Difference Argument Order

[ajb at spamcop.net]

G'day all.

Quoting Henning Thielemann <lemming at henning-thielemann.de>:

> I assume that these function are for computations like
>   subtract :: DegreeCentigrade -> Kelvin -> DegreeCentigrade
>   diff :: DegreeCentigrade -> DegreeCentigrade -> Kelvin
>  and the intentions are different enough to implement distinct functions.
> I assume that there will be an implementation for 'diff' whenever there is
> one for 'subtract' and vice versa, thus considering them as different
> instances of the same class does not seem to be a good design.

That's interesting, because I was thinking about homogeneous spaces:

    subtract :: Point -> Vector -> Point
    diff :: Point -> Point -> Vector

Or:

    subtract :: Time -> Duration -> Time
    diff :: Time -> Time -> Duration

Or more generally:

    class Group g where
        id :: g
        (+) :: g -> g -> g
        negate :: g -> g

    class (Group g) => LeftGroupAction g x where
        add :: g -> x -> x

        subtract :: x -> g -> x
        subtract x g = add g (negate x)

    class (LeftGroupAction g x) => RegularLeftGroupAction g x where
        diff :: x -> x -> g

Cheers,
Andrew Bromage