Functional composition with multi-valued functions in haskell?

Question

I was wondering if it was possible to do functional composition with functions that take more than one argument. I want to be able to do something like this

x = (+3).(*)

setting x equal to a function that adds three to the product of two numbers.

[This](http://stackoverflow.com/questions/9656797/variadic-compose-function) might be what you are looking for. — is7s, Jun 03 '13 at 07:18

leftaroundabout · Accepted Answer · 2013-06-02T23:37:41.273

23

There are multiple ways to do it, but they're all somewhat awkward.

((+3).) . (*)
≡ fmap (+3) . (*)
≡ curry $ (+3) . uncurry (*)
≡ \l r -> l*r + 3

Oh, wait, this was the signature where there's also a compact definition, guess what it's called...

((.).(.)) (+3) (*)

I'd argue that the lambda solution, being most explicit, is rather the best here.

What helps, and is often done just locally as a one(or two)-liner, is to define this composition as a custom infix:

(.:) :: (c->d) -> (a->b->c) -> a->b->d
f .: i = \l r -> f $ i l r

Which allows you to write simply (+3) .: (*).

BTW, for the similar (b->b->c) -> (a->b) -> a->a->c (precompose the right function to both arguments of the infix) there exists a widely-used standard implementation.

edited Jun 02 '13 at 23:37

answered Jun 02 '13 at 23:31

leftaroundabout

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I like `((.).(.))` the best, mainly because I like to imagine [Frankie Howerd](http://en.m.wikipedia.org/wiki/Frankie_Howerd) discovered it – Benjamin Hodgson Jun 03 '13 at 01:17
+1 for fmap (the coolest) and the lambda (the one I'd want in any codebase I was working on!) – monk Jun 03 '13 at 09:12
yes - take the lambda or better give the function a name - in all honesty: the other solutions are intelectual pleasing but more or less unreadable (you can rediscover them easily true but I would say unreadable) - things like this gives Haskell it's "arcane ebony-tower" label that discourages so many good developers to look into Haskell – Random Dev Jun 03 '13 at 09:18
Is there a common, Englihs-language name for (.).(.)? – Boyd Stephen Smith Jr. Jun 13 '13 at 15:26
@BoydStephenSmithJr.: _yes_. – leftaroundabout Jun 13 '13 at 22:34
@leftaroundabout What is that name? – Boyd Stephen Smith Jr. Jun 24 '13 at 17:10
The ((.).(.)) is just bluffing me, i totally understand (.) but i can't understand ((.).(.)), i thing i am going to use pen and paper to get it. – Luc DUZAN Apr 03 '14 at 17:09

score 3 · Answer 2 · answered Jun 03 '13 at 10:13

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Yes, I'd use something like this:

http://hackage.haskell.org/packages/archive/composition/latest/doc/html/Data-Composition.html

answered Jun 03 '13 at 10:13

Tom Ellis

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score 2 · Answer 3 · answered Jun 03 '13 at 10:20

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You could also use the B1 or blackbird combinator from Data.Aviary.Birds. I think for real work I'd use a lambda though.

answered Jun 03 '13 at 10:20

jk.

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Functional composition with multi-valued functions in haskell?

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