Documentation

One or none.

It is useful for modelling any computation that is allowed to fail.

Examples

>>> import Control.Monad.Except

>>> canFail = throwError "it failed" :: Except String Int
>>> final = return 42                :: Except String Int

>>> runExcept $ canFail *> final
Left "it failed"

>>> runExcept $ optional canFail *> final
Right 42

Collects the list of elements of a structure, from left to right.

Examples

>>> biList (18, 42)
[18,42]

>>> biList (Left 18)
[18]

Since: base-4.10.0.0

Determines whether all elements of the structure satisfy their appropriate predicate argument. Empty structures yield True.

Examples

>>> biall even isDigit (27, 't')
False

>>> biall even isDigit (26, '8')
True

>>> biall even isDigit (Left 27)
False

>>> biall even isDigit (Left 26)
True

>>> biall even isDigit (BiList [26, 52] ['3', '8'])
True

>>> biall even isDigit (BiList [] [])
True

Since: base-4.10.0.0

biand 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

>>> biand (True, False)
False

>>> biand (True, True)
True

>>> biand (Left True)
True

>>> biand (BiList [] [])
True

>>> biand (BiList [True, True, False, True] (repeat True))
False

> biand (BiList (repeat True) [False])
* Hangs forever *

> biand (BiList (repeat True) [])
* Hangs forever *

Since: base-4.10.0.0

Determines whether any element of the structure satisfies its appropriate predicate argument. Empty structures yield False.

Examples

>>> biany even isDigit (27, 't')
False

>>> biany even isDigit (27, '8')
True

>>> biany even isDigit (26, 't')
True

>>> biany even isDigit (Left 27)
False

>>> biany even isDigit (Left 26)
True

>>> biany even isDigit (BiList [27, 53] ['t', '8'])
True

>>> biany even isDigit (BiList [] [])
False

Since: base-4.10.0.0

The sum of a collection of actions, generalizing biconcat.

Examples

>>> biasum (Nothing, Nothing)
Nothing

>>> biasum (Nothing, Just 42)
Just 42

>>> biasum (Just 18, Nothing)
Just 18

>>> biasum (Just 18, Just 42)
Just 18

Since: base-4.10.0.0

Does the element occur in the structure?

Examples

>>> bielem 42 (17, 42)
True

>>> bielem 42 (17, 43)
False

>>> bielem 42 (Left 42)
True

>>> bielem 42 (Right 13)
False

>>> bielem 42 (BiList [1..5] [1..100])
True

>>> bielem 42 (BiList [1..5] [1..41])
False

Since: base-4.10.0.0

The bifind function takes a predicate and a structure and returns the leftmost element of the structure matching the predicate, or Nothing if there is no such element.

Examples

>>> bifind even (27, 53)
Nothing

>>> bifind even (27, 52)
Just 52

>>> bifind even (26, 52)
Just 26

>>> bifind even (BiList [] [])
Nothing

Since: base-4.10.0.0

As bifoldl, but strict in the result of the reduction functions at each step.

This ensures that each step of the bifold is forced to weak head normal form before being applied, avoiding the collection of thunks that would otherwise occur. This is often what you want to strictly reduce a finite structure to a single, monolithic result (e.g., bilength).

Since: base-4.10.0.0

Left associative monadic bifold over a structure.

Examples

>>> bifoldlM (\a b -> print b >> pure a) (\a c -> print (show c) >> pure a) 42 ("Hello", True)
"Hello"
"True"
42

>>> bifoldlM (\a b -> print b >> pure a) (\a c -> print (show c) >> pure a) 42 (Right True)
"True"
42

>>> bifoldlM (\a b -> print b >> pure a) (\a c -> print (show c) >> pure a) 42 (Left "Hello")
"Hello"
42

Since: base-4.10.0.0

As bifoldr, but strict in the result of the reduction functions at each step.

Since: base-4.10.0.0

Right associative monadic bifold over a structure.

Since: base-4.10.0.0

As bitraverse_, but with the structure as the primary argument. For a version that doesn't ignore the results, see bifor.

Examples

>>> bifor_ ("Hello", True) print (print . show)
"Hello"
"True"

>>> bifor_ (Right True) print (print . show)
"True"

>>> bifor_ (Left "Hello") print (print . show)
"Hello"

Since: base-4.10.0.0

Returns the size/length of a finite structure as an Int.

Examples

>>> bilength (True, 42)
2

>>> bilength (Right 42)
1

>>> bilength (BiList [1,2,3] [4,5])
5

>>> bilength (BiList [] [])
0

> bilength (BiList [1..] [])
* Hangs forever *

Since: base-4.10.0.0

Test whether the structure is empty.

Examples

>>> binull (18, 42)
False

>>> binull (Right 42)
False

>>> binull (BiList [] [])
True

Since: base-4.10.0.0

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

Examples

>>> bior (True, False)
True

>>> bior (False, False)
False

>>> bior (Left True)
True

>>> bior (BiList [] [])
False

>>> bior (BiList [False, False, True, False] (repeat False))
True

> bior (BiList (repeat False) [True])
* Hangs forever *

> bior (BiList (repeat False) [])
* Hangs forever *

Since: base-4.10.0.0

Evaluate each action in the structure from left to right, and ignore the results. For a version that doesn't ignore the results, see bisequence.

