[Haskell] Generic combination of generic types

[Garrett Mitchener]

I'm not familiar with modal logic, but if modalities stack, you might be
able to do something like this.

-- Garrett Mitchener

{-# OPTIONS_GHC -fglasgow-exts #-}

module Test where

data L a
      = F | T | Atom Int
      | Neg (L a) | And (L a) (L a) | Or (L a) (L a)
      | M (L a) -- the modality a is a phantom type for this
        deriving (Read, Show, Eq)

-- Actually I never use the data constructors, just the types, so you could
leave them out.
data NullModality = NullModality
                    deriving (Read, Show, Eq)

data KModality a = KModality a
                   deriving (Read, Show, Eq)

data KDModality a = KDModality a
                    deriving (Read, Show, Eq)

-- Need multi-parameter type classes for this:
class StripModality m1 m2 | m1 -> m2 where
  stripModality :: L m1 -> L m2
  stripModality F = F
  stripModality T = T
  stripModality (Atom n) = Atom n
  stripModality (Neg p) = Neg (stripModality p)
  stripModality (And p q) = And (stripModality p) (stripModality q)
  stripModality (Or p q) = And (stripModality p) (stripModality q)
  stripModality (M p) = M (stripModality p)

instance StripModality NullModality NullModality

instance StripModality (KModality m) m

instance StripModality (KDModality m) m

expr :: L (KDModality (KModality NullModality))  -- for modality KD on top
of K
expr = And (Atom 1) (M (Atom 2))

-- This is kind of dumb but it shows something this can do

listMAtoms :: StripModality m1 m2 => L m1 -> [L m2]
listMAtoms p@(Atom n) = [stripModality p]
listMAtoms (Neg p) = listMAtoms p
listMAtoms (And p q) = listMAtoms p ++ listMAtoms q
listMAtoms (Or p q) = listMAtoms p ++ listMAtoms q
listMAtoms (M p) = listMAtoms p
listMAtoms _ = []
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