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Polymorphic Variants
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 Date: 2007-01-19 (10:35) From: Tom Subject: Re: Fwd: [Caml-list] Polymorphic Variants
```On 19/01/07, Dirk Thierbach <dthierbach@gmx.de> wrote:
>
> On Thu, Jan 18, 2007 at 09:14:09PM +0000, Jon Harrop wrote:
> > On Thursday 18 January 2007 16:23, Tom wrote:
>
> >> No... i rather thought it that way:
> >>      x is anything
> >>      x * x is either int or float, so x is either int or float
> >>      x * x + x * x is either int or float, so the two (x * x) are
> either
> >> both int or both float
> >>      sqrt accepts a float argument, so x * x + x * x must be float, so
> (x *
> >> x) must be float, so x must be float.
>
> BTW, that's what Haskell's type classes do:

type classes, with an advantage that type classes are infered automatically
by the compiler (or, actually, are not named/declared - the compiler simply
lists all types belonging to the current typeclass

Prelude> :t \x -> x
> \x -> x :: forall t. t -> t
>
> Prelude> :t \x -> x * x
> \x -> x * x :: forall a. (Num a) => a -> a

forall a . (int, float, complex, fraction, bignum, int32, vector2,
vector3, string) => a -> a

or, what I would prefer:

[int -> int | float -> float | complex -> complex | fraction ->
fraction | bignum -> bignum | int32 -> int32 | vector2 -> vector2 | vector3
-> vector3 | string -> string]

(Yes, it seems a lot of writing... but remember that it is not you who
writes that, it's the compiler. While for such short types, a -> a,
Haskell's notation is better, it could become hard to understand with more
complex types:
forall a . (float, complex, fraction) => forall b . (int, string) => a
-> a -> b -> b -> (a, b)
Now, go figure all the possibilities... It's much simpler when the compiler
lists all the combinations for you.

> Hell, I want to overload 0 to mean 0, 0., 0. + 0.i, zero vector and
> > the zero matrix.
>
> No problem either: Number literals like "0" are translated into the