[Haskell-cafe] Restrict values in type

Daniil Frumin difrumin at gmail.com
Mon Jan 13 16:25:26 UTC 2014


I devised the following (unarguably verbose) solution using the
singletons [1] library

{-# LANGUAGE DataKinds, TypeFamilies, MultiParamTypeClasses #-}
{-# LANGUAGE TemplateHaskell, GADTs, FlexibleContexts #-}
module Image where
import Data.Singletons

type Point = (Float,Float)

$(singletons [d|
 data Shape' = Circle' | Rectangle' | Arbitrary'
            deriving (Eq)
 data Stroke' = Line' | Arc' | Spot'
            deriving (Eq)
 |])


data PenShape shape where
    Circle :: SingI Circle' => Float -> PenShape Circle'
    Rectangle :: SingI Rectangle' => Float -> Float -> PenShape Rectangle'
    ArbitraryPen :: PenShape Arbitrary'

class AllowedStroke (a::Stroke') (b::Shape') where

instance AllowedStroke Line' Circle'
instance AllowedStroke Line' Rectangle'
instance AllowedStroke Arc' Circle'
instance AllowedStroke Spot' Circle'
instance AllowedStroke Spot' Rectangle'
instance AllowedStroke Spot' Arbitrary'

data Stroke where
    Line :: AllowedStroke Line' a
         => Point -> Point -> PenShape a -> Stroke
    Arc  :: AllowedStroke Arc' a
         => Point -> Point -> Point -> PenShape a -> Stroke
    Spot :: AllowedStroke Spot' a
         => Point -> PenShape a -> Stroke

{-
h> :t Line (1,1) (1,1) (Circle 3)
Line (1,1) (1,1) (Circle 3) :: Stroke
h> :t Line (1,1) (1,1) (Rectangle 3 3)
Line (1,1) (1,1) (Rectangle 3 3) :: Stroke
h> :t Line (1,1) (1,1) ArbitraryPen

<interactive>:1:1:
    No instance for (AllowedStroke 'Line' 'Arbitrary')
      arising from a use of `Line'
    Possible fix:
      add an instance declaration for (AllowedStroke 'Line' 'Arbitrary')
    In the expression: Line (1, 1) (1, 1) ArbitraryPen
-}

--- unfortunately this still gives non-exhaustive pattern match
    --- warning :(
showStroke :: Stroke -> String
showStroke (Line _ _ (Circle _)) = "Line + Circle"
showStroke (Line _ _ (Rectangle _ _)) = "Line + Rect"
showStroke (Arc _ _ _ (Circle _)) = "Arc"
showStroke (Spot _  _) = "Spot"

The shortcomings of this approach are the following:
  - verbosity and repetition (eg: Shape' and Shape)
  - still gives pattern matching warning ( I suspect that's because
typeclasses are open and there is really no way of determining whether
something is an 'AllowedStroke' or not)

Feel free to improve the code and notify the list :)

[1] http://hackage.haskell.org/package/singletons

On Mon, Jan 13, 2014 at 7:38 AM, 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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>



-- 
Sincerely yours,
-- Daniil


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