Examples

>>> bisequence_ (print "Hello", print "World")
"Hello"
"World"

>>> bisequence_ (Left (print "Hello"))
"Hello"

>>> bisequence_ (Right (print "World"))
"World"

Since: base-4.10.0.0

Map each element of a structure using one of two actions, evaluate these actions from left to right, and ignore the results. For a version that doesn't ignore the results, see bitraverse.

Examples

>>> bitraverse_ print (print . show) ("Hello", True)
"Hello"
"True"

>>> bitraverse_ print (print . show) (Right True)
"True"

>>> bitraverse_ print (print . show) (Left "Hello")
"Hello"

Since: base-4.10.0.0

A default definition of bifoldMap in terms of the Bitraversable operations.

bifoldMapDefault f g ≡
    getConst . bitraverse (Const . f) (Const . g)

Since: base-4.10.0.0

bifor is bitraverse with the structure as the first argument. For a version that ignores the results, see bifor_.

Examples

>>> bifor (Left []) listToMaybe (find even)
Nothing

>>> bifor (Left [1, 2, 3]) listToMaybe (find even)
Just (Left 1)

>>> bifor (Right [4, 5]) listToMaybe (find even)
Just (Right 4)

>>> bifor ([1, 2, 3], [4, 5]) listToMaybe (find even)
Just (1,4)

>>> bifor ([], [4, 5]) listToMaybe (find even)
Nothing

Since: base-4.10.0.0

A default definition of bimap in terms of the Bitraversable operations.

bimapDefault f g ≡
     runIdentity . bitraverse (Identity . f) (Identity . g)

Since: base-4.10.0.0

Sequences all the actions in a structure, building a new structure with the same shape using the results of the actions. For a version that ignores the results, see bisequence_.

bisequence ≡ bitraverse id id

Examples

>>> bisequence (Just 4, Nothing)
Nothing

>>> bisequence (Just 4, Just 5)
Just (4,5)

>>> bisequence ([1, 2, 3], [4, 5])
[(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)]

Since: base-4.10.0.0

This is >$ with its arguments flipped.

This is an infix version of contramap with the arguments flipped.

This is an infix alias for contramap.

Compare using compare.

Check for equivalence with ==.

Note: The instances for Double and Float violate reflexivity for NaN.

If f is both Functor and Contravariant then by the time you factor in the laws of each of those classes, it can't actually use its argument in any meaningful capacity.

This method is surprisingly useful. Where both instances exist and are lawful we have the following laws:

fmap      f ≡ phantom
contramap f ≡ phantom

nonEmpty efficiently turns a normal list into a NonEmpty stream, producing Nothing if the input is empty.

A generalization of cycle to an arbitrary Semigroup. May fail to terminate for some values in some semigroups.

Examples

>>> take 10 $ cycle1 [1, 2, 3]
[1,2,3,1,2,3,1,2,3,1]

>>> cycle1 (Right 1)
Right 1

>>> cycle1 (Left 1)
* Hangs forever *

Repeat a value n times.

mtimesDefault n a = a <> a <> ... <> a  -- using <> (n-1) times

In many cases, stimes 0 a for a Monoid will produce mempty. However, there are situations when it cannot do so. In particular, the following situation is fairly common:

data T a = ...

class Constraint1 a
class Constraint1 a => Constraint2 a

instance Constraint1 a => Semigroup (T a)
instance Constraint2 a => Monoid (T a)

Since Constraint1 is insufficient to implement mempty, stimes for T a cannot do so.

When working with such a type, or when working polymorphically with Semigroup instances, mtimesDefault should be used when the multiplier might be zero. It is implemented using stimes when the multiplier is nonzero and mempty when it is zero.

Examples

>>> mtimesDefault 0 "bark"
""

>>> mtimesDefault 3 "meow"
"meowmeowmeow"

O(n). Convert a ShortByteString into a ByteString.

O(n). Convert a ByteString into a ShortByteString.

This makes a copy, so does not retain the input string.

Deeply stream the contents of the given directory.

This works the same as sourceDirectory, but will not return directories at all. This function also takes an extra parameter to indicate whether symlinks will be followed.

Since: conduit-1.3.0

Flatten out a stream by yielding the values contained in an incoming MonoFoldable as individually yielded values.

Since: conduit-1.3.0

A monadic strict left fold.

Since: conduit-1.3.0

Apply a monadic transformation to all values in a stream.

If you do not need the transformed values, and instead just want the monadic side-effects of running the action, see mapM_.

Since: conduit-1.3.0

Combine two Conduits together into a new Conduit (aka fuse).

Output from the upstream (left) conduit will be fed into the downstream (right) conduit. Processing will terminate when downstream (right) returns. Leftover data returned from the right Conduit will be discarded.

Equivalent to fuse and =$=, however the latter is deprecated and will be removed in a future version.

Note that, while this operator looks like categorical composition (from Control.Category), there are a few reasons it's different:

• The position of the type parameters to ConduitT do not match. We would need to change ConduitT i o m r to ConduitT r m i o, which would preclude a Monad or MonadTrans instance.
• The result value from upstream and downstream are allowed to differ between upstream and downstream. In other words, we would need the type signature here to look like ConduitT a b m r -> ConduitT b c m r -> ConduitT a c m r.
• Due to leftovers, we do not have a left identity in Conduit. This can be achieved with the underlying Pipe datatype, but this is not generally recommended. See https://stackoverflow.com/a/15263700.

