ghc-internal-9.1300.0: Basic libraries
Copyright(c) The University of Glasgow 1992-2002
Licensesee libraries/base/LICENSE
Maintainerghc-devs@haskell.org
Stabilityinternal
Portabilitynon-portable (GHC extensions)
Safe HaskellUnsafe
LanguageHaskell2010

GHC.Internal.Base

Description

Basic data types and classes.

Synopsis

Documentation

($) :: (a -> b) -> a -> b infixr 0 Source #

($) is the function application operator.

Applying ($) to a function f and an argument x gives the same result as applying f to x directly. The definition is akin to this:

($) :: (a -> b) -> a -> b
($) f x = f x

This is id specialized from a -> a to (a -> b) -> (a -> b) which by the associativity of (->) is the same as (a -> b) -> a -> b.

On the face of it, this may appear pointless! But it's actually one of the most useful and important operators in Haskell.

The order of operations is very different between ($) and normal function application. Normal function application has precedence 10 - higher than any operator - and associates to the left. So these two definitions are equivalent:

expr = min 5 1 + 5
expr = ((min 5) 1) + 5

($) has precedence 0 (the lowest) and associates to the right, so these are equivalent:

expr = min 5 $ 1 + 5
expr = (min 5) (1 + 5)

Examples

Expand

A common use cases of ($) is to avoid parentheses in complex expressions.

For example, instead of using nested parentheses in the following Haskell function:

-- | Sum numbers in a string: strSum "100  5 -7" == 98
strSum :: String -> Int
strSum s = sum (mapMaybe readMaybe (words s))

we can deploy the function application operator:

-- | Sum numbers in a string: strSum "100  5 -7" == 98
strSum :: String -> Int
strSum s = sum $ mapMaybe readMaybe $ words s

($) is also used as a section (a partially applied operator), in order to indicate that we wish to apply some yet-unspecified function to a given value. For example, to apply the argument 5 to a list of functions:

applyFive :: [Int]
applyFive = map ($ 5) [(+1), (2^)]
>>> [6, 32]

Technical Remark (Representation Polymorphism)

Expand

($) is fully representation-polymorphic. This allows it to also be used with arguments of unlifted and even unboxed kinds, such as unboxed integers:

fastMod :: Int -> Int -> Int
fastMod (I# x) (I# m) = I# $ remInt# x m

($!) :: (a -> b) -> a -> b infixr 0 Source #

Strict (call-by-value) application operator. It takes a function and an argument, evaluates the argument to weak head normal form (WHNF), then calls the function with that value.

(++) :: [a] -> [a] -> [a] infixr 5 Source #

(++) appends two lists, i.e.,

[x1, ..., xm] ++ [y1, ..., yn] == [x1, ..., xm, y1, ..., yn]
[x1, ..., xm] ++ [y1, ...] == [x1, ..., xm, y1, ...]

If the first list is not finite, the result is the first list.

Performance considerations

Expand

This function takes linear time in the number of elements of the first list. Thus it is better to associate repeated applications of (++) to the right (which is the default behaviour): xs ++ (ys ++ zs) or simply xs ++ ys ++ zs, but not (xs ++ ys) ++ zs. For the same reason concat = foldr (++) [] has linear performance, while foldl (++) [] is prone to quadratic slowdown

Examples

Expand
>>> [1, 2, 3] ++ [4, 5, 6]
[1,2,3,4,5,6]

>>> [] ++ [1, 2, 3]
[1,2,3]

>>> [3, 2, 1] ++ []
[3,2,1]

(.) :: (b -> c) -> (a -> b) -> a -> c infixr 9 Source #

Right to left function composition.

(f . g) x = f (g x)
f . id = f = id . f

Examples

Expand
>>> map ((*2) . length) [[], [0, 1, 2], [0]]
[0,6,2]

>>> foldr (.) id [(+1), (*3), (^3)] 2
25

>>> let (...) = (.).(.) in ((*2)...(+)) 5 10
30

(<**>) :: Applicative f => f a -> f (a -> b) -> f b infixl 4 Source #

A variant of <*> with the types of the arguments reversed. It differs from flip (<*>) in that the effects are resolved in the order the arguments are presented.

Examples

Expand
>>> (<**>) (print 1) (id <$ print 2)
1
2

>>> flip (<*>) (print 1) (id <$ print 2)
2
1

>>> ZipList [4, 5, 6] <**> ZipList [(+1), (*2), (/3)]
ZipList {getZipList = [5.0,10.0,2.0]}

(=<<) :: Monad m => (a -> m b) -> m a -> m b infixr 1 Source #

Same as >>=, but with the arguments interchanged.

as >>= f == f =<< as

absurd :: Void -> a Source #

Since Void values logically don't exist, this witnesses the logical reasoning tool of "ex falso quodlibet".

>>> let x :: Either Void Int; x = Right 5
>>> :{
case x of
    Right r -> r
    Left l  -> absurd l
:}
5

Since: base-4.8.0.0

ap :: Monad m => m (a -> b) -> m a -> m b Source #

In many situations, the liftM operations can be replaced by uses of ap, which promotes function application.

return f `ap` x1 `ap` ... `ap` xn

is equivalent to

liftM<n> f x1 x2 ... xn

Examples

Expand
>>> pure (\x y z -> x + y * z) `ap` Just 1 `ap` Just 5 `ap` Just 10
Just 51

asTypeOf :: a -> a -> a Source #

asTypeOf is a type-restricted version of const. It is usually used as an infix operator, and its typing forces its first argument (which is usually overloaded) to have the same type as the second.

assert :: Bool -> a -> a Source #

If the first argument evaluates to True, then the result is the second argument. Otherwise an AssertionFailed exception is raised, containing a String with the source file and line number of the call to assert.

