Monad m => (a -> b) -> a -> m b
Promote a function to a monad.
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
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.
An infix synonym for fmap.
Lift a function to actions. This function may be used as a value for fmap in a Functor instance.
This function may be used as a value for fmap in a Functor instance.
iterate f x returns an infinite list of repeated applications of f to x:
> iterate f x == [x, f x, f (f x), ...]
O(n). Map a function over all values in the map.
> map (++ "x") (fromList [(5,"a"), (3,"b")]) == fromList [(3, "bx"), (5, "ax")]
mapMonotonic f s == map f s, but works only when f is monotonic. The precondition is not checked. Semi-formally, we have:
> and [x < y ==> f x < f y | x <- ls, y <- ls]
> ==> mapMonotonic f s == map f s
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, ...]
Apply a transformation everywhere in bottom-up manner
Apply a transformation everywhere in top-down manner
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.
O(n). Constructs a sequence by repeated application of a function to a seed value.
> iterateN n f x = fromList (Prelude.take n (Prelude.iterate f x))
until p f yields the result of applying f until p holds.
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