[Haskell-cafe] "Natural" polymorphism for n*(n+1)/2

[MigMit]

A small optimization, maybe: fromInteger ((n * (n+1)) `div` 2)?

> On 16 Dec 2020, at 23:13, Jaro Reinders <jaro.reinders at gmail.com> wrote:
> 
> Num alone is enough: sum [1..n] = sum (map fromInteger [1..n])
> 
> On 12/16/20 11:07 PM, MigMit wrote:
>> Num + Enum would be enough though, since n*(n+1)/2 = sum [1..n], n*(n+1)*(n+2)/6 = sum (map (\m -> sum [1..m]) [1..n]) etc. Not quite effective, of course.
>>> On 16 Dec 2020, at 22:57, David Feuer <david.feuer at gmail.com> wrote:
>>> 
>>> I very much doubt that Num a is sufficient. That's not even enough to check whether a number is even. You can certainly perform the calculation with `Integral a`, but you'll have to apply some external reasoning to see that the result is correct.
>>> 
>>> On Wed, Dec 16, 2020, 4:45 PM M Douglas McIlroy <m.douglas.mcilroy at dartmouth.edu> wrote:
>>> Some nominally rational functions, e.g n*(n+1)/2,
>>> yield integer values for integer arguments. I seek
>>> either a way to wrap such a function so it has type
>>> Num a => a->a or a convincing argument that it can't
>>> be done.
>>> 
>>> Doug
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