Since: conduit-1.2.8

Run a pipeline which acquires resources with ResourceT, and then run the ResourceT transformer. This is equivalent to runResourceT . runConduit.

Since: conduit-1.2.8

Combine two paths with a path separator. If the second path starts with a path separator or a drive letter, then it returns the second. The intention is that readFile (dir </> file) will access the same file as setCurrentDirectory dir; readFile file.

Posix:   "/directory" </> "file.ext" == "/directory/file.ext"
Windows: "/directory" </> "file.ext" == "/directory\\file.ext"
         "directory" </> "/file.ext" == "/file.ext"
Valid x => (takeDirectory x </> takeFileName x) `equalFilePath` x

Combined:

Posix:   "/" </> "test" == "/test"
Posix:   "home" </> "bob" == "home/bob"
Posix:   "x:" </> "foo" == "x:/foo"
Windows: "C:\\foo" </> "bar" == "C:\\foo\\bar"
Windows: "home" </> "bob" == "home\\bob"

Not combined:

Posix:   "home" </> "/bob" == "/bob"
Windows: "home" </> "C:\\bob" == "C:\\bob"

Not combined (tricky):

On Windows, if a filepath starts with a single slash, it is relative to the root of the current drive. In [1], this is (confusingly) referred to as an absolute path. The current behavior of </> is to never combine these forms.

Windows: "home" </> "/bob" == "/bob"
Windows: "home" </> "\\bob" == "\\bob"
Windows: "C:\\home" </> "\\bob" == "\\bob"

On Windows, from [1]: "If a file name begins with only a disk designator but not the backslash after the colon, it is interpreted as a relative path to the current directory on the drive with the specified letter." The current behavior of </> is to never combine these forms.

Windows: "D:\\foo" </> "C:bar" == "C:bar"
Windows: "C:\\foo" </> "C:bar" == "C:bar"

Drop the filename. Unlike takeDirectory, this function will leave a trailing path separator on the directory.

dropFileName "/directory/file.ext" == "/directory/"
dropFileName x == fst (splitFileName x)
isPrefixOf (takeDrive x) (dropFileName x)

Contract a filename, based on a relative path. Note that the resulting path will never introduce .. paths, as the presence of symlinks means ../b may not reach a/b if it starts from a/c. For a worked example see this blog post.

The corresponding makeAbsolute function can be found in System.Directory.

         makeRelative "/directory" "/directory/file.ext" == "file.ext"
         Valid x => makeRelative (takeDirectory x) x `equalFilePath` takeFileName x
         makeRelative x x == "."
         Valid x y => equalFilePath x y || (isRelative x && makeRelative y x == x) || equalFilePath (y </> makeRelative y x) x
Windows: makeRelative "C:\\Home" "c:\\home\\bob" == "bob"
Windows: makeRelative "C:\\Home" "c:/home/bob" == "bob"
Windows: makeRelative "C:\\Home" "D:\\Home\\Bob" == "D:\\Home\\Bob"
Windows: makeRelative "C:\\Home" "C:Home\\Bob" == "C:Home\\Bob"
Windows: makeRelative "/Home" "/home/bob" == "bob"
Windows: makeRelative "/" "//" == "//"
Posix:   makeRelative "/Home" "/home/bob" == "/home/bob"
Posix:   makeRelative "/home/" "/home/bob/foo/bar" == "bob/foo/bar"
Posix:   makeRelative "/fred" "bob" == "bob"
Posix:   makeRelative "/file/test" "/file/test/fred" == "fred"
Posix:   makeRelative "/file/test" "/file/test/fred/" == "fred/"
Posix:   makeRelative "some/path" "some/path/a/b/c" == "a/b/c"

Split a filename into directory and file. </> is the inverse. The first component will often end with a trailing slash.

splitFileName "/directory/file.ext" == ("/directory/","file.ext")
Valid x => uncurry (</>) (splitFileName x) == x || fst (splitFileName x) == "./"
Valid x => isValid (fst (splitFileName x))
splitFileName "file/bob.txt" == ("file/", "bob.txt")
splitFileName "file/" == ("file/", "")
splitFileName "bob" == ("./", "bob")
Posix:   splitFileName "/" == ("/","")
Windows: splitFileName "c:" == ("c:","")
Windows: splitFileName "\\\\?\\A:\\fred" == ("\\\\?\\A:\\","fred")
Windows: splitFileName "\\\\?\\A:" == ("\\\\?\\A:","")

($) 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

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.

(++) 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

Examples

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

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

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

Right to left function composition.

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

f . id = f = id . f

Examples

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

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

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

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

>>> (<**>) (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]}

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

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

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

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 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]

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

flip f x y = f y x

flip . flip = id

Examples

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

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

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

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

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

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

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

>>> 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

atomically :: STM a -> IO a

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

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

Lift a ternary function to actions.

\(\mathcal{O}(n)\). 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

>>> 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]

The fromEnum method restricted to the type Char.

