Function

Documentation

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

Application operator. This operator is redundant, since ordinary application (f x) means the same as (f $ x). However, $ has low, right-associative binding precedence, so it sometimes allows parentheses to be omitted; for example:

f $ g $ h x  =  f (g (h x))

It is also useful in higher-order situations, such as map ($ 0) xs, or zipWith ($) fs xs.

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

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 -> b) -> b infixl 1

& is a reverse application operator. This provides notational convenience. Its precedence is one higher than that of the forward application operator $, which allows & to be nested in $.

>>> 5 & (+1) & show
"6"

Since: base-4.8.0.0

asTypeOf :: a -> a -> a

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.

const :: a -> b -> a

const x is a unary function which evaluates to x for all inputs.

>>> const 42 "hello"
42

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

fix :: (a -> a) -> a

fix f is the least fixed point of the function f, i.e. the least defined x such that f x = x.

For example, we can write the factorial function using direct recursion as

>>> let fac n = if n <= 1 then 1 else n * fac (n-1) in fac 5
120

This uses the fact that Haskell’s let introduces recursive bindings. We can rewrite this definition using fix,

>>> fix (\rec n -> if n <= 1 then 1 else n * rec (n-1)) 5
120

Instead of making a recursive call, we introduce a dummy parameter rec; when used within fix, this parameter then refers to fix' argument, hence the recursion is reintroduced.

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

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

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

loop :: (a -> Either a b) -> a -> b

A looping operation, where the predicate returns Left as a seed for the next loop or Right to abort the loop.

loop (\x -> if x < 10 then Left $ x * 2 else Right $ show x) 1 == "16"

on :: (b -> b -> c) -> (a -> b) -> a -> a -> c infixl 0

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

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

newtype Endo a

The monoid of endomorphisms under composition.

>>> let computation = Endo ("Hello, " ++) <> Endo (++ "!")
>>> appEndo computation "Haskell"
"Hello, Haskell!"

Constructors

Endo

Fields

• appEndo :: a -> a

Instances

Pointed Endo

Defined in Data.Pointed

Methods

point :: a -> Endo a

Generic (Endo a)

Defined in Data.Semigroup.Internal

Associated Types

type Rep (Endo a) :: * -> *

Methods

from :: Endo a -> Rep (Endo a) x

to :: Rep (Endo a) x -> Endo a

Semigroup (Endo a)

Since: base-4.9.0.0

Defined in Data.Semigroup.Internal

Methods

(<>) :: Endo a -> Endo a -> Endo a

sconcat :: NonEmpty (Endo a) -> Endo a

stimes :: Integral b => b -> Endo a -> Endo a

Monoid (Endo a)

Since: base-2.1

Defined in Data.Semigroup.Internal

Methods

mempty :: Endo a

mappend :: Endo a -> Endo a -> Endo a

mconcat :: [Endo a] -> Endo a

Wrapped (Endo a)

Defined in Control.Lens.Wrapped

Associated Types

type Unwrapped (Endo a) :: *

Methods

_Wrapped' :: Iso' (Endo a) (Unwrapped (Endo a))

Lower (Endo a)

Defined in Data.Semilattice.Lower

Methods

lowerBound :: Endo a

t ~ Endo b => Rewrapped (Endo a) t

Defined in Control.Lens.Wrapped

type Rep (Endo a)

Defined in Data.Semigroup.Internal

type Rep (Endo a) = D1 (MetaData "Endo" "Data.Semigroup.Internal" "base" True) (C1 (MetaCons "Endo" PrefixI True) (S1 (MetaSel (Just "appEndo") NoSourceUnpackedness NoSourceStrictness DecidedLazy) (Rec0 (a -> a))))

type Unwrapped (Endo a)

Defined in Control.Lens.Wrapped

type Unwrapped (Endo a) = a -> a

newtype Op a b

Dual function arrows.

Constructors

Op

Fields

• getOp :: b -> a

Instances

Contravariant (Op a)

Defined in Data.Functor.Contravariant

Methods

contramap :: (a0 -> b) -> Op a b -> Op a a0

(>$) :: b -> Op a b -> Op a a0

Monoid r => Divisible (Op r)

Defined in Data.Functor.Contravariant.Divisible

Methods

divide :: (a -> (b, c)) -> Op r b -> Op r c -> Op r a

conquer :: Op r a

Monoid r => Decidable (Op r)

Defined in Data.Functor.Contravariant.Divisible

Methods

lose :: (a -> Void) -> Op r a

choose :: (a -> Either b c) -> Op r b -> Op r c -> Op r a

Category Op

Defined in Data.Functor.Contravariant

Methods

id :: Op a a

(.) :: Op b c -> Op a b -> Op a c

Semigroupoid Op

Defined in Data.Semigroupoid

Methods

o :: Op j k1 -> Op i j -> Op i k1

Floating a => Floating (Op a b)

Defined in Data.Functor.Contravariant

Methods

pi :: Op a b

exp :: Op a b -> Op a b

log :: Op a b -> Op a b

sqrt :: Op a b -> Op a b

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

logBase :: Op a b -> Op a b -> Op a b

sin :: Op a b -> Op a b

cos :: Op a b -> Op a b

tan :: Op a b -> Op a b

asin :: Op a b -> Op a b

acos :: Op a b -> Op a b

atan :: Op a b -> Op a b

sinh :: Op a b -> Op a b

cosh :: Op a b -> Op a b

tanh :: Op a b -> Op a b

asinh :: Op a b -> Op a b

acosh :: Op a b -> Op a b

atanh :: Op a b -> Op a b

log1p :: Op a b -> Op a b

expm1 :: Op a b -> Op a b

log1pexp :: Op a b -> Op a b

log1mexp :: Op a b -> Op a b

Fractional a => Fractional (Op a b)

Defined in Data.Functor.Contravariant

Methods

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

recip :: Op a b -> Op a b

fromRational :: Rational -> Op a b

Num a => Num (Op a b)

Defined in Data.Functor.Contravariant

Methods

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

(-) :: Op a b -> Op a b -> Op a b

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

negate :: Op a b -> Op a b

abs :: Op a b -> Op a b

signum :: Op a b -> Op a b

fromInteger :: Integer -> Op a b

Semigroup a => Semigroup (Op a b)

Defined in Data.Functor.Contravariant

Methods

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

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

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

Monoid a => Monoid (Op a b)

Defined in Data.Functor.Contravariant

Methods

mempty :: Op a b

mappend :: Op a b -> Op a b -> Op a b

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

Wrapped (Op a b)

Defined in Control.Lens.Wrapped

Associated Types

type Unwrapped (Op a b) :: *

Methods

_Wrapped' :: Iso' (Op a b) (Unwrapped (Op a b))

t ~ Op a' b' => Rewrapped (Op a b) t

Defined in Control.Lens.Wrapped

type Unwrapped (Op a b)

Defined in Control.Lens.Wrapped

type Unwrapped (Op a b) = b -> a