Boolean "or"

Boolean "and"

Boolean "not"

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

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

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

This is equivalent to if p then y else x; 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; x = "bar"; y = "foo"
>>> bool x y p == if p then y else x
True
>>> let p = False
>>> bool x y p == if p then y else x
True

Since: base-4.7.0.0

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

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

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

Examples

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

>>> fromMaybe "" Nothing
""

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

Get a First value with a default fallback

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 maybeToList function returns an empty list when given Nothing or a singleton list when not given Nothing.

Examples

>>> maybeToList (Just 7)
[7]

>>> maybeToList Nothing
[]

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

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 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 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 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]

Applicative mapMaybe.

Monadic mapMaybe.

forMaybeA == flip mapMaybeA

forMaybeM == flip mapMaybeM

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 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

Apply a function to a Left constructor

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]

Extract the first component of a pair.

Extract the second component of a pair.

curry converts an uncurried function to a curried function.

Examples

>>> curry fst 1 2
1

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]

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) ...

Convert to an Int. It is implementation-dependent what fromEnum returns when applied to a value that is too large to fit in an Int.

raise a number to a non-negative integral power

Unary negation.

Absolute value.

Sign of a number. The functions abs and signum should satisfy the law:

abs x * signum x == x

For real numbers, the signum is either -1 (negative), 0 (zero) or 1 (positive).

Conversion from an Integer. An integer literal represents the application of the function fromInteger to the appropriate value of type Integer, so such literals have type (Num a) => a.

the same as flip (-).

Because - is treated specially in the Haskell grammar, (- e) is not a section, but an application of prefix negation. However, (subtract exp) is equivalent to the disallowed section.

the rational equivalent of its real argument with full precision

integer division truncated toward zero

integer remainder, satisfying

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

integer division truncated toward negative infinity

integer modulus, satisfying

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

simultaneous quot and rem

simultaneous div and mod

conversion to Integer

gcd x y is the non-negative factor of both x and y of which every common factor of x and y is also a factor; for example gcd 4 2 = 2, gcd (-4) 6 = 2, gcd 0 4 = 4. gcd 0 0 = 0. (That is, the common divisor that is "greatest" in the divisibility preordering.)

Note: Since for signed fixed-width integer types, abs minBound < 0, the result may be negative if one of the arguments is minBound (and necessarily is if the other is 0 or minBound) for such types.

lcm x y is the smallest positive integer that both x and y divide.

general coercion from integral types

fractional division

raise a number to an integral power

reciprocal fraction

Conversion from a Rational (that is Ratio Integer). A floating literal stands for an application of fromRational to a value of type Rational, so such literals have type (Fractional a) => a.

general coercion to fractional types

The function properFraction takes a real fractional number x and returns a pair (n,f) such that x = n+f, and:

• n is an integral number with the same sign as x; and
• f is a fraction with the same type and sign as x, and with absolute value less than 1.

The default definitions of the ceiling, floor, truncate and round functions are in terms of properFraction.

truncate x returns the integer nearest x between zero and x

round x returns the nearest integer to x; the even integer if x is equidistant between two integers

ceiling x returns the least integer not less than x

floor x returns the greatest integer not greater than x

a constant function, returning the radix of the representation (often 2)

a constant function, returning the number of digits of floatRadix in the significand

a constant function, returning the lowest and highest values the exponent may assume

The function decodeFloat applied to a real floating-point number returns the significand expressed as an Integer and an appropriately scaled exponent (an Int). If decodeFloat x yields (m,n), then x is equal in value to m*b^^n, where b is the floating-point radix, and furthermore, either m and n are both zero or else b^(d-1) <= abs m < b^d, where d is the value of floatDigits x. In particular, decodeFloat 0 = (0,0). If the type contains a negative zero, also decodeFloat (-0.0) = (0,0). The result of decodeFloat x is unspecified if either of isNaN x or isInfinite x is True.

encodeFloat performs the inverse of decodeFloat in the sense that for finite x with the exception of -0.0, uncurry encodeFloat (decodeFloat x) = x. encodeFloat m n is one of the two closest representable floating-point numbers to m*b^^n (or ±Infinity if overflow occurs); usually the closer, but if m contains too many bits, the result may be rounded in the wrong direction.

exponent corresponds to the second component of decodeFloat. exponent 0 = 0 and for finite nonzero x, exponent x = snd (decodeFloat x) + floatDigits x. If x is a finite floating-point number, it is equal in value to significand x * b ^^ exponent x, where b is the floating-point radix. The behaviour is unspecified on infinite or NaN values.

