[Haskell-cafe] A question about type families conflicting instances

[Viktor Dukhovni]

On Wed, Nov 22, 2023 at 12:48:52PM +1030, Darryn wrote:

> Thank you to anyone in advance who can help; I do really appreciate it. 

I think a simple redefinition of "Formable" takes care of the described
obstacle.  Do you have other requirements that make it impractical?

-- 
    Viktor.

---------

{-# LANGUAGE TypeFamilies, TypeFamilyDependencies, MultiParamTypeClasses, FlexibleInstances #-} 

import Data.Kind (Type)

-- A simplified model for sentences.
data S a =   SA a (S a)
           | SB a (S a)
           | SC String
          deriving (Eq, Show)

-- A simplified model for what will be abstract case analysis:
data Form a b =   FA a b
                | FB
          deriving (Eq, Show)

-- A simplified a model for the case analysis class:
class Formable b where
    type Aof b :: Type
    f1 :: b -> Form (Aof b) b
    f2 :: b -> b
    f3 :: b -> Bool

-- Simple test instance of Formable for S:
instance Formable (S a) where
    type Aof (S a) = a
    f1 (SA a y) = FA a y
    f1 (SB a y) = FA a y
    f1 (SC x)   = FB
    f2 (SA a y) = SA a y
    f2 (SB a y) = SA a y
    f2 (SC x)   = SC "nothing"
    f3 (SA a y) = False
    f3 (SB a y) = False
    f3 (SC _)   = True

-- Some test instances all work fine:
-- > f1 (SA "a" (SB "b" (SC "c")))
-- > f2 (SA "a" (SB "b" (SC "c")))
-- > f3 (SA "a" (SB "b" (SC "c")))

-- A model of a wrapper for sentences to iadd integer labels:
data W a = W Int (S a)
        deriving (Eq, Show)

-- Test instance modelling an instance for labelled sentences:
instance Formable (W a) where
    type Aof (W a) = a
    f1 (W k (SA a y)) = FA a (W k y)
    f1 (W k (SB a y)) = FA a (W k y)
    f1 (W k (SC x))   = FB
    f2 (W k x)        = W (1+k) x
    f3 (W k (SA a y)) = False
    f3 (W k (SB a y)) = False
    f3 (W k (SC _))   = True
    -- Intend to re-implement f1,f2,f3 in terms of the instance for S once
    -- I can convince GHC to let both instances stand.