How to change the order of arguments?

Question

What if I want to change the order of arguments in a function?

There is flip:

flip :: (a -> b -> c) -> b -> a -> c

but I don't see how to make it work for a larger number of arguments. Is there a general method to permute the arguments?

Answer 1

If you feel like editing functions after they're written, you really really should read Conal Elliott's excellent blog post semantic editor combinators

http://conal.net/blog/posts/semantic-editor-combinators

In fact, everyone should read it anyway. It's a genuinely useful method (which I'm abusing here). Conal uses more constructs than just result and flip to very flexible effect.

result :: (b -> b') -> ((a -> b) -> (a -> b'))
result =  (.)

Suppose I have a function that uses 3 arguments

use3 :: Char -> Double -> Int -> String
use3 c d i = c: show (d^i)

and I'd like to swap the first two, I'd just use flip use3 as you say, but if I wanted to swap the seconnd and third, what I want is to apply flip to the result of applying use3 to its first argument.

use3' :: Char -> Int -> Double -> String
use3' = (result) flip use3

Let's move along and swap the fourth and fifth arguments of a function use5 that uses 5.

use5  :: Char -> Double -> Int -> (Int,Char) -> String     -> String
use5' :: Char -> Double -> Int -> String     -> (Int,Char) -> String

use5 c d i (n,c') s = c : show (d ^ i) ++ replicate n c' ++ s

We need to apply flip to the result of applying use5 to it's first three arguments, so that's the result of the result of the result:

use5' = (result.result.result) flip use5

Why not save thinking later and define

swap_1_2 :: (a1 -> a2 -> other) -> (a2 -> a1 -> other)
swap_2_3 :: (a1 -> a2 -> a3 -> other) -> (a1 -> a3 -> a2 -> other)
--skip a few type signatures and daydream about scrap-your-boilerplate and Template Haskell    

swap_1_2 = flip    
swap_2_3 = result flip
swap_3_4 = (result.result) flip
swap_4_5 = (result.result.result) flip
swap_5_6 = (result.result.result.result) flip

...and that's where you should stop if you like simplicity and elegance. Note that the type other could be b -> c -> d so because of fabulous Curry and right associativity of ->, swap_2_3 works for a function which takes any number of arguments above two. For anything more complicated, you should really write a permuted function by hand. What follows is just for the sake of intellectual curiosity.

Now, what about swapping the second and fourth arguments? [Aside: there's a theorem I remember from my algebra lectures that any permutation can be made as the composition of swapping adjacent items.]

We could do it like this: step 1: move 2 next to 4 (swap_2_3)

a1 -> a2 -> a3 -> a4 -> otherstuff
a1 -> a3 -> a2 -> a4 -> otherstuff

swap them there using swap_3_4

a1 -> a3 -> a2 -> a4 -> otherstuff
a1 -> a3 -> a4 -> a2 -> otherstuff

then swap 4 back to position 2 using swap_2_3 again:

a1 -> a3 -> a4 -> a2 -> otherstuff
a1 -> a4 -> a3 -> a2 -> otherstuff

so

swap_2_4 = swap_2_3.swap_3_4.swap_2_3

Maybe there's a more terse way of getting there directly with lots of results and flips but random messing didn't find it for me!

Similarly, to swap 1 and 5 we can move 1 over to 4, swap with 5, move 5 back from 4 to 1.

swap_1_5 = swap_1_2.swap_2_3.swap_3_4 . swap_4_5 . swap_3_4.swap_2_3.swap_1_2

Or if you prefer you could reuse swap_2_4 by flipping at the ends (swapping 1 with 2 and 5 with 4), swap_2_4 then flipping at the ends again.

swap_1_5' = swap_1_2.swap_4_5. swap_2_4 .swap_4_5.swap_1_2

Of course it's much easier to define

swap_1_5'' f  a b c d e = f  e b c d a

which has the benefit of being clear, consise, efficient and has a helpful type signature in ghci without explicitly annotating it.

However, this was a fantastically entertaining question, thanks.

Answer 2

The best way in general is to just do it manually. Assume you have a function

f :: Arg1 -> Arg2 -> Arg3 -> Arg4 -> Res

and you would like

g :: Arg4 -> Arg1 -> Arg3 -> Arg2 -> Res

then you write

g x4 x1 x3 x2 = f x1 x2 x3 x4

If you need a particular permutation several times, then you can of course abstract from it, like flip does for the two-argument case:

myflip :: (a4 -> a1 -> a3 -> a2 -> r) -> a1 -> a2 -> a3 -> a4 -> r
myflip f x4 x1 x3 x2 = f x1 x2 x3 x4