Re: Functor, Applicative, Monad, Foldable, Traversable instances for (, , ) a b

6 Apr 2017

      I don't think it is the "appropriate" set. It's an example. 0 is in the
set of integers. The value 0 is in many sets. ((,) a) is the set of
things which are Foldable, and consequently, have a length, which
reasoning by the type and kind system, immediately leads to the
conclusion that it is (very obviously) 1. I am deliberately picking on
the argument, "from obviousness", which is the best counter-argument so
far (according to the counter-arguers; hoping not to misrepresent here).
This is not only a weak argument, I hope we can agree, but *the exact
opposite* is true, where we probably disagree.

Our premises:

  Foldable :: (* -> *) -> Constraint
  length :: forall f. * -> *. f a -> Int
  let length = foldl (+) 0 -- or similar
  let f ~ ((,) a)

Anything but length=1 for not only not "obvious", but I argue completely
ridiculous, by the definition of length. I am not fond of the "argument
from obviousness", but if I am forced to use it, I will, and any
counter-argument will still fail.

PS: I didn't see your original question, sorry. I just stopped looking
at the thread for a bit.

On 06/04/17 17:28, Jon Fairbairn wrote:
...
Tony Morris  writes:
...
I did read it. I chose not to respond. I do not believe it to be a
constructive avenue.
I am repeating myself far less than the misunderstanding and
inconsistency around "tuples." To this end, I believe is worthwhile to
continue pointing out the inconsistency, and only slightly less so than
those who hold a contrary inconsistent position, who are inadvertently
pointing out the inconsistency. 0 is not an integer is a statement of
equal validity, buit more obviously not so.
You keep using “integer”, but didn’t answer my question. What
makes you think that integer is the appropriate set? What do the
negative numbers represent in this context? If the answer is
“nothing”, you are actually talking about natural numbers, and
both the sets ℕ and ℕ⁺ are perfectly respectable.
...
The length of ((,) a) is exactly one. Anything else is
ridiculous.
So that I can understand this, please give an example of a
programme where this usage is meaningful.
— Jón
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