## 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.

### 4 Responses to “Haskell: sortBy wrapped_f, sortBy (comparing f), and sortBy (compare `on` f)”

1. gcbenison Says:

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

• llaisdy Says:

Dear Gregory

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.)

2. gcbenison Says:

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!

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