{-# LANGUAGE GADTs #-}

data Expr t where 
  I :: Int -> Expr Int
  B :: Bool -> Expr Bool
  AddInt :: Expr Int -> Expr Int -> Expr Int
  IsZero :: Expr Int -> Expr Bool
  If :: Expr Bool -> Expr t -> Expr t -> Expr t


eval :: Expr t -> t
eval (I i)          = i
eval (B b)          = b
eval (AddInt e1 e2) = eval e1 + eval e2
eval (IsZero e)     = eval e == 0
eval (If e1 e2 e3)  = if eval e1 
                         then eval e2 
                         else eval e3