Documentation

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.

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 _|_ [] = _|_

Extract the first component of a pair.

Extract the second component of a pair.

The trace function outputs the trace message given as its first argument, before returning the second argument as its result.

For example, this returns the value of f x but first outputs the message.

>>> let x = 123; f = show
>>> trace ("calling f with x = " ++ show x) (f x)
"calling f with x = 123
123"

The trace function should only be used for debugging, or for monitoring execution. The function is not referentially transparent: its type indicates that it is a pure function but it has the side effect of outputting the trace message.

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, ...]

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

The function coerce allows you to safely convert between values of types that have the same representation with no run-time overhead. In the simplest case you can use it instead of a newtype constructor, to go from the newtype's concrete type to the abstract type. But it also works in more complicated settings, e.g. converting a list of newtypes to a list of concrete types.

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 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

The Monad class defines the basic operations over a monad, a concept from a branch of mathematics known as category theory. From the perspective of a Haskell programmer, however, it is best to think of a monad as an abstract datatype of actions. Haskell's do expressions provide a convenient syntax for writing monadic expressions.

Instances of Monad should satisfy the following laws:

• return a >>= k  =  k a

• m >>= return  =  m

• m >>= (\x -> k x >>= h)  =  (m >>= k) >>= h

Furthermore, the Monad and Applicative operations should relate as follows:

• pure = return

• (<*>) = ap

The above laws imply:

• fmap f xs  =  xs >>= return . f

• (>>) = (*>)

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

The instances of Monad for lists, Maybe and IO defined in the Prelude satisfy these laws.