Assertions can normally be turned on or off with a compiler flag (for GHC, assertions are normally on unless optimisation is turned on with -O or the -fignore-asserts option is given). When assertions are turned off, the first argument to assert is ignored, and the second argument is returned as the result.

augment :: (forall b. (a -> b -> b) -> b -> b) -> [a] -> [a] Source #

A list producer that can be fused with foldr. This function is merely

   augment g xs = g (:) xs

but GHC's simplifier will transform an expression of the form foldr k z (augment g xs), which may arise after inlining, to g k (foldr k z xs), which avoids producing an intermediate list.

bindIO :: IO a -> (a -> IO b) -> IO b Source #

breakpoint :: a -> a Source #

breakpointCond :: Bool -> a -> a Source #

build :: (forall b. (a -> b -> b) -> b -> b) -> [a] Source #

A list producer that can be fused with foldr. This function is merely

   build g = g (:) []

but GHC's simplifier will transform an expression of the form foldr k z (build g), which may arise after inlining, to g k z, which avoids producing an intermediate list.

const :: a -> b -> a Source #

const x y always evaluates to x, ignoring its second argument.

const x = \_ -> x

This function might seem useless at first glance, but it can be very useful in a higher order context.

Examples

Expand
>>> const 42 "hello"
42

>>> map (const 42) [0..3]
[42,42,42,42]

divInt :: Int -> Int -> Int Source #

Used to implement div for the Integral typeclass. This performs integer division on its two parameters, truncated towards negative infinity.

Example

Expand
>>> 10 `divInt` 2
5

>>> 10 `div` 2
5

divModInt :: Int -> Int -> (Int, Int) Source #

Used to implement divMod for the Integral typeclass. This gives a tuple equivalent to

(div x y, mod x y)

Example

Expand
>>> divModInt 10 2
(5,0)

>>> divMod 10 2
(5,0)

eqString :: String -> String -> Bool Source #

This String equality predicate is used when desugaring pattern-matches against strings.

failIO :: String -> IO a Source #

flip :: (a -> b -> c) -> b -> a -> c Source #

flip f takes its (first) two arguments in the reverse order of f.

flip f x y = f y x
flip . flip = id

Examples

Expand
>>> flip (++) "hello" "world"
"worldhello"

>>> let (.>) = flip (.) in (+1) .> show $ 5
"6"

foldr :: (a -> b -> b) -> b -> [a] -> b Source #

foldr, applied to a binary operator, a starting value (typically the right-identity of the operator), and a list, reduces the list using the binary operator, from right to left:

foldr f z [x1, x2, ..., xn] == x1 `f` (x2 `f` ... (xn `f` z)...)

getTag :: forall {lev :: Levity} (a :: TYPE ('BoxedRep lev)). DataToTag a => a -> Int# Source #

Returns the tag of a constructor application; this function was once used by the deriving code for Eq, Ord and Enum.

iShiftL# :: Int# -> Int# -> Int# Source #

Shift the argument left by the specified number of bits (which must be non-negative).

iShiftRA# :: Int# -> Int# -> Int# Source #

Shift the argument right (signed) by the specified number of bits (which must be non-negative). The RA means "right, arithmetic" (as opposed to RL for logical)

iShiftRL# :: Int# -> Int# -> Int# Source #

Shift the argument right (unsigned) by the specified number of bits (which must be non-negative). The RL means "right, logical" (as opposed to RA for arithmetic)

id :: a -> a Source #

Identity function.

id x = x

This function might seem useless at first glance, but it can be very useful in a higher order context.

Examples

Expand
>>> length $ filter id [True, True, False, True]
3

>>> Just (Just 3) >>= id
Just 3

>>> foldr id 0 [(^3), (*5), (+2)]
1000

join :: Monad m => m (m a) -> m a Source #

The join function is the conventional monad join operator. It is used to remove one level of monadic structure, projecting its bound argument into the outer level.

'join bss' can be understood as the do expression

do bs <- bss
   bs

Examples

Expand
>>> join [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
[1,2,3,4,5,6,7,8,9]

>>> join (Just (Just 3))
Just 3

A common use of join is to run an IO computation returned from an STM transaction, since STM transactions can't perform IO directly. Recall that

atomically :: STM a -> IO a

is used to run STM transactions atomically. So, by specializing the types of atomically and join to

atomically :: STM (IO b) -> IO (IO b)
join       :: IO (IO b)  -> IO b

we can compose them as

join . atomically :: STM (IO b) -> IO b

to run an STM transaction and the IO action it returns.

liftA :: Applicative f => (a -> b) -> f a -> f b Source #

Lift a function to actions. Equivalent to Functor's fmap but implemented using only Applicative's methods: liftA f a = pure f <*> a

As such this function may be used to implement a Functor instance from an Applicative one.

Examples

Expand

Using the Applicative instance for Lists:

>>> liftA (+1) [1, 2]
[2,3]

Or the Applicative instance for Maybe

>>> liftA (+1) (Just 3)
Just 4

liftA3 :: Applicative f => (a -> b -> c -> d) -> f a -> f b -> f c -> f d Source #

Lift a ternary function to actions.

liftM :: Monad m => (a1 -> r) -> m a1 -> m r Source #

Promote a function to a monad. This is equivalent to fmap but specialised to Monads.

liftM2 :: Monad m => (a1 -> a2 -> r) -> m a1 -> m a2 -> m r Source #

Promote a function to a monad, scanning the monadic arguments from left to right.

