[Haskell-beginners] How would you implement Instant and Interval

[Daniel Bergey]

On 2015-10-27 at 13:53, martin <martin.drautzburg at web.de> wrote:
> Hello all
>
> If I define an Instant as a point in Time and an Interval as the difference between two Instants, and I also want to use
> (+) and (-), how can I do this.
>
> My initial thought making them instances of the Num class, but that does not work. (-) is okay on Intervals, but on
> Instant it returns a different type (Interval).
>
> Is it possible at all to define a typeclass with (-) :: Instant -> Instant -> Interval without using language extensions?

I think you are asking for the same type class function to have
the types

`Instant -> Instant -> Interval`

and

`Interval -> Interval -> Interval`

for two different instances.  I don't believe this is possible without
language extensions.  Below is an example of doing it with
TypeFamilies.  If I actually wanted this, I'd probably use the Affine
class from linear[1] or vector-space[2] instead of the Sub class I
define here.  At any event, I don't think I'd want to give up on using -
in it's normal meaning of Num, in order to use it for Time and Interval.

newtype Time = Time Double deriving Show
newtype Interval = Interval Double deriving Show

class Sub a where
  type Diff a
  (.-.) :: a -> a -> Diff a

instance Sub Time where
  type Diff Time = Interval
  (Time a) .-. (Time b) = Interval (a - b)

instance Sub Interval where
  type Diff Interval = Interval
  (Interval a) .-. (Interval b) = Interval (a - b)

Footnotes: 
[1]  http://hackage.haskell.org/package/linear-1.20.2/docs/Linear-Affine.html

[2]  http://hackage.haskell.org/package/vector-space-0.10.2/docs/Data-AffineSpace.html