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

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

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

Conditional execution of Applicative expressions. For example,

Examples

when debug (putStrLn "Debugging")

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

Attempt to convert an Integral type a to an Integral type b using the size of the types as measured by Bits methods.

A simpler version of this function is:

toIntegral :: (Integral a, Integral b) => a -> Maybe b
toIntegral x
  | toInteger x == toInteger y = Just y
  | otherwise                  = Nothing
  where
    y = fromIntegral x

This version requires going through Integer, which can be inefficient. However, toIntegralSized is optimized to allow GHC to statically determine the relative type sizes (as measured by bitSizeMaybe and isSigned) and avoid going through Integer for many types. (The implementation uses fromIntegral, which is itself optimized with rules for base types but may go through Integer for some type pairs.)

Since: base-4.8.0.0

The toEnum method restricted to the type Char.

Exception handling within STM actions.

catchSTM m f catches any exception thrown by m using throwSTM, using the function f to handle the exception. If an exception is thrown, any changes made by m are rolled back, but changes prior to m persist.

Returns the number of Haskell threads that can run truly simultaneously (on separate physical processors) at any given time. To change this value, use setNumCapabilities.

Since: base-4.4.0.0

Create a new TVar holding a value supplied

Return the current value stored in a TVar.

A variant of throw that can only be used within the STM monad.

Throwing an exception in STM aborts the transaction and propagates the exception. If the exception is caught via catchSTM, only the changes enclosed by the catch are rolled back; changes made outside of catchSTM persist.

If the exception is not caught inside of the STM, it is re-thrown by atomically, and the entire STM is rolled back.

Although throwSTM has a type that is an instance of the type of throw, the two functions are subtly different:

throw e    `seq` x  ===> throw e
throwSTM e `seq` x  ===> x

The first example will cause the exception e to be raised, whereas the second one won't. In fact, throwSTM will only cause an exception to be raised when it is used within the STM monad. The throwSTM variant should be used in preference to throw to raise an exception within the STM monad because it guarantees ordering with respect to other STM operations, whereas throw does not.

Write the supplied value into a TVar.

Right-to-left composition. This is a synonym for (.), but it can be useful to make the order of composition more apparent.

Left-to-right composition. This is useful if you want to write a morphism as a pipeline going from left to right.

Strict version of <$>.

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

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

This generalizes the list-based filter function.

runIdentity (filterM (Identity . p) xs) == filter p xs

Examples

>>> filterM (\x -> do
      putStrLn ("Keep: " ++ show x ++ "?")
      answer <- getLine
      pure (answer == "y"))
    [1, 2, 3]
Keep: 1?
y
Keep: 2?
n
Keep: 3?
y
[1,3]

>>> filterM (\x -> do
      putStr (show x)
      x' <- readLn
      pure (x == x'))
    [1, 2, 3]
12
22
33
[2,3]

Repeat an action indefinitely.

Examples

echoServer :: Socket -> IO ()
echoServer socket = forever $ do
  client <- accept socket
  forkFinally (echo client) (\_ -> hClose client)
  where
    echo :: Handle -> IO ()
    echo client = forever $
      hGetLine client >>= hPutStrLn client

Conditional failure of Alternative computations. Defined by

guard True  = pure ()
guard False = empty

Examples

>>> safeDiv 4 0
Nothing

>>> safeDiv 4 2
Just 2

safeDiv :: Int -> Int -> Maybe Int
safeDiv x y | y /= 0    = Just (x `div` y)
            | otherwise = Nothing

safeDiv :: Int -> Int -> Maybe Int
safeDiv x y = do
  guard (y /= 0)
  return (x `div` y)

The mapAndUnzipM function maps its first argument over a list, returning the result as a pair of lists. This function is mainly used with complicated data structures or a state monad.

Direct MonadPlus equivalent of filter.

Examples

filter = ( mfilter :: (a -> Bool) -> [a] -> [a] )

>>> mfilter odd (Just 1)
Just 1
>>> mfilter odd (Just 2)
Nothing

replicateM n act performs the action act n times, and then returns the list of results.

replicateM n (pure x) == replicate n x

Examples

>>> replicateM 3 getLine
hi
heya
hiya
["hi","heya","hiya"]

>>> import Control.Monad.State
>>> runState (replicateM 3 $ state $ \s -> (s, s + 1)) 1
([1,2,3],4)

Like replicateM, but discards the result.

Examples

>>> replicateM_ 3 (putStr "a")
aaa

The reverse of when.

Examples

>>> do x <- getLine
       unless (x == "hi") (putStrLn "hi!")
comingupwithexamplesisdifficult
hi!

>>> unless (pi > exp 1) Nothing
Just ()

The zipWithM function generalizes zipWith to arbitrary applicative functors.

zipWithM_ is the extension of zipWithM which ignores the final result.

Case analysis for the Bool type. bool f t p evaluates to f when p is False, and evaluates to t when p is True.

This is equivalent to if p then t else f; that is, one can think of it as an if-then-else construct with its arguments reordered.

Examples

>>> bool "foo" "bar" True
"bar"
>>> bool "foo" "bar" False
"foo"

>>> let p = True; f = "bar"; t = "foo"
>>> bool f t p == if p then t else f
True
>>> let p = False
>>> bool f t p == if p then t else f
True

Since: base-4.7.0.0

Case analysis for the Either type. If the value is Left a, apply the first function to a; if it is Right b, apply the second function to b.