Examples

Expand
>>> liftM2 (+) [0,1] [0,2]
[0,2,1,3]

>>> liftM2 (+) (Just 1) Nothing
Nothing

>>> liftM2 (+) (+ 3) (* 2) 5
18

liftM3 :: Monad m => (a1 -> a2 -> a3 -> r) -> m a1 -> m a2 -> m a3 -> m r Source #

Promote a function to a monad, scanning the monadic arguments from left to right (cf. liftM2).

liftM4 :: Monad m => (a1 -> a2 -> a3 -> a4 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m r Source #

Promote a function to a monad, scanning the monadic arguments from left to right (cf. liftM2).

liftM5 :: Monad m => (a1 -> a2 -> a3 -> a4 -> a5 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m a5 -> m r Source #

Promote a function to a monad, scanning the monadic arguments from left to right (cf. liftM2).

map :: (a -> b) -> [a] -> [b] Source #

\(\mathcal{O}(n)\). map f xs is the list obtained by applying f to each element of xs, i.e.,

map f [x1, x2, ..., xn] == [f x1, f x2, ..., f xn]
map f [x1, x2, ...] == [f x1, f x2, ...]

this means that map id == id

Examples

Expand
>>> map (+1) [1, 2, 3]
[2,3,4]

>>> map id [1, 2, 3]
[1,2,3]

>>> map (\n -> 3 * n + 1) [1, 2, 3]
[4,7,10]

mapFB :: (elt -> lst -> lst) -> (a -> elt) -> a -> lst -> lst Source #

mapM :: Monad m => (a -> m b) -> [a] -> m [b] Source #

mapM f is equivalent to sequence . map f.

maxInt :: Int Source #

minInt :: Int Source #

modInt :: Int -> Int -> Int Source #

Used to implement mod for the Integral typeclass. This performs the modulo operation, satisfying

((x `div` y) * y) + (x `mod` y) == x

Example

Expand
>>> 7 `modInt` 3
1

>>> 7 `mod` 3
1

ord :: Char -> Int Source #

The fromEnum method restricted to the type Char.

otherwise :: Bool Source #

otherwise is defined as the value True. It helps to make guards more readable. eg.

 f x | x < 0     = ...
     | otherwise = ...

quotInt :: Int -> Int -> Int Source #

Used to implement quot for the Integral typeclass. This performs integer division on its two parameters, truncated towards zero.

Example

Expand
>>> quotInt 10 2
5

>>> quot 10 2
5

quotRemInt :: Int -> Int -> (Int, Int) Source #

Used to implement quotRem for the Integral typeclass. This gives a tuple equivalent to

(quot x y, mod x y)

Example

Expand
>>> quotRemInt 10 2
(5,0)

>>> quotRem 10 2
(5,0)

remInt :: Int -> Int -> Int Source #

Used to implement rem for the Integral typeclass. This gives the remainder after integer division of its two parameters, satisfying

((x `quot` y) * y) + (x `rem` y) == x

Example

Expand
>>> remInt 3 2
1

>>> rem 3 2
1

returnIO :: a -> IO a Source #

sequence :: Monad m => [m a] -> m [a] Source #

Evaluate each action in the sequence from left to right, and collect the results.

shiftL# :: Word# -> Int# -> Word# Source #

Shift the argument left by the specified number of bits (which must be non-negative).

shiftRL# :: Word# -> Int# -> Word# Source #

Shift the argument right by the specified number of bits (which must be non-negative). The RL means "right, logical" (as opposed to RA for arithmetic) (although an arithmetic right shift wouldn't make sense for Word#)

shift_mask :: Int# -> Int# -> Int# Source #

This function is used to implement branchless shifts. If the number of bits to shift is greater than or equal to the type size in bits, then the shift must return 0. Instead of doing a test, we use a mask obtained via this function which is branchless too.

shift_mask m b | b < m = 0xFF..FF | otherwise = 0

thenIO :: IO a -> IO b -> IO b Source #

unIO :: IO a -> State# RealWorld -> (# State# RealWorld, a #) Source #

unsafeChr :: Int -> Char Source #

until :: (a -> Bool) -> (a -> a) -> a -> a Source #

until p f yields the result of applying f until p holds.

vacuous :: Functor f => f Void -> f a Source #

If Void is uninhabited then any Functor that holds only values of type Void is holding no values. It is implemented in terms of fmap absurd.

Since: base-4.8.0.0

when :: Applicative f => Bool -> f () -> f () Source #

Conditional execution of Applicative expressions. For example,

Examples

Expand
when debug (putStrLn "Debugging")

will output the string Debugging if the Boolean value debug is True, and otherwise do nothing.

>>> putStr "pi:" >> when False (print 3.14159)
pi:

class Applicative f => Alternative (f :: Type -> Type) where Source #

A monoid on applicative functors.

If defined, some and many should be the least solutions of the equations:

Examples

Expand
>>> Nothing <|> Just 42
Just 42

>>> [1, 2] <|> [3, 4]
[1,2,3,4]

>>> empty <|> print (2^15)
32768

Minimal complete definition

empty, (<|>)

Methods

empty :: f a Source #

The identity of <|>

empty <|> a     == a
a     <|> empty == a

(<|>) :: f a -> f a -> f a infixl 3 Source #

An associative binary operation

some :: f a -> f [a] Source #

One or more.

Examples

Expand
>>> some (putStr "la")
lalalalalalalalala... * goes on forever *

>>> some Nothing
nothing

>>> take 5 <$> some (Just 1)
* hangs forever *

Note that this function can be used with Parsers based on Applicatives. In that case some parser will attempt to parse parser one or more times until it fails.

many :: f a -> f [a] Source #

Zero or more.

Examples

Expand
>>> many (putStr "la")
lalalalalalalalala... * goes on forever *

>>> many Nothing
Just []

>>> take 5 <$> many (Just 1)
* hangs forever *

Note that this function can be used with Parsers based on Applicatives. In that case many parser will attempt to parse parser zero or more times until it fails.

Instances

Instances details
Alternative STM Source #

Takes the first non-retrying STM action.

