Alias for sequenceA

Alias for sequenceA_

Boolean "and", lazy in the second argument

& 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

Right-to-left composition of Kleisli arrows. (>=>), with the arguments flipped.

Note how this operator resembles function composition (.):

(.)   ::            (b ->   c) -> (a ->   b) -> a ->   c
(<=<) :: Monad m => (b -> m c) -> (a -> m b) -> a -> m c

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

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

Left-to-right composition of Kleisli arrows.

'(bs >=> cs) a' can be understood as the do expression

do b <- bs a
   cs b

or in terms of (>>=) as

bs a >>= cs

raise a number to a non-negative integral power

raise a number to an integral power

Boolean "or", lazy in the second argument

Strict version of <$>.

Since: base-4.8.0.0

An infix synonym for fmap.

The name of this operator is an allusion to $. Note the similarities between their types:

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

Whereas $ is function application, <$> is function application lifted over a Functor.

Examples

>>> show <$> Nothing
Nothing

>>> show <$> Just 3
Just "3"

>>> show <$> Left 17
Left 17

>>> show <$> Right 17
Right "17"

>>> (*2) <$> [1,2,3]
[2,4,6]

>>> even <$> (2,2)
(2,True)

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.

Computation getArgs returns a list of the program's command line arguments (not including the program name).

Computation getProgName returns the name of the program as it was invoked.

However, this is hard-to-impossible to implement on some non-Unix OSes, so instead, for maximum portability, we just return the leafname of the program as invoked. Even then there are some differences between platforms: on Windows, for example, a program invoked as foo is probably really FOO.EXE, and that is what getProgName will return.

Returns the absolute pathname of the current executable, or argv[0] if the operating system does not provide a reliable way query the current executable.

Note that for scripts and interactive sessions, this is the path to the interpreter (e.g. ghci.)

Since base 4.11.0.0, getExecutablePath resolves symlinks on Windows. If an executable is launched through a symlink, getExecutablePath returns the absolute path of the original executable.

If the executable has been deleted, behaviour is ill-defined and varies by operating system. See executablePath for a more reliable way to query the current executable.

Since: base-4.6.0.0

Return the value of the environment variable var, or Nothing if there is no such value.

For POSIX users, this is equivalent to getEnv.

Since: base-4.6.0.0

setEnv name value sets the specified environment variable to value.

Early versions of this function operated under the mistaken belief that setting an environment variable to the empty string on Windows removes that environment variable from the environment. For the sake of compatibility, it adopted that behavior on POSIX. In particular

setEnv name ""

has the same effect as

unsetEnv name

If you'd like to be able to set environment variables to blank strings, use setEnv.

Throws IOException if name is the empty string or contains an equals sign.

Beware that this function must not be executed concurrently with getEnv, lookupEnv, getEnvironment and such. One thread reading environment variables at the same time with another one modifying them can result in a segfault, see Setenv is not Thread Safe for discussion.

Since: base-4.7.0.0

unsetEnv name removes the specified environment variable from the environment of the current process.

Throws IOException if name is the empty string or contains an equals sign.

Beware that this function must not be executed concurrently with getEnv, lookupEnv, getEnvironment and such. One thread reading environment variables at the same time with another one modifying them can result in a segfault, see Setenv is not Thread Safe for discussion.

Since: base-4.7.0.0

withArgs args act - while executing action act, have getArgs return args.

withProgName name act - while executing action act, have getProgName return name.

getEnvironment retrieves the entire environment as a list of (key,value) pairs.

If an environment entry does not contain an '=' character, the key is the whole entry and the value is the empty string.

($) 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

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

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

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

Technical Remark (Representation Polymorphism)

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

Determines whether all elements of the structure satisfy the predicate.

Examples

>>> all (> 3) []
True

>>> all (> 3) [1,2]
False

>>> all (> 3) [1,2,3,4,5]
False

>>> all (> 3) [1..]
False

>>> all (> 3) [4..]
* Hangs forever *

A monoid on applicative functors.

