Re: [Haskell-cafe] Restrict values in type

Oh, I didn't know that the singletons library provides the equality type family, that's nice On Wed, Jan 15, 2014 at 5:55 PM, Andras Slemmer <0slemi0@gmail.com> wrote:

...

I have been looking at DataKinds and GADTs, but I can't quite figure out if they actually help me here at all. You are on the right track. With DataKinds and GADTs you can create an index type for PenShape:

data Shape = Circle | Rectangle | Arbitrary

data PenShape s where PenCircle :: Float -> PenShape Circle PenRectangle :: Float -> Float -> PenShape Rectangle ArbitraryPen :: PenShape Arbitrary

You can use this index 's' to restrict PenShape to a particular constructor, or none at all:

data Stroke where Spot :: Point -> PenShape s -> Stroke -- any shape allowed Arc :: Point -> Point -> Point -> PenShape Circle -> Stroke -- only circle

In the Spot case the type variable 's' will be existentially hidden, meaning any type can go there.

The tricky part comes when you want to have a notion of "or" in the case of Line. We basically need decidable type equality for this. Let's assume we have a way of deciding whether two lifted Shape types are equal and we get back a lifted Bool. Now we can write a type level "or" function:

type family Or (a :: Bool) (b :: Bool) :: Bool type instance Or False False = False type instance Or True b = True type instance Or a True = True

Now the Line case in the GADT would look something like this:

Line :: Or (s :== Circle) (s :== Rectangle) ~ True => -- circle or rectangle Point -> Point -> PenShape s -> Stroke

where :== is our type equality predicate. You can write this by hand if you'd like but it's pretty tedious and really should be inferred by the compiler or some automated process. And indeed the 'singletons' library does just this (and more), all you need to do is wrap your Shape definition in some th:

$(singletons [d|data Shape = Circle | Rectangle | Arbitrary deriving (Eq)|])

And voila you have a nice type safe datastructure:)

A full module can be found here: http://lpaste.net/98527

On 13 January 2014 16:25, Daniil Frumin wrote:

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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 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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