[Haskell-cafe] Restrict values in type

[Carter Schonwald]

Hey Luke,
have you seen the diagrams project? http://projects.haskell.org/diagrams/
they've struggled through some of the same problems, and they've worked
very hard to write a power user friendly expressive DSL lib for that
problem domain.
check it out!
-Carter


On Sun, Jan 12, 2014 at 10:38 PM, Luke Clifton <ltclifton at gmail.com> wrote:

> Hi,
>
> I'm quite new to Haskell, and have been loving exploring it. I've always
> been a huge fan of languages that let me catch errors at compile time,
> finding dynamic languages like Python a nightmare to work in. I'm finding
> with Haskell I can take this compile time checking even further than most
> static languages and it has gotten me rather excited. So I was wondering if
> there is a Haskell way of solving my problem.
>
> I'm trying to represent an image made up of a list of strokes. Strokes are
> either lines, arcs or spots, and can be made using different pen shapes.
>
> data Image = Image [Stroke]
>
> data Stroke = Line Point Point PenShape
>     | Arc Point Point Point PenShape
>     | Spot Point PenShape
>
> data PenShape = Circle Float
>     | Rectangle Float Float
>     | ArbitraryPen -- Stuff (not relevant)
>
> And this is all great and works.
>
> But now I have a problem. I want to extend this such that Arc strokes are
> only allowed to have the Circle pen shape, and Lines are only allowed to
> have the Rectangle or Circle pen shapes.
>
> What is the best way of enforcing this in the type system.
>
> I could make more Strokes like LineCircle, LineRectangle, Arc,
> PointCircle, PointRectangle, PointArbitrary and get rid of the PenShape
> type altogether. But this doesn't really feel good to me (and seems like
> the amount of work I have to do is bigger than it needs to be, especially
> if I added more basic pen shapes).
>
> I thought about making the different PenShapes different types, using
> typeclasses and making Stroke an algebraic data type, but then my strokes
> would be of different types, and I wouldn't be able to have a list of
> strokes.
>
> I have been looking at DataKinds and GADTs, but I can't quite figure out
> if they actually help me here at all.
>
> I'm sure there is a way to do this, I'm just not googling properly.
>
> What I want to write is...
>
> data Image = Image [Stroke]
>
> data Stroke = Line Point Point (Circle or Rectangle)
>     | Arc Point Point Point Circle
>     | Spot Point PenShape
>
> data PenShape = Circle Float
>     | Rectangle Float Float
>     | ArbitraryPen -- Stuff (not relevant)
>
> Regards,
>
> Luke
>
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