Question

I want to put my typed GADT (GExpr) into a hashmap, so I first convert it to a corresponding monomorphic ADT (Expr). When I lookup from the hashmap I’m having trouble converting the monomorphic ADT back into a GADT.

The following is a simplified version. Essentially there are two functions, “dim” and “gexprOfExpr” and I can only get one of them to work at once. Is what I’m trying to do impossible?

{-# OPTIONS_GHC -Wall #-}
{-# Language GADTs #-}

type ListDim = [Int]

data DIM0 = DIM0
data DIM1 = DIM1

class Shape sh where
  shapeOfList :: ListDim -> sh

instance Shape DIM0 where
  shapeOfList _ = DIM0
instance Shape DIM1 where
  shapeOfList _ = DIM1

data Expr = EConst ListDim Double
          | ESum ListDim Int

data GExpr sh where
  GRef :: sh -> Int -> GExpr sh
  GConst :: sh -> Double -> GExpr sh
  GSum :: GExpr DIM1 -> GExpr DIM0  -- GADT, this works for "dim"
--  GSum :: GExpr DIM1 -> GExpr sh -- phantom type, this works for "gexprOfExpr"

dim :: GExpr sh -> sh
dim (GRef sh _) = sh
dim (GConst sh _) = sh
dim (GSum _) = DIM0

gexprOfExpr :: Shape sh => Expr -> GExpr sh
gexprOfExpr (EConst lsh x) = GConst (shapeOfList lsh) x
gexprOfExpr (ESum lsh k) = GSum $ GRef (shapeOfList lsh) k

Note: I do know the type I’m trying to recover. If it would help, this would be fine:

gexprOfExpr :: Shape sh => sh -> Expr -> GExpr sh

Answer 1

Saizan from #haskell gave me a tip that led to an answer. Here’s the working version:

{-# OPTIONS_GHC -Wall #-}
{-# Language GADTs #-}

import Data.Maybe

type ListDim = [Int]

data DIM0 = DIM0
data DIM1 = DIM1

class Shape sh where
  shapeOfList :: ListDim -> sh
  maybeGExprOfExpr :: Expr -> Maybe (GExpr sh)
  maybeGExprOfExpr _ = Nothing

instance Shape DIM0 where
  shapeOfList _ = DIM0
  maybeGExprOfExpr (ESum lsh k) = Just $ GSum $ GRef (shapeOfList lsh) k
  maybeGExprOfExpr _ = Nothing

instance Shape DIM1 where
  shapeOfList _ = DIM1


data Expr = EConst ListDim Double
          | ESum ListDim Int

data GExpr sh where
  GRef :: sh -> Int -> GExpr sh
  GConst :: sh -> Double -> GExpr sh
  GSum :: GExpr DIM1 -> GExpr DIM0

dim :: GExpr sh -> sh
dim (GRef sh _) = sh
dim (GConst sh _) = sh
dim (GSum _) = DIM0

gexprOfExpr :: Shape sh => Expr -> GExpr sh
gexprOfExpr (EConst lsh x) = GConst (shapeOfList lsh) x
gexprOfExpr e@(ESum _ _) = fromJust $ maybeGExprOfExpr e