The first component of decodeFloat, scaled to lie in the open interval (-1,1), either 0.0 or of absolute value >= 1/b, where b is the floating-point radix. The behaviour is unspecified on infinite or NaN values.

multiplies a floating-point number by an integer power of the radix

True if the argument is an IEEE "not-a-number" (NaN) value

True if the argument is an IEEE infinity or negative infinity

True if the argument is too small to be represented in normalized format

True if the argument is an IEEE negative zero

True if the argument is an IEEE floating point number

a version of arctangent taking two real floating-point arguments. For real floating x and y, atan2 y x computes the angle (from the positive x-axis) of the vector from the origin to the point (x,y). atan2 y x returns a value in the range [-pi, pi]. It follows the Common Lisp semantics for the origin when signed zeroes are supported. atan2 y 1, with y in a type that is RealFloat, should return the same value as atan y. A default definition of atan2 is provided, but implementors can provide a more accurate implementation.

Swap bytes in Word16.

Since: base-4.7.0.0

Reverse order of bytes in Word32.

Since: base-4.7.0.0

Reverse order of bytes in Word64.

Since: base-4.7.0.0

An associative operation.

Identity of mappend

An associative operation

NOTE: This method is redundant and has the default implementation mappend = '(<>)' since base-4.11.0.0.

Fold a list using the monoid.

For most types, the default definition for mconcat will be used, but the function is included in the class definition so that an optimized version can be provided for specific types.

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)

Replace all locations in the input with the same value. The default definition is fmap . const, but this may be overridden with a more efficient version.

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

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

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

Lift a value.

Sequential application.

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

Sequence actions, discarding the value of the second argument.

Sequence actions, discarding the value of the first argument.

Lift a function to actions. This function may be used as a value for fmap in a Functor instance.

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 <*>.

Lift a ternary function to actions.

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

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

for_ is traverse_ with its arguments flipped. For a version that doesn't ignore the results see for.

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

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.

This generalizes the list-based filter function.

Like replicateM, but discards the result.

The zipWithM function generalizes zipWith to arbitrary applicative functors.

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

Inject a value into the monadic type.

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.

Examples

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

Sequentially compose two actions, passing any value produced by the first as an argument to the second.

Sequentially compose two actions, discarding any value produced by the first, like sequencing operators (such as the semicolon) in imperative languages.

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

Left-to-right composition of Kleisli arrows.

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

Strict version of <$>.

Since: base-4.8.0.0

Promote a function to a monad.

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

liftM2 (+) [0,1] [0,2] = [0,2,1,3]
liftM2 (+) (Just 1) Nothing = Nothing

Run the second value if the first value returns True

Run the second value if the first value returns False

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.

As of base 4.8.0.0, mapM_ is just traverse_, specialized to Monad.

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

As of base 4.8.0.0, forM_ is just for_, specialized to Monad.

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.

As of base 4.8.0.0, sequence_ is just sequenceA_, specialized to Monad.

The foldM function is analogous to foldl, except that its result is encapsulated in a monad. Note that foldM works from left-to-right over the list arguments. This could be an issue where (>>) and the `folded function' are not commutative.

foldM f a1 [x1, x2, ..., xm]

==

do
  a2 <- f a1 x1
  a3 <- f a2 x2
  ...
  f am xm

If right-to-left evaluation is required, the input list should be reversed.

Note: foldM is the same as foldlM

Like foldM, but discards the result.

Right-associative fold of a structure.

In the case of lists, foldr, when 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)...)

Note that, since the head of the resulting expression is produced by an application of the operator to the first element of the list, foldr can produce a terminating expression from an infinite list.

For a general Foldable structure this should be semantically identical to,

foldr f z = foldr f z . toList

Left-associative fold of a structure but with strict application of the operator.

This ensures that each step of the fold 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 list to a single, monolithic result (e.g. length).

