[Haskell-beginners] Points-free style

[Ertugrul Soeylemez]

Alexander Shendi <Alexander.Shendi at bawue.de> wrote:

> I am working my way through "Learn You a Haskell for Great Good" and
> have reached page 84, where the book recommends that you define your
> functions in a "points-free style", using the "." and "$" operators.
>
> Now I have:
>
> sumProducts' :: Num a => [a] -> [a] -> a
> sumProducts' x y = sum (zipWith (*) x y)
>
> I would like to eliminate the "x" and the "y" in the definition, but
> all I have managed to contrive is:
>
> sumProducts :: Num a => [a] -> [a] -> a
> sumProducts x = sum . zipWith (*) x
>
> How do I proceed from here? Any advice is welcome :)

Honestly, don't!  The definition you have there is perfectly fine.
Please remember:  If the point-free style isn't easy to write, it's
probably also not easy to read.

In general, I would refrain from removing the points from functions with
more than one argument.  But the rule I use is a bit more complicated:
When I have a function with two arguments and both arguments have the
same "subjectness" or are combined in a "monoidic" way, then I don't
remove the points, unless the point-free style is really trivial to
derive.  Examples:

    -- Good (because trivial):
    add = (+)

    -- Good (very readable, point-free would be pointless):
    hypot x y = sqrt (x^2 + y^2)

    -- Bad (I don't even want to derive this by hand):
    hypot = undefined

However, in many cases the two arguments of a binary function have a
different "subjectness".  The last argument is the subject to be
transformed and the earlier argument modifies the transformation, but is
not itself a subject to be transformed.  In these cases I remove only
the last point:

    -- Bad:
    chunksOf n xs =
        takeWhile (not . null) (map (take n) (iterate (drop n) xs))

    -- Good:
    chunksOf n =
        takeWhile (not . null) . map (take n) . iterate (drop n)

    -- Bad:
    chunksOf =
        liftA2 ((.) . (takeWhile (not . null) .))
               (map . take)
               (iterate . drop)

Use point-free style, when it actually makes your code more readable!
Point-free style is used to give definitions in terms of data flow
instead of function applications.

Then there are the many cases, where an argument is just passed to
multiple functions and then the results of the individual functions are
combined.  In this case you can use the fact that (e ->) is an
applicative functor.  Simple example:  Calculating the average value of
a list.

    -- Good:
    average xs = sum xs / fromIntegral (length xs)

    -- Perhaps better:
    average = liftA2 (/) sum (fromIntegral . length)

To get back to your example:  The two arguments your function has have
the same "subjectness".  They are combined in a "monoidic" way and thus
what you really have is a mathematical formula.  Though not always it's
often difficult to get rid of the points in a formula.  Also even if
it's easy, it doesn't always improve the readability in any way.
Example:

    -- Good:
    \x -> 2*x + 1

    -- Bad:
    (+1) . (2*)

    -- Matter of taste (I still don't like it):
    let double = (2*) in
    succ . double


Greets,
Ertugrul


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