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

• some v = (:) <$> v <*> many v

• many v = some v <|> pure []

Examples

>>> Nothing <|> Just 42
Just 42

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

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

and returns the conjunction of a container of Bools. For the result to be True, the container must be finite; False, however, results from a False value finitely far from the left end.

Examples

>>> and []
True

>>> and [True]
True

>>> and [False]
False

>>> and [True, True, False]
False

>>> and (False : repeat True) -- Infinite list [False,True,True,True,...
False

>>> and (repeat True)
* Hangs forever *

Determines whether any element of the structure satisfies the predicate.

Examples

>>> any (> 3) []
False

>>> any (> 3) [1,2]
False

>>> any (> 3) [1,2,3,4,5]
True

>>> any (> 3) [1..]
True

>>> any (> 3) [0, -1..]
* Hangs forever *

The computation appendFile file str function appends the string str, to the file file.

Note that writeFile and appendFile write a literal string to a file. To write a value of any printable type, as with print, use the show function to convert the value to a string first.

main = appendFile "squares" (show [(x,x*x) | x <- [0,0.1..2]])

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:

• u *> v = (id <$ u) <*> v

• u <* v = liftA2 const u v

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

• fmap f x = pure f <*> x

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

• pure = return

• m1 <*> m2 = m1 >>= (\x1 -> m2 >>= (\x2 -> return (x1 x2)))

• (*>) = (>>)

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

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.

The sum of a collection of actions using (<|>), generalizing concat.

asum is just like msum, but generalised to Alternative.

Examples

>>> asum [Just "Hello", Nothing, Just "World"]
Just "Hello"

The Bounded class is used to name the upper and lower limits of a type. Ord is not a superclass of Bounded since types that are not totally ordered may also have upper and lower bounds.

The Bounded class may be derived for any enumeration type; minBound is the first constructor listed in the data declaration and maxBound is the last. Bounded may also be derived for single-constructor datatypes whose constituent types are in Bounded.

break, applied to a predicate p and a list xs, returns a tuple where first element is longest prefix (possibly empty) of xs of elements that do not satisfy p and second element is the remainder of the list:

break p is equivalent to span (not . p) and consequently to (takeWhile (not . p) xs, dropWhile (not . p) xs), even if p is _|_.

Laziness

>>> break undefined []
([],[])

>>> fst (break (const True) undefined)
*** Exception: Prelude.undefined

>>> fst (break (const True) (undefined : undefined))
[]

>>> take 1 (fst (break (const False) (1 : undefined)))
[1]

>>> take 10 (fst (break (const False) [1..]))
[1,2,3,4,5,6,7,8,9,10]

Examples

>>> break (> 3) [1,2,3,4,1,2,3,4]
([1,2,3],[4,1,2,3,4])

>>> break (< 9) [1,2,3]
([],[1,2,3])

>>> break (> 9) [1,2,3]
([1,2,3],[])

Three kinds of buffering are supported: line-buffering, block-buffering or no-buffering. These modes have the following effects. For output, items are written out, or flushed, from the internal buffer according to the buffer mode:

• line-buffering: the entire output buffer is flushed whenever a newline is output, the buffer overflows, a hFlush is issued, or the handle is closed.
• block-buffering: the entire buffer is written out whenever it overflows, a hFlush is issued, or the handle is closed.
• no-buffering: output is written immediately, and never stored in the buffer.

An implementation is free to flush the buffer more frequently, but not less frequently, than specified above. The output buffer is emptied as soon as it has been written out.

Similarly, input occurs according to the buffer mode for the handle:

• line-buffering: when the buffer for the handle is not empty, the next item is obtained from the buffer; otherwise, when the buffer is empty, characters up to and including the next newline character are read into the buffer. No characters are available until the newline character is available or the buffer is full.
• block-buffering: when the buffer for the handle becomes empty, the next block of data is read into the buffer.
• no-buffering: the next input item is read and returned. The hLookAhead operation implies that even a no-buffered handle may require a one-character buffer.

