# [Haskell-beginners] Function application versus function composition performance

KC kc1956 at gmail.com
Wed Jun 20 00:08:31 CEST 2012

```A good functional programming language has a good "code algebra" after
parsing to which algebraic transformations can be applied for optimization.

For example, reducing the need for generating intermediate data structures.

See: fusion.

On Tue, Jun 19, 2012 at 3:01 PM, Matt Ford <matt at dancingfrog.co.uk> wrote:

> Hi All,
>
> My last question got me thinking (always dangerous): an expression
> that doubles a list and takes the 2nd element (index 1), I assume,
> goes through the following steps.
>
> double (double [1,2,3,4]) !! 1
> double ( 1*2 : double [2,3,4]) !! 1
> 1*2*2 : double ( double [2,3,4] ) !! 1
> 1*2*2 : double ( 2*2 : double [3,4] ) !! 1
> 1*2*2 : 2*2*2 : double ( double [3,4] ) !! 1
> 2*2*2
> 8
>
> Up until the element requested all the proceeding elements have to
> have the expression formed as Haskell process the calculation.
>
> Now, I want to compare this to using function composition
>
> ( double . double ) [ 1 ,2, 3, 4 ] !! 1
>
> This is the bit I'm unsure of - what does the composition look like.
> It is easy to see that it could be simplified to something like:
>
> ( double . double) (x:xs) = x*4 : (double . double) xs
>
> This would mean the steps could be written
>
> (double . double) [ 1,2,3,4 ] !! 1
> (1*4 : (double.double) [2,3,4]) !! 1
> (1*4 : 2*4 : (double.double) [ 3,4 ]) !! 1
> 2*4
> 8
>
> Ignoring the start and end steps, it will be half the number of steps
> compared to the application version.  Significant then, over long
> lists.
>
> So is this true, are composite functions simplified in Haskell in
> general so that they may have improved performance over function
> application?
>
> I've seen posts on the internet that say it's a matter of style only:
>
> http://stackoverflow.com/questions/3030675/haskell-function-composition-and-function-application-idioms-correct-us
> .
>  But my reasoning suggests it could be more than that.
>
> Perhaps, function application is similarly optimised - maybe by
> replacing all functions applications with composition and then
> simplifying?  Or maybe the simplifying/optimisation step never
> happens?  As you can see I'm just guessing at things :-)  But it's
> nice to wonder.
>
> Many thanks for any pointers,
>
> Matt.
>
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--
--
Regards,
KC
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