Examples

>>> let s = Left "foo" :: Either String Int
>>> let n = Right 3 :: Either String Int
>>> either length (*2) s
3
>>> either length (*2) n
6

Return the contents of a Left-value or a default value otherwise.

Examples

>>> fromLeft 1 (Left 3)
3
>>> fromLeft 1 (Right "foo")
1

Since: base-4.10.0.0

Return the contents of a Right-value or a default value otherwise.

Examples

>>> fromRight 1 (Right 3)
3
>>> fromRight 1 (Left "foo")
1

Since: base-4.10.0.0

Return True if the given value is a Left-value, False otherwise.

Examples

>>> isLeft (Left "foo")
True
>>> isLeft (Right 3)
False

>>> import Control.Monad ( when )
>>> let report e = when (isLeft e) $ putStrLn "ERROR"
>>> report (Right 1)
>>> report (Left "parse error")
ERROR

Since: base-4.7.0.0

Return True if the given value is a Right-value, False otherwise.

Examples

>>> isRight (Left "foo")
False
>>> isRight (Right 3)
True

>>> import Control.Monad ( when )
>>> let report e = when (isRight e) $ putStrLn "SUCCESS"
>>> report (Left "parse error")
>>> report (Right 1)
SUCCESS

Since: base-4.7.0.0

Extracts from a list of Either all the Left elements. All the Left elements are extracted in order.

Examples

>>> let list = [ Left "foo", Right 3, Left "bar", Right 7, Left "baz" ]
>>> lefts list
["foo","bar","baz"]

Partitions a list of Either into two lists. All the Left elements are extracted, in order, to the first component of the output. Similarly the Right elements are extracted to the second component of the output.

Examples

>>> let list = [ Left "foo", Right 3, Left "bar", Right 7, Left "baz" ]
>>> partitionEithers list
(["foo","bar","baz"],[3,7])

>>> let list = [ Left "foo", Right 3, Left "bar", Right 7, Left "baz" ]
>>> partitionEithers list == (lefts list, rights list)
True

Extracts from a list of Either all the Right elements. All the Right elements are extracted in order.

Examples

>>> let list = [ Left "foo", Right 3, Left "bar", Right 7, Left "baz" ]
>>> rights list
[3,7]

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 *

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 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 concatenation of all the elements of a container of lists.

Examples

>>> concat (Just [1, 2, 3])
[1,2,3]

>>> concat (Left 42)
[]

>>> concat [[1, 2, 3], [4, 5], [6], []]
[1,2,3,4,5,6]

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]

The find function takes a predicate and a structure and returns the leftmost element of the structure matching the predicate, or Nothing if there is no such element.

Examples

>>> find (> 42) [0, 5..]
Just 45

>>> find (> 12) [1..7]
Nothing

Left-to-right monadic fold over the elements of a structure.

Given a structure t with elements (a, b, ..., w, x, y), the result of a fold with an operator function f is equivalent to:

foldlM f z t = do
    aa <- f z a
    bb <- f aa b
    ...
    xx <- f ww x
    yy <- f xx y
    return yy -- Just @return z@ when the structure is empty

For a Monad m, given two functions f1 :: a -> m b and f2 :: b -> m c, their Kleisli composition (f1 >=> f2) :: a -> m c is defined by:

(f1 >=> f2) a = f1 a >>= f2

Another way of thinking about foldlM is that it amounts to an application to z of a Kleisli composition:

foldlM f z t =
    flip f a >=> flip f b >=> ... >=> flip f x >=> flip f y $ z

The monadic effects of foldlM are sequenced from left to right.

If at some step the bind operator (>>=) short-circuits (as with, e.g., mzero in a MonadPlus), the evaluated effects will be from an initial segment of the element sequence. If you want to evaluate the monadic effects in right-to-left order, or perhaps be able to short-circuit after processing a tail of the sequence of elements, you'll need to use foldrM instead.

If the monadic effects don't short-circuit, the outermost application of f is to the rightmost element y, so that, ignoring effects, the result looks like a left fold:

((((z `f` a) `f` b) ... `f` w) `f` x) `f` y

Examples

>>> let f a e = do { print e ; return $ e : a }
>>> foldlM f [] [0..3]
0
1
2
3
[3,2,1,0]

forM_ is mapM_ with its arguments flipped. For a version that doesn't ignore the results see forM.

forM_ is just like for_, but specialised to monadic actions.

for_ is traverse_ with its arguments flipped. For a version that doesn't ignore the results see for. This is forM_ generalised to Applicative actions.

for_ is just like forM_, but generalised to Applicative actions.

Examples

>>> for_ [1..4] print
1
2
3
4

Map each element of a structure to a monadic action, evaluate these actions from left to right, and ignore the results. For a version that doesn't ignore the results see mapM.

mapM_ is just like traverse_, but specialised to monadic actions.

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

Examples

>>> or []
False

>>> or [True]
True

>>> or [False]
False

>>> or [True, True, False]
True

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

>>> or (repeat False)
* Hangs forever *

Evaluate each action in the structure from left to right, and ignore the results. For a version that doesn't ignore the results see sequenceA.

sequenceA_ is just like sequence_, but generalised to Applicative actions.