For a general Foldable structure this should be semantically identical to,

foldl f z = foldl' f z . toList

Combine the elements of a structure using a monoid.

Map each element of the structure to a monoid, and combine the results.

Extend foldMap to allow side effects.

Internally, this is implemented using a strict left fold. This is used for performance reasons. It also necessitates that this function has a Monad constraint and not just an Applicative constraint. For more information, see https://github.com/commercialhaskell/rio/pull/99#issuecomment-394179757.

Since: 0.1.3.0

Does the element occur in the structure?

notElem is the negation of elem.

Test whether the structure is empty. The default implementation is optimized for structures that are similar to cons-lists, because there is no general way to do better.

Returns the size/length of a finite structure as an Int. The default implementation is optimized for structures that are similar to cons-lists, because there is no general way to do better.

The sum function computes the sum of the numbers of a structure.

The product function computes the product of the numbers of a structure.

Determines whether all elements of the structure satisfy the predicate.

Determines whether any element of the structure satisfies the predicate.

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.

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.

List of elements of a structure, from left to right.

The concatenation of all the elements of a container of lists.

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

Map each element of a structure to an action, evaluate these actions from left to right, and collect the results. For a version that ignores the results see traverse_.

for is traverse with its arguments flipped. For a version that ignores the results see for_.

Evaluate each action in the structure from left to right, and collect the results. For a version that ignores the results see sequenceA_.

Map each element of a structure to a monadic action, evaluate these actions from left to right, and collect the results. For a version that ignores the results see mapM_.

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

Evaluate each monadic action in the structure from left to right, and collect the results. For a version that ignores the results see sequence_.

An associative binary operation

One or more.

Zero or more.

One or none.

The sum of a collection of actions, generalizing concat.

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

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)

Conditional execution of Applicative expressions. For example,

when debug (putStrLn "Debugging")

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

The reverse of when.

The identity of mplus. It should also satisfy the equations

mzero >>= f  =  mzero
v >> mzero   =  mzero

The default definition is

mzero = empty

An associative operation. The default definition is

mplus = (<|>)

The sum of a collection of actions, generalizing concat. As of base 4.8.0.0, msum is just asum, specialized to MonadPlus.

Direct MonadPlus equivalent of filter.

Examples

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

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

Send the first component of the input through the argument arrow, and copy the rest unchanged to the output.

A mirror image of first.

The default definition may be overridden with a more efficient version if desired.

Fanout: send the input to both argument arrows and combine their output.

The default definition may be overridden with a more efficient version if desired.

Split the input between the two argument arrows and combine their output. Note that this is in general not a functor.

The default definition may be overridden with a more efficient version if desired.

Left-to-right composition

Identity function.

id x = x

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]

Function composition.

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.

Note that ($) is levity-polymorphic in its result type, so that foo $ True where foo :: Bool -> Int# is well-typed

& 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

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

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

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.

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.

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

Typical usage: sortBy (compare `on` fst).

Algebraic properties:

• (*) `on` id = (*) -- (if (*) ∉ {⊥, const ⊥})

• ((*) `on` f) `on` g = (*) `on` (f . g)

• flip on f . flip on g = flip on (g . f)

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.

The value of seq a b is bottom if a is bottom, and otherwise equal to b. In other words, it evaluates the first argument a to weak head normal form (WHNF). seq is usually introduced to improve performance by avoiding unneeded laziness.

A note on evaluation order: the expression seq a b does not guarantee that a will be evaluated before b. The only guarantee given by seq is that the both a and b will be evaluated before seq returns a value. In particular, this means that b may be evaluated before a. If you need to guarantee a specific order of evaluation, you must use the function pseq from the "parallel" package.

error stops execution and displays an error message.

A special case of error. It is expected that compilers will recognize this and insert error messages which are more appropriate to the context in which undefined appears.

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.

Helper function to force an action to run in IO. Especially useful for overly general contexts, like hspec tests.

Since: 0.1.3.0

Append 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.

