Constraints on definition of `length` should be strengthened

[Henrik Nilsson]

On 04/09/2017 12:51 AM, Nathan Bouscal wrote:
> - You're trying to establish an analogy between these tuple instances
> and non-law-abiding instances, but that analogy really doesn't work.
> These are the only law-abiding instances that the types can possibly have.

Yes. But that is, actually, more of a syntactic accident than any deeply
mathematical property: mathematically, there are n ways to make an
n-tuple a functor,

And if we, for "consistency", continue to add functor instances for
tuples for n > 2, the situation, in the view of many reasonable
people at least, becomes increasingly absurd, or at least it becomes
increasingly clear that that the utility we get is a smaller and
smaller part of what we really need. Simply because tuples actually
are "morally unbiased", as Vladislav Zavialov phrased it; i.e.,
there are perfectly legitimate uses where the fields are of equal
importance: there is no a priori "pay load" field, and no a priori
"annotation" fields. And in fact, that is *exactly* what tuples
originally were in Haskell, and how many very reasonably people
still prefers to think about them.

And of course, if, in a hypothetical future version of Haskell
where we could make all possible functor instances for tuples,
the question becomes: which one do we pick? The answer might well
be "none" (in the prelude, at least). (A newtype wrapper approach, e.g.
a la numeric Monid instances, would be both unpalatable and ultimately
pointless.)

So, in summary, I'd find the argument for the present tuple instances
much more compelling if it *mathematically* were the case that the
only law-abiding instances are those ones. But that is not the case.

Best,

/Henrik









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