Question

I’d like to sort by one property and then by another (if the first property is the same.)

What’s the idiomatic way in Haskell of composing two comparison functions, i.e. a function used with sortBy?

Given

f :: Ord a => a -> a -> Ordering
g :: Ord a => a -> a -> Ordering

composing f and g would yield:

h x y = case v of
          EQ -> g x y
          otherwise -> v
        where v = f x y

Answer 1

vitus points out the very cool instance of Monoid for Ordering. If you combine it with the instance instance Monoid b => Monoid (a -> b) it turns out your composition function is just (get ready):

mappend

Check it out:

Prelude Data.Monoid> let f a b = EQ
Prelude Data.Monoid> let g a b = LT
Prelude Data.Monoid> :t f `mappend` g
f `mappend` g :: t -> t1 -> Ordering
Prelude Data.Monoid> (f `mappend` g) undefined undefined 
LT
Prelude Data.Monoid> let f a b = GT
Prelude Data.Monoid> (f `mappend` g) undefined undefined 
GT

+1 for powerful and simple abstractions