a b -> Const a b -> Bool

max :: Const a b -> Const a b -> Const a b

min :: Const a b -> Const a b -> Const a b

Read a => Read (Const a b)

This instance would be equivalent to the derived instances of the Const newtype if the getConst field were removed

Since: base-4.8.0.0

Defined in Data.Functor.Const

Methods

readsPrec :: Int -> ReadS (Const a b)

readList :: ReadS [Const a b]

readPrec :: ReadPrec (Const a b)

readListPrec :: ReadPrec [Const a b]

Real a => Real (Const a b)

Since: base-4.9.0.0

Defined in Data.Functor.Const

Methods

toRational :: Const a b -> Rational

RealFloat a => RealFloat (Const a b)

Since: base-4.9.0.0

Defined in Data.Functor.Const

Methods

floatRadix :: Const a b -> Integer

floatDigits :: Const a b -> Int

floatRange :: Const a b -> (Int, Int)

decodeFloat :: Const a b -> (Integer, Int)

encodeFloat :: Integer -> Int -> Const a b

exponent :: Const a b -> Int

significand :: Const a b -> Const a b

scaleFloat :: Int -> Const a b -> Const a b

isNaN :: Const a b -> Bool

isInfinite :: Const a b -> Bool

isDenormalized :: Const a b -> Bool

isNegativeZero :: Const a b -> Bool

isIEEE :: Const a b -> Bool

atan2 :: Const a b -> Const a b -> Const a b

RealFrac a => RealFrac (Const a b)

Since: base-4.9.0.0

Defined in Data.Functor.Const

Methods

properFraction :: Integral b0 => Const a b -> (b0, Const a b)

truncate :: Integral b0 => Const a b -> b0

round :: Integral b0 => Const a b -> b0

ceiling :: Integral b0 => Const a b -> b0

floor :: Integral b0 => Const a b -> b0

Show a => Show (Const a b)

This instance would be equivalent to the derived instances of the Const newtype if the getConst field were removed

Since: base-4.8.0.0

Defined in Data.Functor.Const

Methods

showsPrec :: Int -> Const a b -> ShowS

show :: Const a b -> String

showList :: [Const a b] -> ShowS

Ix a => Ix (Const a b)

Since: base-4.9.0.0

Defined in Data.Functor.Const

Methods

range :: (Const a b, Const a b) -> [Const a b]

index :: (Const a b, Const a b) -> Const a b -> Int

unsafeIndex :: (Const a b, Const a b) -> Const a b -> Int

inRange :: (Const a b, Const a b) -> Const a b -> Bool

rangeSize :: (Const a b, Const a b) -> Int

unsafeRangeSize :: (Const a b, Const a b) -> Int

IsString a => IsString (Const a b)

Since: base-4.9.0.0

Defined in Data.String

Methods

fromString :: String -> Const a b

Generic (Const a b)

Defined in Data.Functor.Const

Associated Types

type Rep (Const a b) :: Type -> Type

Methods

from :: Const a b -> Rep (Const a b) x

to :: Rep (Const a b) x -> Const a b

Semigroup a => Semigroup (Const a b)

Since: base-4.9.0.0

Defined in Data.Functor.Const

Methods

(<>) :: Const a b -> Const a b -> Const a b

sconcat :: NonEmpty (Const a b) -> Const a b

stimes :: Integral b0 => b0 -> Const a b -> Const a b

Monoid a => Monoid (Const a b)

Since: base-4.9.0.0

Defined in Data.Functor.Const

Methods

mempty :: Const a b

mappend :: Const a b -> Const a b -> Const a b

mconcat :: [Const a b] -> Const a b

Storable a => Storable (Const a b)

Since: base-4.9.0.0

Defined in Data.Functor.Const

Methods

sizeOf :: Const a b -> Int

alignment :: Const a b -> Int

peekElemOff :: Ptr (Const a b) -> Int -> IO (Const a b)

pokeElemOff :: Ptr (Const a b) -> Int -> Const a b -> IO ()

peekByteOff :: Ptr b0 -> Int -> IO (Const a b)

pokeByteOff :: Ptr b0 -> Int -> Const a b -> IO ()

peek :: Ptr (Const a b) -> IO (Const a b)

poke :: Ptr (Const a b) -> Const a b -> IO ()

FiniteBits a => FiniteBits (Const a b)

Since: base-4.9.0.0

Defined in Data.Functor.Const

Methods

finiteBitSize :: Const a b -> Int

countLeadingZeros :: Const a b -> Int

countTrailingZeros :: Const a b -> Int

Bits a => Bits (Const a b)