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 (> 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],[])

break p is equivalent to span (not . p).

drop n xs returns the suffix of xs after the first n elements, or [] if n > length xs:

drop 6 "Hello World!" == "World!"
drop 3 [1,2,3,4,5] == [4,5]
drop 3 [1,2] == []
drop 3 [] == []
drop (-1) [1,2] == [1,2]
drop 0 [1,2] == [1,2]

It is an instance of the more general genericDrop, in which n may be of any integral type.

dropWhile p xs returns the suffix remaining after takeWhile p xs:

dropWhile (< 3) [1,2,3,4,5,1,2,3] == [3,4,5,1,2,3]
dropWhile (< 9) [1,2,3] == []
dropWhile (< 0) [1,2,3] == [1,2,3]

filter, applied to a predicate and a list, returns the list of those elements that satisfy the predicate; i.e.,

filter p xs = [ x | x <- xs, p x]

lookup key assocs looks up a key in an association list.

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, ...]

replicate n x is a list of length n with x the value of every element. It is an instance of the more general genericReplicate, in which n may be of any integral type.

reverse xs returns the elements of xs in reverse order. xs must be finite.

span, 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 satisfy p and second element is the remainder of the list:

span (< 3) [1,2,3,4,1,2,3,4] == ([1,2],[3,4,1,2,3,4])
span (< 9) [1,2,3] == ([1,2,3],[])
span (< 0) [1,2,3] == ([],[1,2,3])

span p xs is equivalent to (takeWhile p xs, dropWhile p xs)

take n, applied to a list xs, returns the prefix of xs of length n, or xs itself if n > length xs:

take 5 "Hello World!" == "Hello"
take 3 [1,2,3,4,5] == [1,2,3]
take 3 [1,2] == [1,2]
take 3 [] == []
take (-1) [1,2] == []
take 0 [1,2] == []

It is an instance of the more general genericTake, in which n may be of any integral type.

takeWhile, applied to a predicate p and a list xs, returns the longest prefix (possibly empty) of xs of elements that satisfy p:

takeWhile (< 3) [1,2,3,4,1,2,3,4] == [1,2]
takeWhile (< 9) [1,2,3] == [1,2,3]
takeWhile (< 0) [1,2,3] == []

zip takes two lists and returns a list of corresponding pairs.

zip [1, 2] ['a', 'b'] = [(1, 'a'), (2, 'b')]

If one input list is short, excess elements of the longer list are discarded:

zip [1] ['a', 'b'] = [(1, 'a')]
zip [1, 2] ['a'] = [(1, 'a')]

zip is right-lazy:

zip [] _|_ = []
zip _|_ [] = _|_

zipWith generalises zip by zipping with the function given as the first argument, instead of a tupling function. For example, zipWith (+) is applied to two lists to produce the list of corresponding sums.

zipWith is right-lazy:

zipWith f [] _|_ = []

Strip out duplicates

lines breaks a string up into a list of strings at newline characters. The resulting strings do not contain newlines.

Note that after splitting the string at newline characters, the last part of the string is considered a line even if it doesn't end with a newline. For example,

>>> lines ""
[]

>>> lines "\n"
[""]

>>> lines "one"
["one"]

>>> lines "one\n"
["one"]

>>> lines "one\n\n"
["one",""]

>>> lines "one\ntwo"
["one","two"]

>>> lines "one\ntwo\n"
["one","two"]

Thus lines s contains at least as many elements as newlines in s.

unlines is an inverse operation to lines. It joins lines, after appending a terminating newline to each.

>>> unlines ["Hello", "World", "!"]
"Hello\nWorld\n!\n"

unwords is an inverse operation to words. It joins words with separating spaces.

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

words breaks a string up into a list of words, which were delimited by white space.

>>> words "Lorem ipsum\ndolor"
["Lorem","ipsum","dolor"]

A specialised variant of showsPrec, using precedence context zero, and returning an ordinary String.

Parse a string using the Read instance. Succeeds if there is exactly one valid result.

>>> readMaybe "123" :: Maybe Int
Just 123

>>> readMaybe "hello" :: Maybe Int
Nothing

Since: base-4.6.0.0

the deep analogue of $!. In the expression f $!! x, x is fully evaluated before the function f is applied to it.

Since: deepseq-1.2.0.0

rnf should reduce its argument to normal form (that is, fully evaluate all sub-components), and then return '()'.

Generic NFData deriving

Starting with GHC 7.2, you can automatically derive instances for types possessing a Generic instance.