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Conc.Sync

Methods

empty :: STM a Source #

(<|>) :: STM a -> STM a -> STM a Source #

some :: STM a -> STM [a] Source #

many :: STM a -> STM [a] Source #

Alternative ZipList Source #

Since: base-4.11.0.0

Instance details

Defined in GHC.Internal.Functor.ZipList

Methods

empty :: ZipList a Source #

(<|>) :: ZipList a -> ZipList a -> ZipList a Source #

some :: ZipList a -> ZipList [a] Source #

many :: ZipList a -> ZipList [a] Source #

Alternative ReadP Source #

Since: base-4.6.0.0

Instance details

Defined in GHC.Internal.Text.ParserCombinators.ReadP

Methods

empty :: ReadP a Source #

(<|>) :: ReadP a -> ReadP a -> ReadP a Source #

some :: ReadP a -> ReadP [a] Source #

many :: ReadP a -> ReadP [a] Source #

Alternative ReadPrec Source #

Since: base-4.6.0.0

Instance details

Defined in GHC.Internal.Text.ParserCombinators.ReadPrec

Methods

empty :: ReadPrec a Source #

(<|>) :: ReadPrec a -> ReadPrec a -> ReadPrec a Source #

some :: ReadPrec a -> ReadPrec [a] Source #

many :: ReadPrec a -> ReadPrec [a] Source #

Alternative IO Source #

Takes the first non-throwing IO action's result. empty throws an exception.

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Base

Methods

empty :: IO a Source #

(<|>) :: IO a -> IO a -> IO a Source #

some :: IO a -> IO [a] Source #

many :: IO a -> IO [a] Source #

Alternative Maybe Source #

Picks the leftmost Just value, or, alternatively, Nothing.

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Methods

empty :: Maybe a Source #

(<|>) :: Maybe a -> Maybe a -> Maybe a Source #

some :: Maybe a -> Maybe [a] Source #

many :: Maybe a -> Maybe [a] Source #

Alternative [] Source #

Combines lists by concatenation, starting from the empty list.

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Methods

empty :: [a] Source #

(<|>) :: [a] -> [a] -> [a] Source #

some :: [a] -> [[a]] Source #

many :: [a] -> [[a]] Source #

ArrowPlus a => Alternative (ArrowMonad a) Source #

Since: base-4.6.0.0

Instance details

Defined in GHC.Internal.Control.Arrow

Methods

empty :: ArrowMonad a a0 Source #

(<|>) :: ArrowMonad a a0 -> ArrowMonad a a0 -> ArrowMonad a a0 Source #

some :: ArrowMonad a a0 -> ArrowMonad a [a0] Source #

many :: ArrowMonad a a0 -> ArrowMonad a [a0] Source #

Alternative (Proxy :: Type -> Type) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Data.Proxy

Methods

empty :: Proxy a Source #

(<|>) :: Proxy a -> Proxy a -> Proxy a Source #

some :: Proxy a -> Proxy [a] Source #

many :: Proxy a -> Proxy [a] Source #

Alternative (U1 :: Type -> Type) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

empty :: U1 a Source #

(<|>) :: U1 a -> U1 a -> U1 a Source #

some :: U1 a -> U1 [a] Source #

many :: U1 a -> U1 [a] Source #

Alternative m => Alternative (Kleisli m a) Source #

Since: base-4.14.0.0

Instance details

Defined in GHC.Internal.Control.Arrow

Methods

empty :: Kleisli m a a0 Source #

(<|>) :: Kleisli m a a0 -> Kleisli m a a0 -> Kleisli m a a0 Source #

some :: Kleisli m a a0 -> Kleisli m a [a0] Source #

many :: Kleisli m a a0 -> Kleisli m a [a0] Source #

Alternative f => Alternative (Ap f) Source #

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

empty :: Ap f a Source #

(<|>) :: Ap f a -> Ap f a -> Ap f a Source #

some :: Ap f a -> Ap f [a] Source #

many :: Ap f a -> Ap f [a] Source #

Alternative f => Alternative (Alt f) Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

empty :: Alt f a Source #

(<|>) :: Alt f a -> Alt f a -> Alt f a Source #

some :: Alt f a -> Alt f [a] Source #

many :: Alt f a -> Alt f [a] Source #

(Generic1 f, Alternative (Rep1 f)) => Alternative (Generically1 f) Source #

Since: base-4.17.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

empty :: Generically1 f a Source #

(<|>) :: Generically1 f a -> Generically1 f a -> Generically1 f a Source #

some :: Generically1 f a -> Generically1 f [a] Source #

many :: Generically1 f a -> Generically1 f [a] Source #

Alternative f => Alternative (Rec1 f) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

empty :: Rec1 f a Source #

(<|>) :: Rec1 f a -> Rec1 f a -> Rec1 f a Source #

some :: Rec1 f a -> Rec1 f [a] Source #

many :: Rec1 f a -> Rec1 f [a] Source #

(Alternative f, Alternative g) => Alternative (f :*: g) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

empty :: (f :*: g) a Source #

(<|>) :: (f :*: g) a -> (f :*: g) a -> (f :*: g) a Source #

some :: (f :*: g) a -> (f :*: g) [a] Source #

many :: (f :*: g) a -> (f :*: g) [a] Source #

(Alternative f, Applicative g) => Alternative (f :.: g) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

empty :: (f :.: g) a Source #

(<|>) :: (f :.: g) a -> (f :.: g) a -> (f :.: g) a Source #

some :: (f :.: g) a -> (f :.: g) [a] Source #

many :: (f :.: g) a -> (f :.: g) [a] Source #

Alternative f => Alternative (M1 i c f) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

empty :: M1 i c f a Source #

(<|>) :: M1 i c f a -> M1 i c f a -> M1 i c f a Source #

some :: M1 i c f a -> M1 i c f [a] Source #

many :: M1 i c f a -> M1 i c f [a] Source #

class Functor f => Applicative (f :: Type -> Type) where Source #

A functor with application, providing operations to

  • embed pure expressions (pure), and
  • sequence computations and combine their results (<*> and liftA2).