Since: base-4.9.0.0

Defined in Data.Functor.Const

Methods

(.&.) :: Const a b -> Const a b -> Const a b

(.|.) :: Const a b -> Const a b -> Const a b

xor :: Const a b -> Const a b -> Const a b

complement :: Const a b -> Const a b

shift :: Const a b -> Int -> Const a b

rotate :: Const a b -> Int -> Const a b

zeroBits :: Const a b

bit :: Int -> Const a b

setBit :: Const a b -> Int -> Const a b

clearBit :: Const a b -> Int -> Const a b

complementBit :: Const a b -> Int -> Const a b

testBit :: Const a b -> Int -> Bool

bitSizeMaybe :: Const a b -> Maybe Int

bitSize :: Const a b -> Int

isSigned :: Const a b -> Bool

shiftL :: Const a b -> Int -> Const a b

unsafeShiftL :: Const a b -> Int -> Const a b

shiftR :: Const a b -> Int -> Const a b

unsafeShiftR :: Const a b -> Int -> Const a b

rotateL :: Const a b -> Int -> Const a b

rotateR :: Const a b -> Int -> Const a b

popCount :: Const a b -> Int

Hashable a => Hashable (Const a b)

Defined in Data.Hashable.Class

Methods

hashWithSalt :: Int -> Const a b -> Int

hash :: Const a b -> Int

type Rep1 (Const a :: k -> Type)

Since: base-4.9.0.0

Defined in Data.Functor.Const

type Rep1 (Const a :: k -> Type) = D1 ('MetaData "Const" "Data.Functor.Const" "base" 'True) (C1 ('MetaCons "Const" 'PrefixI 'True) (S1 ('MetaSel ('Just "getConst") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

type Rep (Const a b)

Since: base-4.9.0.0

Defined in Data.Functor.Const

type Rep (Const a b) = D1 ('MetaData "Const" "Data.Functor.Const" "base" 'True) (C1 ('MetaCons "Const" 'PrefixI 'True) (S1 ('MetaSel ('Just "getConst") 'NoSourceUnpackedness 'NoSourceStrictness 'DecidedLazy) (Rec0 a)))

Linear traversable hierarchy

class Functor t => Traversable t where

A linear data traversible is a functor of type t a where you can apply a linear effectful action of type a %1-> f b on each value of type a and compose this to perform an action on the whole functor, resulting in a value of type f (t b).

To learn more about Traversable, see here:

• "Applicative Programming with Effects", by Conor McBride and Ross Paterson, Journal of Functional Programming 18:1 (2008) 1-13, online at http://www.soi.city.ac.uk/~ross/papers/Applicative.html.
• "The Essence of the Iterator Pattern", by Jeremy Gibbons and Bruno Oliveira, in Mathematically-Structured Functional Programming, 2006, online at http://web.comlab.ox.ac.uk/oucl/work/jeremy.gibbons/publications/#iterator.
• "An Investigation of the Laws of Traversals", by Mauro Jaskelioff and Ondrej Rypacek, in Mathematically-Structured Functional Programming, 2012, online at http://arxiv.org/pdf/1202.2919.

Minimal complete definition

traverse | sequence

Methods

traverse :: Applicative f => (a %1 -> f b) -> t a %1 -> f (t b)

sequence :: Applicative f => t (f a) %1 -> f (t a)

Instances

Traversable []

Defined in Data.Functor.Linear.Internal.Traversable

Methods

traverse :: Applicative f => (a %1 -> f b) -> [a] %1 -> f [b]

sequence :: Applicative f => [f a] %1 -> f [a]

Traversable Maybe

Defined in Data.Functor.Linear.Internal.Traversable

Methods

traverse :: Applicative f => (a %1 -> f b) -> Maybe a %1 -> f (Maybe b)

sequence :: Applicative f => Maybe (f a) %1 -> f (Maybe a)

Traversable (Either a)

Defined in Data.Functor.Linear.Internal.Traversable

Methods

traverse :: Applicative f => (a0 %1 -> f b) -> Either a a0 %1 -> f (Either a b)

sequence :: Applicative f => Either a (f a0) %1 -> f (Either a a0)

Traversable ((,) a)

Defined in Data.Functor.Linear.Internal.Traversable

Methods

traverse :: Applicative f => (a0 %1 -> f b) -> (a, a0) %1 -> f (a, b)

sequence :: Applicative f => (a, f a0) %1 -> f (a, a0)

KnownNat n => Traversable (V n)

Defined in Data.V.Linear.Internal.Instances

Methods

traverse :: Applicative f => (a %1 -> f b) -> V n a %1 -> f (V n b)

sequence :: Applicative f => V n (f a) %1 -> f (V n a)

Traversable (Const a :: Type -> Type)

Defined in Data.Functor.Linear.Internal.Traversable

Methods

traverse :: Applicative f => (a0 %1 -> f b) -> Const a a0 %1 -> f (Const a b)

sequence :: Applicative f => Const a (f a0) %1 -> f (Const a a0)

mapM :: (Traversable t, Monad m) => (a %1 -> m b) -> t a %1 -> m (t b)

sequenceA :: (Traversable t, Applicative f) => t (f a) %1 -> f (t a)

for :: (Traversable t, Applicative f) => t a %1 -> (a %1 -> f b) -> f (t b)

forM :: (Traversable t, Monad m) => t a %1 -> (a %1 -> m b) -> m (t b)

mapAccumL :: Traversable t => (a %1 -> b %1 -> (a, c)) -> a %1 -> t b %1 -> (a, t c)

mapAccumR :: Traversable t => (a %1 -> b %1 -> (a, c)) -> a %1 -> t b %1 -> (a, t c)