Examples

>>> sequenceA_ [print "Hello", print "world", print "!"]
"Hello"
"world"
"!"

Evaluate each monadic action in the structure from left to right, and ignore the results. For a version that doesn't ignore the results see sequence.

sequence_ is just like sequenceA_, but specialised to monadic actions.

Map each element of a structure to an Applicative action, evaluate these actions from left to right, and ignore the results. For a version that doesn't ignore the results see traverse.

traverse_ is just like mapM_, but generalised to Applicative actions.

Examples

>>> traverse_ print ["Hello", "world", "!"]
"Hello"
"world"
"!"

& 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

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

When f is strict, this means that because, by the definition of strictness, f ⊥ = ⊥ and such the least defined fixed point of any strict function is ⊥.

Examples

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

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

>>> take 10 $ fix (0:)
[0,0,0,0,0,0,0,0,0,0]

>>> map (fix (\rec n -> if n < 2 then n else rec (n - 1) + rec (n - 2))) [1..10]
[1,1,2,3,5,8,13,21,34,55]

Implementation Details

fix f = let x = f x in x

fix f = f (fix f)

on b u x y runs the binary function b on the results of applying unary function u to two arguments x and y. From the opposite perspective, it transforms two inputs and combines the outputs.

(op `on` f) x y = f x `op` f y

Examples

>>> sortBy (compare `on` length) [[0, 1, 2], [0, 1], [], [0]]
[[],[0],[0,1],[0,1,2]]

>>> ((+) `on` length) [1, 2, 3] [-1]
4

>>> ((,) `on` (*2)) 2 3
(4,6)

Algebraic properties

Flipped version of <$.

Examples

>>> Nothing $> "foo"
Nothing

>>> Just 90210 $> "foo"
Just "foo"

>>> Left 8675309 $> "foo"
Left 8675309

>>> Right 8675309 $> "foo"
Right "foo"

>>> [1,2,3] $> "foo"
["foo","foo","foo"]

>>> (1,2) $> "foo"
(1,"foo")

Since: base-4.7.0.0

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)

Flipped version of <$>.

(<&>) = flip fmap

Examples

>>> Just 2 <&> (+1)
Just 3

>>> [1,2,3] <&> (+1)
[2,3,4]

>>> Right 3 <&> (+1)
Right 4

Since: base-4.11.0.0

void value discards or ignores the result of evaluation, such as the return value of an IO action.

Examples

>>> void Nothing
Nothing

>>> void (Just 3)
Just ()

>>> void (Left 8675309)
Left 8675309

>>> void (Right 8675309)
Right ()

>>> void [1,2,3]
[(),(),()]

>>> void (1,2)
(1,())

>>> mapM print [1,2]
1
2
[(),()]

>>> void $ mapM print [1,2]
1
2

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 listToMaybe function returns Nothing on an empty list or Just a where a is the first element of the list.

Examples

>>> listToMaybe []
Nothing

>>> listToMaybe [9]
Just 9

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

>>> maybeToList $ listToMaybe [5]
[5]
>>> maybeToList $ listToMaybe []
[]

>>> maybeToList $ listToMaybe [1,2,3]
[1]

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]

The maybe function takes a default value, a function, and a Maybe value. If the Maybe value is Nothing, the function returns the default value. Otherwise, it applies the function to the value inside the Just and returns the result.

Examples

>>> maybe False odd (Just 3)
True

>>> maybe False odd Nothing
False

>>> import GHC.Internal.Text.Read ( readMaybe )
>>> maybe 0 (*2) (readMaybe "5")
10
>>> maybe 0 (*2) (readMaybe "")
0

>>> maybe "" show (Just 5)
"5"
>>> maybe "" show Nothing
""

The maybeToList function returns an empty list when given Nothing or a singleton list when given Just.

Examples

>>> maybeToList (Just 7)
[7]

>>> maybeToList Nothing
[]

>>> import GHC.Internal.Text.Read ( readMaybe )
>>> sum $ maybeToList (readMaybe "3")
3
>>> sum $ maybeToList (readMaybe "")
0

The genericDrop function is an overloaded version of drop, which accepts any Integral value as the number of elements to drop.

\(\mathcal{O}(n)\). The genericLength function is an overloaded version of length. In particular, instead of returning an Int, it returns any type which is an instance of Num. It is, however, less efficient than length.

Examples

>>> genericLength [1, 2, 3] :: Int
3
>>> genericLength [1, 2, 3] :: Float
3.0

>>> genericLength [1..200] :: Int8
-56

The genericReplicate function is an overloaded version of replicate, which accepts any Integral value as the number of repetitions to make.

The genericSplitAt function is an overloaded version of splitAt, which accepts any Integral value as the position at which to split.

The genericTake function is an overloaded version of take, which accepts any Integral value as the number of elements to take.

The group function takes a list and returns a list of lists such that the concatenation of the result is equal to the argument. Moreover, each sublist in the result is non-empty, all elements are equal to the first one, and consecutive equal elements of the input end up in the same element of the output list.

group is a special case of groupBy, which allows the programmer to supply their own equality test.

