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 computation appendFile file str function appends the string str, to the file file.
Note that writeFile and appendFile write a literal string to a file. To write a value of any printable type, as with print, use the show function to convert the value to a string first.
> main = appendFile "squares" (show [(x,x*x) | x <- [0,0.1..2]])

approxRational, applied to two real fractional numbers x and epsilon, returns the simplest rational number within epsilon of x. A rational number y is said to be *simpler* than another y' if
* abs (numerator y) <= abs (numerator y'), and
* denominator y <= denominator y'.
Any real interval contains a unique simplest rational; in particular, note that 0/1 is the simplest rational of all.

A functor with application.
Instances should satisfy the following laws:
* *identity* pure id <*> v = v
* *composition* pure (.) <*> u <*> v <*> w = u <*> (v <*> w)
* *homomorphism* pure f <*> pure x = pure (f x)
* *interchange* u <*> pure y = pure ($ y) <*> u
* *ignore left value* u *> v = pure (const id) <*> u <*> v
* *ignore right value* u <* v = pure const <*> u <*> v
The Functor instance should satisfy
> fmap f x = pure f <*> x
If f is also a Monad, define pure = return and (<*>) = ap.
Minimal complete definition: pure and <*>.

This module describes a structure intermediate between a functor and a monad: it provides pure expressions and sequencing, but no binding. (Technically, a strong lax monoidal functor.) For more details, see *Applicative Programming with Effects*, by Conor McBride and Ross Paterson, online at http://www.soi.city.ac.uk/~ross/papers/Applicative.html.
This interface was introduced for parsers by Niklas Röjemo, because it admits more sharing than the monadic interface. The names here are mostly based on recent parsing work by Doaitse Swierstra.
This class is also useful with instances of the Data.Traversable.Traversable class.

Map a function over a list and concatenate the results.

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, ...]

Some arrows allow application of arrow inputs to other inputs.

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