A minimal complete definition must include implementations of pure and of either <*> or liftA2. If it defines both, then they must behave the same as their default definitions:

(<*>) = liftA2 id
liftA2 f x y = f <$> x <*> y

Further, any definition must satisfy the following:

Identity
pure id <*> v = v
Composition
pure (.) <*> u <*> v <*> w = u <*> (v <*> w)
Homomorphism
pure f <*> pure x = pure (f x)
Interchange
u <*> pure y = pure ($ y) <*> u

The other methods have the following default definitions, which may be overridden with equivalent specialized implementations:

As a consequence of these laws, the Functor instance for f will satisfy

It may be useful to note that supposing

forall x y. p (q x y) = f x . g y

it follows from the above that

liftA2 p (liftA2 q u v) = liftA2 f u . liftA2 g v

If f is also a Monad, it should satisfy

(which implies that pure and <*> satisfy the applicative functor laws).

Minimal complete definition

pure, ((<*>) | liftA2)

Methods

pure :: a -> f a Source #

Lift a value into the Structure.

Examples

Expand
>>> pure 1 :: Maybe Int
Just 1

>>> pure 'z' :: [Char]
"z"

>>> pure (pure ":D") :: Maybe [String]
Just [":D"]

(<*>) :: f (a -> b) -> f a -> f b infixl 4 Source #

Sequential application.

A few functors support an implementation of <*> that is more efficient than the default one.

Example

Expand

Used in combination with (<$>), (<*>) can be used to build a record.

>>> data MyState = MyState {arg1 :: Foo, arg2 :: Bar, arg3 :: Baz}

>>> produceFoo :: Applicative f => f Foo
>>> produceBar :: Applicative f => f Bar
>>> produceBaz :: Applicative f => f Baz

>>> mkState :: Applicative f => f MyState
>>> mkState = MyState <$> produceFoo <*> produceBar <*> produceBaz

liftA2 :: (a -> b -> c) -> f a -> f b -> f c Source #

Lift a binary function to actions.

Some functors support an implementation of liftA2 that is more efficient than the default one. In particular, if fmap is an expensive operation, it is likely better to use liftA2 than to fmap over the structure and then use <*>.

This became a typeclass method in 4.10.0.0. Prior to that, it was a function defined in terms of <*> and fmap.

Example

Expand
>>> liftA2 (,) (Just 3) (Just 5)
Just (3,5)

>>> liftA2 (+) [1, 2, 3] [4, 5, 6]
[5,6,7,6,7,8,7,8,9]

(*>) :: f a -> f b -> f b infixl 4 Source #

Sequence actions, discarding the value of the first argument.

Examples

Expand

If used in conjunction with the Applicative instance for Maybe, you can chain Maybe computations, with a possible "early return" in case of Nothing.

>>> Just 2 *> Just 3
Just 3

>>> Nothing *> Just 3
Nothing

Of course a more interesting use case would be to have effectful computations instead of just returning pure values.

>>> import Data.Char
>>> import GHC.Internal.Text.ParserCombinators.ReadP
>>> let p = string "my name is " *> munch1 isAlpha <* eof
>>> readP_to_S p "my name is Simon"
[("Simon","")]

(<*) :: f a -> f b -> f a infixl 4 Source #

Sequence actions, discarding the value of the second argument.

Instances

Instances details
Applicative NonEmpty Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Base

Methods

pure :: a -> NonEmpty a Source #

(<*>) :: NonEmpty (a -> b) -> NonEmpty a -> NonEmpty b Source #

liftA2 :: (a -> b -> c) -> NonEmpty a -> NonEmpty b -> NonEmpty c Source #

(*>) :: NonEmpty a -> NonEmpty b -> NonEmpty b Source #

(<*) :: NonEmpty a -> NonEmpty b -> NonEmpty a Source #

Applicative STM Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Conc.Sync

Methods

pure :: a -> STM a Source #

(<*>) :: STM (a -> b) -> STM a -> STM b Source #

liftA2 :: (a -> b -> c) -> STM a -> STM b -> STM c Source #

(*>) :: STM a -> STM b -> STM b Source #

(<*) :: STM a -> STM b -> STM a Source #

Applicative Identity Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Identity

Methods

pure :: a -> Identity a Source #

(<*>) :: Identity (a -> b) -> Identity a -> Identity b Source #

liftA2 :: (a -> b -> c) -> Identity a -> Identity b -> Identity c Source #

(*>) :: Identity a -> Identity b -> Identity b Source #

(<*) :: Identity a -> Identity b -> Identity a Source #

Applicative First Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

pure :: a -> First a Source #

(<*>) :: First (a -> b) -> First a -> First b Source #

liftA2 :: (a -> b -> c) -> First a -> First b -> First c Source #

(*>) :: First a -> First b -> First b Source #

(<*) :: First a -> First b -> First a Source #

Applicative Last Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

pure :: a -> Last a Source #

(<*>) :: Last (a -> b) -> Last a -> Last b Source #

liftA2 :: (a -> b -> c) -> Last a -> Last b -> Last c Source #

(*>) :: Last a -> Last b -> Last b Source #

(<*) :: Last a -> Last b -> Last a Source #

Applicative Down Source #

Since: base-4.11.0.0

Instance details

Defined in GHC.Internal.Data.Ord

Methods

pure :: a -> Down a Source #

(<*>) :: Down (a -> b) -> Down a -> Down b Source #

liftA2 :: (a -> b -> c) -> Down a -> Down b -> Down c Source #

(*>) :: Down a -> Down b -> Down b Source #

(<*) :: Down a -> Down b -> Down a Source #

Applicative Dual Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

pure :: a -> Dual a Source #

(<*>) :: Dual (a -> b) -> Dual a -> Dual b Source #

liftA2 :: (a -> b -> c) -> Dual a -> Dual b -> Dual c Source #

(*>) :: Dual a -> Dual b -> Dual b Source #

(<*) :: Dual a -> Dual b -> Dual a Source #

Applicative Product Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

pure :: a -> Product a Source #

(<*>) :: Product (a -> b) -> Product a -> Product b Source #

liftA2 :: (a -> b -> c) -> Product a -> Product b -> Product c Source #

(*>) :: Product a -> Product b -> Product b Source #

(<*) :: Product a -> Product b -> Product a Source #

Applicative Sum Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

pure :: a -> Sum a Source #

(<*>) :: Sum (a -> b) -> Sum a -> Sum b Source #

liftA2 :: (a -> b -> c) -> Sum a -> Sum b -> Sum c Source #

(*>) :: Sum a -> Sum b -> Sum b Source #

(<*) :: Sum a -> Sum b -> Sum a Source #

Applicative ZipList Source #
f <$> ZipList xs1 <*> ... <*> ZipList xsN
    = ZipList (zipWithN f xs1 ... xsN)

where zipWithN refers to the zipWith function of the appropriate arity (zipWith, zipWith3, zipWith4, ...). For example:

