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

[MigMit]

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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