How is the Foldable instance of (,) useful?

Question

I mistakenly applied length to a (pa,ir) and took a little while to find out, because the code would compile!

So I looked up :t length, which told me that its argument is only required to be a Foldable.

That's how I found that there's a Foldable instance for (,):

instance Foldable ((,) a) where
    foldMap f (_, y) = f y

    foldr f z (_, y) = f y z
    length _  = 1
    null _ = False

which incidentally overrides what would be the automatic definition of length.

What is a Foldable instance for (,) useful for? Especially considering that some of what derives from a minimal definition (null and length) of it has been overridden anyway.

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Related question.

Answer 1

One way through which something nontrivial can be done with Foldable ((,) a) is bringing in the Foldable instance for Compose:

ghci> import Data.Functor.Compose
ghci> sum $ Compose [("apple", 1), ("banana", 2), ("orange", 3)]
6

Also, Foldable happens to be a superclass of Traversable, which in turn grants us sequenceA:

ghci> sequenceA ("strawberry", [4, 5, 6])
[("strawberry",4),("strawberry",5),("strawberry",6)]

The perspective these instances suggest is that of (a, b) values seen as b values annotated with an a tag. sequenceA, then, shifts the tag to the values in the other functorial structure (in the example above, a list).