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

[Tom Smeding]

You say 'abs x = x/2', but what's that (/)? For example, what is 'abs' supposed to give when called on (the representation of) the polynomial X^2 + 3X + 2?

Interesting also to think about what the meaning of 'n*(n+1)/2' on polynomials should even be. What is the sum of the numbers (polynomials?) from 1 to X + 1?

- Tom

-------- Original Message --------

On 16 Dec 2020, 23:48, Henning Thielemann < lemming at henning-thielemann.de> wrote:

On Wed, 16 Dec 2020, Tom Smeding wrote:

> I'm not sure what "sound" means if the documentation[1] for Num states that the only reasonable expectation is

> that of a ring.

>

> However, if we are to have laws for signum and abs, then I would expect that 'abs n = n * signum n'. My

> definitions satisfy that law.

What about abs x = x/2 and signum _ = 2?

Would satisfy your law and solve the problem of the original poster.
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