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

[Jaro Reinders]

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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