The default buffering mode when a handle is opened is implementation-dependent and may depend on the file system object which is attached to that handle. For most implementations, physical files will normally be block-buffered and terminals will normally be line-buffered.

The character type Char represents Unicode codespace and its elements are code points as in definitions D9 and D10 of the Unicode Standard.

Character literals in Haskell are single-quoted: 'Q', 'Я' or 'Ω'. To represent a single quote itself use '\'', and to represent a backslash use '\\'. The full grammar can be found in the section 2.6 of the Haskell 2010 Language Report.

To specify a character by its code point one can use decimal, hexadecimal or octal notation: '\65', '\x41' and '\o101' are all alternative forms of 'A'. The largest code point is '\x10ffff'.

There is a special escape syntax for ASCII control characters:

Data.Char provides utilities to work with Char.

Map a function over all the elements of a container and concatenate the resulting lists.

Examples

>>> concatMap (take 3) [[1..], [10..], [100..], [1000..]]
[1,2,3,10,11,12,100,101,102,1000,1001,1002]

>>> concatMap (take 3) (Just [1..])
[1,2,3]

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

>>> const 42 "hello"
42

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

Convert an uncurried function to a curried function.

Examples

>>> curry fst 1 2
1

cycle ties a finite list into a circular one, or equivalently, the infinite repetition of the original list. It is the identity on infinite lists.

Examples

>>> cycle []
*** Exception: Prelude.cycle: empty list

>>> take 10 (cycle [42])
[42,42,42,42,42,42,42,42,42,42]

>>> take 10 (cycle [2, 5, 7])
[2,5,7,2,5,7,2,5,7,2]

>>> take 1 (cycle (42 : undefined))
[42]

The catMaybes function takes a list of Maybes and returns a list of all the Just values.

Examples

>>> catMaybes [Just 1, Nothing, Just 3]
[1,3]

>>> import GHC.Internal.Text.Read ( readMaybe )
>>> [readMaybe x :: Maybe Int | x <- ["1", "Foo", "3"] ]
[Just 1,Nothing,Just 3]
>>> catMaybes $ [readMaybe x :: Maybe Int | x <- ["1", "Foo", "3"] ]
[1,3]

The fromMaybe function takes a default value and a Maybe value. If the Maybe is Nothing, it returns the default value; otherwise, it returns the value contained in the Maybe.

Examples

>>> fromMaybe "" (Just "Hello, World!")
"Hello, World!"

>>> fromMaybe "" Nothing
""

>>> import GHC.Internal.Text.Read ( readMaybe )
>>> fromMaybe 0 (readMaybe "5")
5
>>> fromMaybe 0 (readMaybe "")
0

The isJust function returns True iff its argument is of the form Just _.

Examples

>>> isJust (Just 3)
True

>>> isJust (Just ())
True

>>> isJust Nothing
False

>>> isJust (Just Nothing)
True

The isNothing function returns True iff its argument is Nothing.

Examples

>>> isNothing (Just 3)
False

>>> isNothing (Just ())
False

>>> isNothing Nothing
True

>>> isNothing (Just Nothing)
False

The mapMaybe function is a version of map which can throw out elements. In particular, the functional argument returns something of type Maybe b. If this is Nothing, no element is added on to the result list. If it is Just b, then b is included in the result list.

Examples

>>> import GHC.Internal.Text.Read ( readMaybe )
>>> let readMaybeInt = readMaybe :: String -> Maybe Int
>>> mapMaybe readMaybeInt ["1", "Foo", "3"]
[1,3]
>>> catMaybes $ map readMaybeInt ["1", "Foo", "3"]
[1,3]

>>> mapMaybe Just [1,2,3]
[1,2,3]

Double-precision floating point numbers. It is desirable that this type be at least equal in range and precision to the IEEE double-precision type.