What does Haskell's Data.Function.on do?

Question

I am finding it hard to find examples of on in Haskell and I don't understand the explanation on Hoogle's Data.Function page. Please, can I have examples of its use and examples of problems/code where using it makes a solution simpler or more efficient?

Answer 1

Suppose we have a function f that takes two arguments. We want a similar function which acts as f, but only after both its arguments have been modified by some other function g.

We could write a new definition

new_f x y = f (g x) (g y)

or, exploiting on,

new_f = f `on` g

Nicely, the latter can be used directly, without defining a new symbol new_f. (Using a lambda is also viable, but not as nice)

This is typically used with compare, a library binary function that checks the ordering between its two arguments. So, we can use

sortBy (compare `on` name)   somePeopleList
sortBy (compare `on` age)    somePeopleList
sortBy (compare `on` height) somePeopleList
...

to sort according different criteria. Above, we assume that name, etc. are functions that can extract the relevant information from a person.

(In more modern Haskell we also have sortBy (comparing age) somePeopleList, or even sortOn age somePeopleList for the same task)