Note: Generic1 can be auto-derived starting with GHC 7.4

{-# LANGUAGE DeriveGeneric #-}

import GHC.Generics (Generic, Generic1)
import Control.DeepSeq

data Foo a = Foo a String
             deriving (Eq, Generic, Generic1)

instance NFData a => NFData (Foo a)
instance NFData1 Foo

data Colour = Red | Green | Blue
              deriving Generic

instance NFData Colour

Starting with GHC 7.10, the example above can be written more concisely by enabling the new DeriveAnyClass extension:

{-# LANGUAGE DeriveGeneric, DeriveAnyClass #-}

import GHC.Generics (Generic)
import Control.DeepSeq

data Foo a = Foo a String
             deriving (Eq, Generic, Generic1, NFData, NFData1)

data Colour = Red | Green | Blue
              deriving (Generic, NFData)

Compatibility with previous deepseq versions

Prior to version 1.4.0.0, the default implementation of the rnf method was defined as

rnf a = seq a ()

However, starting with deepseq-1.4.0.0, the default implementation is based on DefaultSignatures allowing for more accurate auto-derived NFData instances. If you need the previously used exact default rnf method implementation semantics, use

instance NFData Colour where rnf x = seq x ()

or alternatively

instance NFData Colour where rnf = rwhnf

or

{-# LANGUAGE BangPatterns #-}
instance NFData Colour where rnf !_ = ()

deepseq: fully evaluates the first argument, before returning the second.

The name deepseq is used to illustrate the relationship to seq: where seq is shallow in the sense that it only evaluates the top level of its argument, deepseq traverses the entire data structure evaluating it completely.

deepseq can be useful for forcing pending exceptions, eradicating space leaks, or forcing lazy I/O to happen. It is also useful in conjunction with parallel Strategies (see the parallel package).

There is no guarantee about the ordering of evaluation. The implementation may evaluate the components of the structure in any order or in parallel. To impose an actual order on evaluation, use pseq from Control.Parallel in the parallel package.

Since: deepseq-1.1.0.0

a variant of deepseq that is useful in some circumstances:

force x = x `deepseq` x

force x fully evaluates x, and then returns it. Note that force x only performs evaluation when the value of force x itself is demanded, so essentially it turns shallow evaluation into deep evaluation.

force can be conveniently used in combination with ViewPatterns:

{-# LANGUAGE BangPatterns, ViewPatterns #-}
import Control.DeepSeq

someFun :: ComplexData -> SomeResult
someFun (force -> !arg) = {- 'arg' will be fully evaluated -}

Another useful application is to combine force with evaluate in order to force deep evaluation relative to other IO operations:

import Control.Exception (evaluate)
import Control.DeepSeq

main = do
  result <- evaluate $ force $ pureComputation
  {- 'result' will be fully evaluated at this point -}
  return ()

Finally, here's an exception safe variant of the readFile' example:

readFile' :: FilePath -> IO String
readFile' fn = bracket (openFile fn ReadMode) hClose $ \h ->
                       evaluate . force =<< hGetContents h

Since: deepseq-1.2.0.0

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

Lift a computation from the argument monad to the constructed monad.

Retrieves the monad environment.

Retrieves a function of the current environment.

Executes a computation in a modified environment.

Runs a Reader and extracts the final value from it. (The inverse of reader.)

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

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

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

Decode a ByteString containing UTF-8 encoded text.

If the input contains any invalid UTF-8 data, the relevant exception will be returned, otherwise the decoded text.

Decode a ByteString containing UTF-8 encoded text.

NOTE: The replacement character returned by OnDecodeError MUST be within the BMP plane; surrogate code points will automatically be remapped to the replacement char U+FFFD (since 0.11.3.0), whereas code points beyond the BMP will throw an error (since 1.2.3.1); For earlier versions of text using those unsupported code points would result in undefined behavior.

Encode text using UTF-8 encoding.

Encode text to a ByteString Builder using UTF-8 encoding.

Since: text-1.1.0.0

Replace an invalid input byte with the Unicode replacement character U+FFFD.

Execute a primitive operation

Return the value computed by a state transformer computation. The forall ensures that the internal state used by the ST computation is inaccessible to the rest of the program.