It's often preferable to use Data.List.NonEmpty.group, which provides type-level guarantees of non-emptiness of inner lists. A common idiom to squash repeating elements map head . group is better served by map Data.List.NonEmpty.head . Data.List.NonEmpty.group because it avoids partial functions.

Examples

>>> group "Mississippi"
["M","i","ss","i","ss","i","pp","i"]

>>> group [1, 1, 1, 2, 2, 3, 4, 5, 5]
[[1,1,1],[2,2],[3],[4],[5,5]]

The inits function returns all initial segments of the argument, shortest first.

inits is semantically equivalent to map reverse . scanl (flip (:)) [], but under the hood uses a queue to amortize costs of reverse.

Laziness

Examples

>>> inits "abc"
["","a","ab","abc"]

>>> inits []
[[]]

>>> take 5 $ inits [1..]
[[],[1],[1,2],[1,2,3],[1,2,3,4]]

intercalate xs xss is equivalent to (concat (intersperse xs xss)). It inserts the list xs in between the lists in xss and concatenates the result.

Laziness

>>> take 5 (intercalate undefined ("Lorem" : undefined))
"Lorem"

>>> take 6 (intercalate ", " ("Lorem" : undefined))
"Lorem*** Exception: Prelude.undefined

Examples

>>> intercalate ", " ["Lorem", "ipsum", "dolor"]
"Lorem, ipsum, dolor"

>>> intercalate [0, 1] [[2, 3], [4, 5, 6], []]
[2,3,0,1,4,5,6,0,1]

>>> intercalate [1, 2, 3] [[], []]
[1,2,3]

\(\mathcal{O}(n)\). The intersperse function takes an element and a list and `intersperses' that element between the elements of the list.

Laziness

>>> take 1 (intersperse undefined ('a' : undefined))
"a"

>>> take 2 (intersperse ',' ('a' : undefined))
"a*** Exception: Prelude.undefined

Examples

>>> intersperse ',' "abcde"
"a,b,c,d,e"

>>> intersperse 1 [3, 4, 5]
[3,1,4,1,5]

\(\mathcal{O}(\min(m,n))\). The isPrefixOf function takes two lists and returns True iff the first list is a prefix of the second.

Examples

>>> "Hello" `isPrefixOf` "Hello World!"
True

>>> "Hello" `isPrefixOf` "Wello Horld!"
False

>>> [0..] `isPrefixOf` [1..]
False

>>> [0..] `isPrefixOf` [0..99]
False

>>> [0..99] `isPrefixOf` [0..]
True

>>> [0..] `isPrefixOf` [0..]
* Hangs forever *

>>> isPrefixOf [] undefined
True

The permutations function returns the list of all permutations of the argument.

Note that the order of permutations is not lexicographic. It satisfies the following property:

map (take n) (take (product [1..n]) (permutations ([1..n] ++ undefined))) == permutations [1..n]

Laziness

Examples

>>> permutations "abc"
["abc","bac","cba","bca","cab","acb"]

>>> permutations [1, 2]
[[1,2],[2,1]]

>>> permutations []
[[]]

>>> take 6 $ map (take 3) $ permutations ['a'..]
["abc","bac","cba","bca","cab","acb"]

The sort function implements a stable sorting algorithm. It is a special case of sortBy, which allows the programmer to supply their own comparison function.

Elements are arranged from lowest to highest, keeping duplicates in the order they appeared in the input.

The argument must be finite.

Examples

>>> sort [1,6,4,3,2,5]
[1,2,3,4,5,6]

>>> sort "haskell"
"aehklls"

>>> import Data.Semigroup(Arg(..))
>>> sort [Arg ":)" 0, Arg ":D" 0, Arg ":)" 1, Arg ":3" 0, Arg ":D" 1]
[Arg ":)" 0,Arg ":)" 1,Arg ":3" 0,Arg ":D" 0,Arg ":D" 1]

The sortBy function is the non-overloaded version of sort. The argument must be finite.

The supplied comparison relation is supposed to be reflexive and antisymmetric, otherwise, e. g., for _ _ -> GT, the ordered list simply does not exist. The relation is also expected to be transitive: if it is not then sortBy might fail to find an ordered permutation, even if it exists.

Examples

>>> sortBy (\(a,_) (b,_) -> compare a b) [(2, "world"), (4, "!"), (1, "Hello")]
[(1,"Hello"),(2,"world"),(4,"!")]

Sort a list by comparing the results of a key function applied to each element. sortOn f is equivalent to sortBy (comparing f), but has the performance advantage of only evaluating f once for each element in the input list. This is called the decorate-sort-undecorate paradigm, or Schwartzian transform.

Elements are arranged from lowest to highest, keeping duplicates in the order they appeared in the input.

The argument must be finite.

Examples

>>> sortOn fst [(2, "world"), (4, "!"), (1, "Hello")]
[(1,"Hello"),(2,"world"),(4,"!")]

>>> sortOn length ["jim", "creed", "pam", "michael", "dwight", "kevin"]
["jim","pam","creed","kevin","dwight","michael"]

Performance notes

>>> sortBy (comparing fst) [(3, 1), (2, 2), (1, 3)]
[(1,3),(2,2),(3,1)]

>>> (sortBy . comparing) fst [(3, 1), (2, 2), (1, 3)]
[(1,3),(2,2),(3,1)]

Since: base-4.8.0.0

The subsequences function returns the list of all subsequences of the argument.