(\a b c -> stimes c [a, b]) <$> ZipList "abcd" <*> ZipList "567" <*> ZipList [1..]
    = ZipList (zipWith3 (\a b c -> stimes c [a, b]) "abcd" "567" [1..])
    = ZipList {getZipList = ["a5","b6b6","c7c7c7"]}

Since: base-2.1

Instance details

Defined in GHC.Internal.Functor.ZipList

Methods

pure :: a -> ZipList a Source #

(<*>) :: ZipList (a -> b) -> ZipList a -> ZipList b Source #

liftA2 :: (a -> b -> c) -> ZipList a -> ZipList b -> ZipList c Source #

(*>) :: ZipList a -> ZipList b -> ZipList b Source #

(<*) :: ZipList a -> ZipList b -> ZipList a Source #

Applicative NoIO Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.GHCi

Methods

pure :: a -> NoIO a Source #

(<*>) :: NoIO (a -> b) -> NoIO a -> NoIO b Source #

liftA2 :: (a -> b -> c) -> NoIO a -> NoIO b -> NoIO c Source #

(*>) :: NoIO a -> NoIO b -> NoIO b Source #

(<*) :: NoIO a -> NoIO b -> NoIO a Source #

Applicative Par1 Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

pure :: a -> Par1 a Source #

(<*>) :: Par1 (a -> b) -> Par1 a -> Par1 b Source #

liftA2 :: (a -> b -> c) -> Par1 a -> Par1 b -> Par1 c Source #

(*>) :: Par1 a -> Par1 b -> Par1 b Source #

(<*) :: Par1 a -> Par1 b -> Par1 a Source #

Applicative Q Source # 
Instance details

Defined in GHC.Internal.TH.Syntax

Methods

pure :: a -> Q a Source #

(<*>) :: Q (a -> b) -> Q a -> Q b Source #

liftA2 :: (a -> b -> c) -> Q a -> Q b -> Q c Source #

(*>) :: Q a -> Q b -> Q b Source #

(<*) :: Q a -> Q b -> Q a Source #

Applicative ReadP Source #

Since: base-4.6.0.0

Instance details

Defined in GHC.Internal.Text.ParserCombinators.ReadP

Methods

pure :: a -> ReadP a Source #

(<*>) :: ReadP (a -> b) -> ReadP a -> ReadP b Source #

liftA2 :: (a -> b -> c) -> ReadP a -> ReadP b -> ReadP c Source #

(*>) :: ReadP a -> ReadP b -> ReadP b Source #

(<*) :: ReadP a -> ReadP b -> ReadP a Source #

Applicative ReadPrec Source #

Since: base-4.6.0.0

Instance details

Defined in GHC.Internal.Text.ParserCombinators.ReadPrec

Methods

pure :: a -> ReadPrec a Source #

(<*>) :: ReadPrec (a -> b) -> ReadPrec a -> ReadPrec b Source #

liftA2 :: (a -> b -> c) -> ReadPrec a -> ReadPrec b -> ReadPrec c Source #

(*>) :: ReadPrec a -> ReadPrec b -> ReadPrec b Source #

(<*) :: ReadPrec a -> ReadPrec b -> ReadPrec a Source #

Applicative IO Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Methods

pure :: a -> IO a Source #

(<*>) :: IO (a -> b) -> IO a -> IO b Source #

liftA2 :: (a -> b -> c) -> IO a -> IO b -> IO c Source #

(*>) :: IO a -> IO b -> IO b Source #

(<*) :: IO a -> IO b -> IO a Source #

Applicative Maybe Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Methods

pure :: a -> Maybe a Source #

(<*>) :: Maybe (a -> b) -> Maybe a -> Maybe b Source #

liftA2 :: (a -> b -> c) -> Maybe a -> Maybe b -> Maybe c Source #

(*>) :: Maybe a -> Maybe b -> Maybe b Source #

(<*) :: Maybe a -> Maybe b -> Maybe a Source #

Applicative Solo Source #

Since: base-4.15

Instance details

Defined in GHC.Internal.Base

Methods

pure :: a -> Solo a Source #

(<*>) :: Solo (a -> b) -> Solo a -> Solo b Source #

liftA2 :: (a -> b -> c) -> Solo a -> Solo b -> Solo c Source #

(*>) :: Solo a -> Solo b -> Solo b Source #

(<*) :: Solo a -> Solo b -> Solo a Source #

Applicative [] Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Methods

pure :: a -> [a] Source #

(<*>) :: [a -> b] -> [a] -> [b] Source #

liftA2 :: (a -> b -> c) -> [a] -> [b] -> [c] Source #

(*>) :: [a] -> [b] -> [b] Source #

(<*) :: [a] -> [b] -> [a] Source #

Arrow a => Applicative (ArrowMonad a) Source #

Since: base-4.6.0.0

Instance details

Defined in GHC.Internal.Control.Arrow

Methods

pure :: a0 -> ArrowMonad a a0 Source #

(<*>) :: ArrowMonad a (a0 -> b) -> ArrowMonad a a0 -> ArrowMonad a b Source #

liftA2 :: (a0 -> b -> c) -> ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a c Source #

