Haskell: sortBy wrapped_f, sortBy (comparing f), and sortBy (compare `on` f)
Sunday, 28th June, 2009
Here are three version of sortByLength:
import Data.List -- [1] longer :: [a] -> [a] -> Ordering longer a b = compare (length a) (length b) sortByLength0 :: [[a]] -> [[a]] sortByLength0 a = sortBy longer a -- [2] import Data.Ord sortByLength1 = sortBy (comparing length) -- [3] import Data.Function sortByLength = sortBy (compare `on` length)
As discussed in my previous post, the first was my answer to the exercise in Real World Haskell, the second is from comment 5 by Yair, the third is based on comment 8 by David. Thank you Yair and David for these suggestions.
The three versions are equivalent (although I admit I haven’t tested them for speed). With particular relevance to my previous post, none of these use decorate-sort-undecorate. [2] and [3] are clearly better than [1] as they obviate the need for the wrapper function longer
. [2] is my favourite for its readability.
Another thing worth noting is that [2] and [3] omit the parameter a
from the definition.
comparing
and `on`
are new to me, so I’ll outline them briefly here.
comparing
comparing
is in Data.Ord:
comparing :: Ord a => (b -> a) -> b -> b -> Ordering comparing p x y = compare (p x) (p y)
So longer a b
is equivalent to comparing length a b
.
`on`
Using backticks around a function allows us to use the function as an infix rather than a prefix (see rwh ch 4, section Infix functions p 76), so the following are exactly equivalent:
(compare `on` length) (on compare length)
on
is from Data.Function:
on :: (b -> b -> c) -> (a -> b) -> a -> a -> c (*) `on` f = \x y -> f x * f y
I can understand the type signature, and I can see how on compare length a b
would fit, but I’m afraid the definition is opaque. I might be able to come back to it after I’ve written about .
, $
and &&&
. Otherwise, I shall spend some time with my eyes open for different usages of on
in the wild. It was very difficult finding information on on
(many thanks to a contact on haskell-beginners who pointed me to Hoogle), so I think it will be worth writing up when I can.
Discussion
It took the omission of parameters from [2] and [3] for me to realise that perhaps the thing about Haskell is how much it facilitates combining and mixing functions in different ways. Duh.
Thursday, 24th May, 2012 at 3:59 pm
Good explanation. I think the definition of “comparing” is easier to understand, but the function “on” is more general and powerful. You could even implement “comparing” in terms of “on”:
comparing f = compare `on` f
Thursday, 24th May, 2012 at 9:16 pm
Dear Gregory
Thank you for your comment.
I agree that on is more general and powerful. I think I’d like to see more concrete examples of it in use.
(three years on, I’m still only an occasional dabbler in Haskell.)
Thursday, 24th May, 2012 at 9:24 pm
Yeah, I also tried to think of an example of ‘on’ outside of ‘compare’. Here’s what I came up with:
> :type (zip `on` words)
(zip `on` words) :: String -> String -> [(String, String)]
> (zip `on` words) “hello, world!” “goodbye, sam!”
[(“hello,”,”goodbye,”),(“world!”,”sam!”)]
So it’s a kind of transpose operator for text. Kind of contrived, but it works!
Sunday, 27th May, 2012 at 8:22 am
Nice! I’ll try and think of something too.