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

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.

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On 16 Dec 2020, at 22:57, David Feuer 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 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.

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