(*>) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a b Source #

(<*) :: ArrowMonad a a0 -> ArrowMonad a b -> ArrowMonad a a0 Source #

Applicative (ST s) Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Control.Monad.ST.Lazy.Imp

Methods

pure :: a -> ST s a Source #

(<*>) :: ST s (a -> b) -> ST s a -> ST s b Source #

liftA2 :: (a -> b -> c) -> ST s a -> ST s b -> ST s c Source #

(*>) :: ST s a -> ST s b -> ST s b Source #

(<*) :: ST s a -> ST s b -> ST s a Source #

Applicative (Either e) Source #

Since: base-3.0

Instance details

Defined in GHC.Internal.Data.Either

Methods

pure :: a -> Either e a Source #

(<*>) :: Either e (a -> b) -> Either e a -> Either e b Source #

liftA2 :: (a -> b -> c) -> Either e a -> Either e b -> Either e c Source #

(*>) :: Either e a -> Either e b -> Either e b Source #

(<*) :: Either e a -> Either e b -> Either e a Source #

Applicative (StateL s) Source #

Since: base-4.0

Instance details

Defined in GHC.Internal.Data.Functor.Utils

Methods

pure :: a -> StateL s a Source #

(<*>) :: StateL s (a -> b) -> StateL s a -> StateL s b Source #

liftA2 :: (a -> b -> c) -> StateL s a -> StateL s b -> StateL s c Source #

(*>) :: StateL s a -> StateL s b -> StateL s b Source #

(<*) :: StateL s a -> StateL s b -> StateL s a Source #

Applicative (StateR s) Source #

Since: base-4.0

Instance details

Defined in GHC.Internal.Data.Functor.Utils

Methods

pure :: a -> StateR s a Source #

(<*>) :: StateR s (a -> b) -> StateR s a -> StateR s b Source #

liftA2 :: (a -> b -> c) -> StateR s a -> StateR s b -> StateR s c Source #

(*>) :: StateR s a -> StateR s b -> StateR s b Source #

(<*) :: StateR s a -> StateR s b -> StateR s a Source #

Applicative (Proxy :: Type -> Type) Source #

Since: base-4.7.0.0

Instance details

Defined in GHC.Internal.Data.Proxy

Methods

pure :: a -> Proxy a Source #

(<*>) :: Proxy (a -> b) -> Proxy a -> Proxy b Source #

liftA2 :: (a -> b -> c) -> Proxy a -> Proxy b -> Proxy c Source #

(*>) :: Proxy a -> Proxy b -> Proxy b Source #

(<*) :: Proxy a -> Proxy b -> Proxy a Source #

Applicative (U1 :: Type -> Type) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

pure :: a -> U1 a Source #

(<*>) :: U1 (a -> b) -> U1 a -> U1 b Source #

liftA2 :: (a -> b -> c) -> U1 a -> U1 b -> U1 c Source #

(*>) :: U1 a -> U1 b -> U1 b Source #

(<*) :: U1 a -> U1 b -> U1 a Source #

Applicative (ST s) Source #

Since: base-4.4.0.0

Instance details

Defined in GHC.Internal.ST

Methods

pure :: a -> ST s a Source #

(<*>) :: ST s (a -> b) -> ST s a -> ST s b Source #

liftA2 :: (a -> b -> c) -> ST s a -> ST s b -> ST s c Source #

(*>) :: ST s a -> ST s b -> ST s b Source #

(<*) :: ST s a -> ST s b -> ST s a Source #

Monoid a => Applicative ((,) a) Source #

For tuples, the Monoid constraint on a determines how the first values merge. For example, Strings concatenate:

("hello ", (+15)) <*> ("world!", 2002)
("hello world!",2017)

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Methods

pure :: a0 -> (a, a0) Source #

(<*>) :: (a, a0 -> b) -> (a, a0) -> (a, b) Source #

liftA2 :: (a0 -> b -> c) -> (a, a0) -> (a, b) -> (a, c) Source #

(*>) :: (a, a0) -> (a, b) -> (a, b) Source #

(<*) :: (a, a0) -> (a, b) -> (a, a0) Source #

Applicative m => Applicative (Kleisli m a) Source #

Since: base-4.14.0.0

Instance details

Defined in GHC.Internal.Control.Arrow

Methods

pure :: a0 -> Kleisli m a a0 Source #

(<*>) :: Kleisli m a (a0 -> b) -> Kleisli m a a0 -> Kleisli m a b Source #

liftA2 :: (a0 -> b -> c) -> Kleisli m a a0 -> Kleisli m a b -> Kleisli m a c Source #

