phantom typeの型推論

Term.hs

data Term t = Zero
            | Succ (Term Int)
            | Pred (Term Int)
            | IsZero (Term Int)
            | If (Term Bool) (Term Int) (Term Int)

-- eval :: Term t -> T
eval Zero       = I 0
eval (Succ e)   = I $ succ $ int $ eval e
eval (Pred e)   = I $ pred $ int $ eval e
eval (IsZero e) = B $ int (eval e) == 0
eval (If b t e) = if bool (eval b) then eval t else eval e

data T = I { int :: Int }
       | B { bool :: Bool }
       deriving Show

{- eval (If b t e)の節で型エラー。evalの型を明示すれば型チェックは通る。

    Couldn't match expected type `Int' with actual type `Bool'
    Expected type: Term Int
      Actual type: Term Bool
    In the first argument of `eval', namely `b'
    In the first argument of `bool', namely `(eval b)'
Failed, modules loaded: none.
-}