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, ...]

A combination of parList and map, encapsulating a common pattern:
> parMap strat f = withStrategy (parList strat) . map f

An infix synonym for fmap.

Promote a function to a monad.

A variant of <*> with the arguments reversed.

iterate f x returns an infinite list of repeated applications of f to x:
> iterate f x == [x, f x, f (f x), ...]

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]

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] == []

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 Data.List.zipWith ($) fs xs.

Strict (call-by-value) application, defined in terms of seq.

Applied to a predicate and a list, all determines if all elements of the list satisfy the predicate. For the result to be True, the list must be finite; False, however, results from a False value for the predicate applied to an element at a finite index of a finite or infinite list.

Applied to a predicate and a list, any determines if any element of the list satisfies the predicate. For the result to be False, the list must be finite; True, however, results from a True value for the predicate applied to an element at a finite index of a finite or infinite list.

In many situations, the liftM operations can be replaced by uses of ap, which promotes function application.
> return f `ap` x1 `ap` ... `ap` xn
is equivalent to
> liftMn f x1 x2 ... xn

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

This function may be used as a value for Data.Foldable.foldMap in a Foldable instance.

Direct MonadPlus equivalent of filter filter = (mfilter:: (a -> Bool) -> [a] -> [a] applicable to any MonadPlus, for example mfilter odd (Just 1) == Just 1 mfilter odd (Just 2) == Nothing

Sequential function application. The argument is evaluated using the given strategy before it is given to the function.

Parallel function application. The argument is evaluated using the given strategy, in parallel with the function application.

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

Determines whether all elements of the structure satisfy the predicate.

Determines whether any element of the structure satisfies the predicate.

The groupWith function uses the user supplied function which projects an element out of every list element in order to to first sort the input list and then to form groups by equality on these projected elements

until p f yields the result of applying f until p holds.

Function composition.

Put something inside an HTML element.

(*) `on` f = \x y -> f x * f y.
Typical usage: Data.List.sortBy (compare `on` fst).
Algebraic properties:
* (*) `on` id = (*) (if (*) {¥, const ¥})
* (*) `on` f) `on` g = (*) `on` (f .
* on f . flip on g = flip on (g .
>

Sequential function composition. The result of the second function is evaluated using the given strategy, and then given to the first function.

Parallel function composition. The result of the second function is evaluated using the given strategy, in parallel with the application of the first function.

Sequential inverse function composition, for those who read their programs from left to right. The result of the first function is evaluated using the given strategy, and then given to the second function.

Parallel inverse function composition, for those who read their programs from left to right. The result of the first function is evaluated using the given strategy, in parallel with the application of the second function.

> 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) ...