ex6.hs

class HasVars a where
  var :: String -> a

data VarExprT
  = Lit' Integer
  | Var String
  | Add' VarExprT VarExprT
  | Mul' VarExprT VarExprT
  deriving (Eq, Show)

instance Expr VarExprT where
  lit = Lit'
  add = Add'
  mul = Mul'

instance HasVars VarExprT where
  var = Var

instance HasVars (M.Map String Integer -> Maybe Integer) where
  var = M.lookup

instance Expr (M.Map String Integer -> Maybe Integer) where
  lit x m = Just x
  add f g m = liftA2 (+) (f m) (g m)
  mul f g m = liftA2 (*) (f m) (g m)

withVars :: [(String, Integer)]
         -> (M.Map String Integer -> Maybe Integer)
         -> Maybe Integer
withVars vs exp = exp $ M.fromList vs