:: a -> (a -> b) -> b -package:turtle

& 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 $. This is a version of flip id, where id is specialized from a -> a to (a -> b) -> (a -> b) which by the associativity of (->) is (a -> b) -> a -> b. flipping this yields a -> (a -> b) -> b which is the type signature of &

Examples

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

>>> sqrt $ [1 / n^2 | n <- [1..1000]] & sum & (*6)
3.1406380562059946

& 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"

& 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 $. This is a version of flip id, where id is specialized from a -> a to (a -> b) -> (a -> b) which by the associativity of (->) is (a -> b) -> a -> b. flipping this yields a -> (a -> b) -> b which is the type signature of &

Examples

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

>>> sqrt $ [1 / n^2 | n <- [1..1000]] & sum & (*6)
3.1406380562059946

@since base-4.8.0.0

Postfix function application, for conveniently applying attributes. Unlike ($), (#) has a high precedence (8), so d # foo # bar can be combined with other things using operators like (|||) or (<>) without needing parentheses.

Helper to make code using records of clients more readable. Can be mixed with (/:) for supplying arguments. Example:

type Api = NamedRoutes RootApi

data RootApi mode = RootApi
{ subApi :: mode :- NamedRoutes SubApi
, …
} deriving Generic

data SubApi mode = SubApi
{ endpoint :: mode :- Get '[JSON] Person
, …
} deriving Generic

api :: Proxy API
api = Proxy

rootClient :: RootApi (AsClientT ClientM)
rootClient = client api

endpointClient :: ClientM Person
endpointClient = client // subApi // endpoint

Flipped version of ($).

& is a reverse application operator

Reverse function application which binds tighter than <$> and <*>. Useful for refining grammar specification.

<*> monoidalFieldAla "extensions"           (alaList' FSep MQuoted)       oldExtensions
^^^ deprecatedSince [1,12] "Please use 'default-extensions' or 'other-extensions' fields."

Field access, inspired by the lens library. This is merely reverse application, but allows us to write things like (1, 2)^._1 which is likely to be familiar to most Haskell programmers out there. Note that this is precisely equivalent to _1 (1, 2), but perhaps it reads a little nicer.

Left-associative apply operator. Read as "apply forward" or "pipe into". Use this to create long chains of computation that suggest which direction things move in.

>>> 3 |> succ |> recip |> negate
-0.25

Or use it anywhere you would use (&).

\ x -> (x |> f) == f x

\ x -> (x |> f |> g) == g (f x)

Function application. This function usually isn't necessary, but it can be more readable than some alternatives when used with higher-order functions like map.

>>> map (apply 2) [succ, recip, negate]
[3.0,0.5,-2.0]

In general you should prefer using an explicit lambda or operator section.

>>> map (\ f -> 2 |> f) [succ, recip, negate]
[3.0,0.5,-2.0]

>>> map (2 |>) [succ, recip, negate]
[3.0,0.5,-2.0]

>>> map (<| 2) [succ, recip, negate]
[3.0,0.5,-2.0]

\ x -> apply x f == f x

Left-associative apply' operator. Read as "strict apply forward" or "strict pipe into". Use this to create long chains of computation that suggest which direction things move in.

>>> 3 !> succ !> recip !> negate
-0.25

The difference between this and (|>) is that this evaluates its argument before passing it to the function.

>>> undefined |> const True
True

>>> undefined !> const True
*** Exception: Prelude.undefined
...

\ x -> (x !> f) == seq x (f x)

\ x -> (x !> f !> g) == let y = seq x (f x) in seq y (g y)

Strict function application. This function usually isn't necessary, but it can be more readable than some alternatives when used with higher-order functions like map.

>>> map (apply' 2) [succ, recip, negate]
[3.0,0.5,-2.0]

The different between this and apply is that this evaluates its argument before passing it to the function.

>>> apply undefined (const True)
True

>>> apply' undefined (const True)
*** Exception: Prelude.undefined
...

In general you should prefer using an explicit lambda or operator section.

>>> map (\ f -> 2 !> f) [succ, recip, negate]
[3.0,0.5,-2.0]

>>> map (2 !>) [succ, recip, negate]
[3.0,0.5,-2.0]

>>> map (<! 2) [succ, recip, negate]
[3.0,0.5,-2.0]

\ x -> apply' x f == seq x (f x)

& 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 $. This is a version of flip id, where id is specialized from a -> a to (a -> b) -> (a -> b) which by the associativity of (->) is (a -> b) -> a -> b. flipping this yields a -> (a -> b) -> b which is the type signature of &

Examples

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

>>> sqrt $ [1 / n^2 | n <- [1..1000]] & sum & (*6)
3.1406380562059946

Reverse function application. Allows convenient notation for setting properties. Example usage.

mkElement "div"
# set style     [("color","#CCAABB")]
# set draggable True
# set children  otherElements

The #-operator is the Haskell analog to the .-operator in JavaScript. Example:

grd # addColorStop(0, "#8ED6FF");

This can be seen as equivalent of grd.addColorStop(0, "#8ED6FF").

Operator for postfix notation (same as Data.Function.(&))

>>> 255 .@hex
"0x0000_0000_0000_00ff"

>>> 0xf1 .@bin
"0b1111_0001"

>>> 2^12 .@dec
"4096"

>>> 4 * giga .@pos1
[32]

0x0 .@color (bits 31 24)
0b0000_0000_0000_0000_0000_0000_0000_0000_1111_1111_0000_0000_0000_0000_0000_0000
^^^^ ^^^^

Hang on function application, a.k.a. non-operator version of &.

onApp = (&)

postfix function application (flip ($))

A flipped version of ($).

An operator that allows you to write C-style ternary conditionals of the form:

p ? t ?? f

Note that parentheses are required in order to chain sequences of conditionals together. This is probably a good thing.

($) is the function application operator. Applying ($) 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

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)

($) 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

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.