[Haskell-beginners] Foldable for (,)

[Francesco Ariis]

On Sun, Apr 23, 2017 at 08:21:34AM +0000, Jonathon Delgado wrote:
> I've seen many threads, including the one going on now, about why we need
> to have:
> 
> length (2,3) = 1
> product (2,3) = 3
> sum (2,3) = 3
> or (True,False) = False
> 
> but the justifications all go over my head. Is there a beginner-friendly
> explanation for why such seemingly unintuitive operations should be
> allowed by default?

Hello Jonathon,
    the proponents of `Foldable (a,)` see `(2,3)` not as a pair of 'equal'
values, but as a value *and* an annotation, much like some other folks
see Either as having a value (Right a) *or* an annotation (usually an
error in the form of Left e).

So to go back to your examples:

    (2,3)
     ^ ^
     | +------------- I am the value
     |
     +--------------- I am an annotation (and since tuples arguments can
                      be heterogeneous, I could be a String, a Bool,
                      anything).

If you agree with this paradigm, `length`, `sum` and friend become a
bit less icky.

I would prefer tuples to be unbiased, but this intuition helped me
connect with the people on the other side of the line.
Does this help?