Laziness

>>> take 1 (subsequences undefined)
[[]]
>>> take 2 (subsequences ('a' : undefined))
["","a"]

Examples

>>> subsequences "abc"
["","a","b","ab","c","ac","bc","abc"]

>>> take 8 $ subsequences ['a'..]
["","a","b","ab","c","ac","bc","abc"]

\(\mathcal{O}(n)\). The tails function returns all final segments of the argument, longest first.

Laziness

>>> tails undefined
[*** Exception: Prelude.undefined

>>> drop 1 (tails [undefined, 1, 2])
[[1, 2], [2], []]

Examples

>>> tails "abc"
["abc","bc","c",""]

>>> tails [1, 2, 3]
[[1,2,3],[2,3],[3],[]]

>>> tails []
[[]]

The transpose function transposes the rows and columns of its argument.

Laziness

>>> take 1 (transpose ['a' : undefined, 'b' : undefined])
["ab"]

Examples

>>> transpose [[1,2,3],[4,5,6]]
[[1,4],[2,5],[3,6]]

>>> transpose [[10,11],[20],[],[30,31,32]]
[[10,20,30],[11,31],[32]]

>>> transpose (repeat [])
* Hangs forever *

The unfoldr function is a `dual' to foldr: while foldr reduces a list to a summary value, unfoldr builds a list from a seed value. The function takes the element and returns Nothing if it is done producing the list or returns Just (a,b), in which case, a is a prepended to the list and b is used as the next element in a recursive call. For example,

iterate f == unfoldr (\x -> Just (x, f x))

In some cases, unfoldr can undo a foldr operation:

unfoldr f' (foldr f z xs) == xs

if the following holds:

f' (f x y) = Just (x,y)
f' z       = Nothing

Laziness

>>> take 1 (unfoldr (\x -> Just (x, undefined)) 'a')
"a"

Examples

>>> unfoldr (\b -> if b == 0 then Nothing else Just (b, b-1)) 10
[10,9,8,7,6,5,4,3,2,1]

>>> take 10 $ unfoldr (\(x, y) -> Just (x, (y, x + y))) (0, 1)
[0,1,1,2,3,5,8,13,21,54]

comparing p x y = compare (p x) (p y)

Useful combinator for use in conjunction with the xxxBy family of functions from Data.List, for example:

  ... sortBy (comparing fst) ...

This is a valid definition of stimes for an idempotent Semigroup.

When x <> x = x, this definition should be preferred, because it works in \(\mathcal{O}(1)\) rather than \(\mathcal{O}(\log n)\).

This is a valid definition of stimes for an idempotent Monoid.

When x <> x = x, this definition should be preferred, because it works in \(\mathcal{O}(1)\) rather than \(\mathcal{O}(\log n)\)

This is a valid definition of stimes for a Monoid.

Unlike the default definition of stimes, it is defined for 0 and so it should be preferred where possible.

forM is mapM with its arguments flipped. For a version that ignores the results see forM_.

The mapAccumL function behaves like a combination of fmap and foldl; it applies a function to each element of a structure, passing an accumulating parameter from left to right, and returning a final value of this accumulator together with the new structure.

Examples

>>> mapAccumL (\a b -> (a + b, a)) 0 [1..10]
(55,[0,1,3,6,10,15,21,28,36,45])

>>> mapAccumL (\a b -> (a <> show b, a)) "0" [1..5]
("012345",["0","01","012","0123","01234"])

The mapAccumR function behaves like a combination of fmap and foldr; it applies a function to each element of a structure, passing an accumulating parameter from right to left, and returning a final value of this accumulator together with the new structure.

Examples

>>> mapAccumR (\a b -> (a + b, a)) 0 [1..10]
(55,[54,52,49,45,40,34,27,19,10,0])

>>> mapAccumR (\a b -> (a <> show b, a)) "0" [1..5]
("054321",["05432","0543","054","05","0"])

Convert an uncurried function to a curried function.

Examples

>>> curry fst 1 2
1

Extract the first component of a pair.

Extract the second component of a pair.

Swap the components of a pair.

uncurry converts a curried function to a function on pairs.

Examples

>>> uncurry (+) (1,2)
3

>>> uncurry ($) (show, 1)
"1"

>>> map (uncurry max) [(1,2), (3,4), (6,8)]
[2,4,8]

Get a trace of the current execution stack state.

Returns Nothing if stack trace support isn't available on host machine.

Get a string representation of the current execution stack state.

The sortWith function sorts a list of elements using the user supplied function to project something out of each element

In general if the user supplied function is expensive to compute then you should probably be using sortOn, as it only needs to compute it once for each element. sortWith, on the other hand must compute the mapping function for every comparison that it performs.

stderr is a handle managing the programs standard error.

stdin is a handle managing the programs standard input.

stdout is a handle managing the programs standard output.

The computation withFile path mode action opens the file and runs action with the obtained handle before closing the file.

Even when an exception is raised within the action, the file will still be closed. This is why withFile path mode act is preferable to

openFile path mode >>= (\hdl -> act hdl >>= hClose hdl)

See also: bracket