(*>) :: Kleisli m a a0 -> Kleisli m a b -> Kleisli m a b Source #

(<*) :: Kleisli m a a0 -> Kleisli m a b -> Kleisli m a a0 Source #

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

Since: base-2.0.1

Instance details

Defined in GHC.Internal.Data.Functor.Const

Methods

pure :: a -> Const m a Source #

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

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

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

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

Monad m => Applicative (StateT s m) Source #

Since: base-4.18.0.0

Instance details

Defined in GHC.Internal.Data.Functor.Utils

Methods

pure :: a -> StateT s m a Source #

(<*>) :: StateT s m (a -> b) -> StateT s m a -> StateT s m b Source #

liftA2 :: (a -> b -> c) -> StateT s m a -> StateT s m b -> StateT s m c Source #

(*>) :: StateT s m a -> StateT s m b -> StateT s m b Source #

(<*) :: StateT s m a -> StateT s m b -> StateT s m a Source #

Applicative f => Applicative (Ap f) Source #

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Data.Monoid

Methods

pure :: a -> Ap f a Source #

(<*>) :: Ap f (a -> b) -> Ap f a -> Ap f b Source #

liftA2 :: (a -> b -> c) -> Ap f a -> Ap f b -> Ap f c Source #

(*>) :: Ap f a -> Ap f b -> Ap f b Source #

(<*) :: Ap f a -> Ap f b -> Ap f a Source #

Applicative f => Applicative (Alt f) Source #

Since: base-4.8.0.0

Instance details

Defined in GHC.Internal.Data.Semigroup.Internal

Methods

pure :: a -> Alt f a Source #

(<*>) :: Alt f (a -> b) -> Alt f a -> Alt f b Source #

liftA2 :: (a -> b -> c) -> Alt f a -> Alt f b -> Alt f c Source #

(*>) :: Alt f a -> Alt f b -> Alt f b Source #

(<*) :: Alt f a -> Alt f b -> Alt f a Source #

(Generic1 f, Applicative (Rep1 f)) => Applicative (Generically1 f) Source #

Since: base-4.17.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

pure :: a -> Generically1 f a Source #

(<*>) :: Generically1 f (a -> b) -> Generically1 f a -> Generically1 f b Source #

liftA2 :: (a -> b -> c) -> Generically1 f a -> Generically1 f b -> Generically1 f c Source #

(*>) :: Generically1 f a -> Generically1 f b -> Generically1 f b Source #

(<*) :: Generically1 f a -> Generically1 f b -> Generically1 f a Source #

Applicative f => Applicative (Rec1 f) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

pure :: a -> Rec1 f a Source #

(<*>) :: Rec1 f (a -> b) -> Rec1 f a -> Rec1 f b Source #

liftA2 :: (a -> b -> c) -> Rec1 f a -> Rec1 f b -> Rec1 f c Source #

(*>) :: Rec1 f a -> Rec1 f b -> Rec1 f b Source #

(<*) :: Rec1 f a -> Rec1 f b -> Rec1 f a Source #

(Monoid a, Monoid b) => Applicative ((,,) a b) Source #

Since: base-4.14.0.0

Instance details

Defined in GHC.Internal.Base

Methods

pure :: a0 -> (a, b, a0) Source #

(<*>) :: (a, b, a0 -> b0) -> (a, b, a0) -> (a, b, b0) Source #

liftA2 :: (a0 -> b0 -> c) -> (a, b, a0) -> (a, b, b0) -> (a, b, c) Source #

(*>) :: (a, b, a0) -> (a, b, b0) -> (a, b, b0) Source #

(<*) :: (a, b, a0) -> (a, b, b0) -> (a, b, a0) Source #

(Applicative f, Applicative g) => Applicative (f :*: g) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

pure :: a -> (f :*: g) a Source #

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

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

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

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

Monoid c => Applicative (K1 i c :: Type -> Type) Source #

Since: base-4.12.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

pure :: a -> K1 i c a Source #

(<*>) :: K1 i c (a -> b) -> K1 i c a -> K1 i c b Source #

liftA2 :: (a -> b -> c0) -> K1 i c a -> K1 i c b -> K1 i c c0 Source #

(*>) :: K1 i c a -> K1 i c b -> K1 i c b Source #

(<*) :: K1 i c a -> K1 i c b -> K1 i c a Source #

(Monoid a, Monoid b, Monoid c) => Applicative ((,,,) a b c) Source #

Since: base-4.14.0.0

Instance details

Defined in GHC.Internal.Base

Methods

pure :: a0 -> (a, b, c, a0) Source #

(<*>) :: (a, b, c, a0 -> b0) -> (a, b, c, a0) -> (a, b, c, b0) Source #

liftA2 :: (a0 -> b0 -> c0) -> (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, c0) Source #

(*>) :: (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, b0) Source #

(<*) :: (a, b, c, a0) -> (a, b, c, b0) -> (a, b, c, a0) Source #

Applicative ((->) r) Source #

Since: base-2.1

Instance details

Defined in GHC.Internal.Base

Methods

pure :: a -> r -> a Source #

(<*>) :: (r -> (a -> b)) -> (r -> a) -> r -> b Source #

liftA2 :: (a -> b -> c) -> (r -> a) -> (r -> b) -> r -> c Source #

(*>) :: (r -> a) -> (r -> b) -> r -> b Source #

(<*) :: (r -> a) -> (r -> b) -> r -> a Source #

(Applicative f, Applicative g) => Applicative (f :.: g) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

pure :: a -> (f :.: g) a Source #

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

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

(*>) :: (f :.: g) a -> (f :.: g) b -> (f :.: g) b Source #

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

Applicative f => Applicative (M1 i c f) Source #

Since: base-4.9.0.0

Instance details

Defined in GHC.Internal.Generics

Methods

pure :: a -> M1 i c f a Source #

(<*>) :: M1 i c f (a -> b) -> M1 i c f a -> M1 i c f b Source #

liftA2 :: (a -> b -> c0) -> M1 i c f a -> M1 i c f b -> M1 i c f c0 Source #

(*>) :: M1 i c f a -> M1 i c f b -> M1 i c f b Source #

(<*) :: M1 i c f a -> M1 i c f b -> M1 i c f a Source #

class Functor (f :: Type -> Type) where Source #

A type f is a Functor if it provides a function fmap which, given any types a and b lets you apply any function from (a -> b) to turn an f a into an f b, preserving the structure of f. Furthermore f needs to adhere to the following:

Identity
fmap id == id
Composition
fmap (f . g) == fmap f . fmap g

Note, that the second law follows from the free theorem of the type fmap and the first law, so you need only check that the former condition holds. See these articles by School of Haskell or David Luposchainsky for an explanation.

Minimal complete definition

fmap

Methods

fmap :: (a -> b) -> f a -> f b Source #

fmap is used to apply a function of type (a -> b) to a value of type f a, where f is a functor, to produce a value of type f b. Note that for any type constructor with more than one parameter (e.g., Either), only the last type parameter can be modified with fmap (e.g., b in `Either a b`).

Some type constructors with two parameters or more have a Bifunctor instance that allows both the last and the penultimate parameters to be mapped over.