Join-ing the Blogosphere

I'd like to share a little Haskell snippet (I wanted to say "idiom" but actually I'm not sure if I've seen it used anywhere else...) that I quite like:


join (,) 9


What does this do? On its own, not much - in fact you just get:


(9,9)


...which you'd have been much better off typing in yourself. Where it can come-in handy though is when writing code in a pointfree style if you have a need to duplicate an anonymous value into both parts of a pair:


functionWhichTakesAPair . join (,) . functionWhichProducesASingleValue


Anyway, how / why does this construct work....?

The (,) is just the standard data constructor for a 2-tuple, a pair. (This constructor has type a -> b -> (a,b) so you can always write (,) 9 9 as an alternative notation for (9,9) if you wish).

The join is the standard function :: Monad m => m (m a) -> m a we know from monadic programming (Control.Monad). But this just raises the question of how it can make sense to apply it to (,) which as we've seen is a function of type a -> b -> (a,b).

The answer is of course that this function may be considered to be of type m (m a). This is because Control.Monad.Instances declares any partially applied function (eg a -> ...) to be a monad (the type a can be seen as representing an encapsulated environment which is threaded through by the monadic bind). This then means that a function of two arguments (such as (,)) can be seen as having type m (m a) which is just what we need to be able to apply join. The net result is that the single argument of the resulting function (join (,)) is passed in twice as desired.

This of course generalises to functions other than (,) - whenever we use join f where f is a function of two arguments, we end up with a function of one argument which is passed into f twice.