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Clark Gaebel

5 Mar 2012 5 Mar '12

4:04 p.m.

Is there any way in Haskell to have the correct function selected based on the types of two different types? For example, let's say I'm writing intersection tests: aABBandAABB :: AABB -> AABB -> Bool oBBandOBB :: OBB -> OBB -> Bool oBBandPoint :: OBB -> Point -> Bool Is there some way (such as with Type Families) that I can write some sort of generic method for this: intersects :: Intersectable -> Intersectable -> Bool which automatically selects the right function to call based on the types of the two intersectables? Regards, - clark

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Felipe Almeida Lessa

5 Mar 5 Mar

4:07 p.m.

{-# LANGUAGE MultiParamTypeClasses #-} class Intersectable a b where intersectsWith :: a -> b -> Bool -- Felipe.

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Clark Gaebel

4:24 p.m.

Well look at that. Thanks! On Mon, Mar 5, 2012 at 4:07 PM, Felipe Almeida Lessa wrote:

{-# LANGUAGE MultiParamTypeClasses #-}

class Intersectable a b where intersectsWith :: a -> b -> Bool

-- Felipe.

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wren ng thornton

6 Mar 6 Mar

12:28 a.m.

On 3/5/12 4:24 PM, Clark Gaebel wrote:

Well look at that.

Thanks!

On Mon, Mar 5, 2012 at 4:07 PM, Felipe Almeida Lessa wrote:

...
{-# LANGUAGE MultiParamTypeClasses #-}

class Intersectable a b where intersectsWith :: a -> b -> Bool

Assuming that intersectsWith is something like unification, equality, or similar operations: Do note that this can lead to needing quadratically many instances, about half of which will be redundant if intersectsWith is supposed to be symmetric. Often times we know that the vast majority of these quadratically many instances should be vacuous (i.e., always return False), and it'd be nice to avoid writing them out. This can be achieved via -XOverlappingInstances where you give a default instance: instance Intersectable a b where intersectsWith _ _ = False and then override it for more specific choices of a and b. Beware that if you want to have other polymorphic instances you may be forced to use -XIncoherentInstances, or else resolve the incoherence by filling out the lattice of instances. The other notable complication is if you want your collection of types to have more than just a set structure (e.g., if you want some kind of subtyping hierarchy). It's doable, but things get complicated quickly. Other than those caveats, have at it! The ability to do this sort of thing is part of what makes Haskell great. Few languages have multiple-dispatch this powerful. -- Live well, ~wren

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Clark Gaebel

12:40 a.m.

Wow, that's a lot of freedom in the type system. Haskell never fails to amaze me how it can remove features and increase expressiveness in one fell sweep. I also like how the user will get type errors if attempting intersection between two geometries which do not have intersection defined. It makes the API really intuitive. In terms of the extra features, in my case (geometric intersection tests), MultiParamTypeClasses seem to be the perfect fit. However, thanks for giving me a much more comprehensive arsenal of type system hacks! Regards, - clark On Tue, Mar 6, 2012 at 12:28 AM, wren ng thornton wrote:

On 3/5/12 4:24 PM, Clark Gaebel wrote:

...
Well look at that.

Thanks!

On Mon, Mar 5, 2012 at 4:07 PM, Felipe Almeida Lessa wrote:

...
{-# LANGUAGE MultiParamTypeClasses #-}

class Intersectable a b where intersectsWith :: a -> b -> Bool

Assuming that intersectsWith is something like unification, equality, or similar operations:

Do note that this can lead to needing quadratically many instances, about half of which will be redundant if intersectsWith is supposed to be symmetric.

Often times we know that the vast majority of these quadratically many instances should be vacuous (i.e., always return False), and it'd be nice to avoid writing them out. This can be achieved via -XOverlappingInstances where you give a default instance:

instance Intersectable a b where intersectsWith _ _ = False

and then override it for more specific choices of a and b. Beware that if you want to have other polymorphic instances you may be forced to use -XIncoherentInstances, or else resolve the incoherence by filling out the lattice of instances.

The other notable complication is if you want your collection of types to have more than just a set structure (e.g., if you want some kind of subtyping hierarchy). It's doable, but things get complicated quickly.

Other than those caveats, have at it! The ability to do this sort of thing is part of what makes Haskell great. Few languages have multiple-dispatch this powerful.

-- Live well, ~wren

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Clark Gaebel
Felipe Almeida Lessa
wren ng thornton