[Haskell-cafe] phantom types
wren ng thornton
wren at freegeek.org
Sun Aug 19 05:29:46 CEST 2012
On 8/17/12 5:35 AM, TP wrote:
> I am currently reading documentation on Generalized Algebraic Data Types:
> I have a question concerning this page. Let us consider the following code
> proposed in the page:
> -- Phantom type variable a (does not appear in any Expr: it is just a
> -- dummy variable).
> data Expr a = I Int
> | B Bool
> | Add (Expr a) (Expr a)
> | Mul (Expr a) (Expr a)
> | Eq (Expr a) (Expr a)
> deriving (Show)
> I don't understand. When we write "eval (I n) = n", as I is a constructor
> which takes an Int as argument, we are able to deduce that the type of n is
> Int; so the type of eval should be in this case "Expr Int -> Int".
> What do I miss?
Perhaps it'd help to rewrite the above ADT using GADT syntax (but note
that its the exact same data type):
data Expr :: * -> * where
I :: Int -> Expr a
B :: Bool -> Expr a
Add :: Expr a -> Expr a -> Expr a
Mul :: Expr a -> Expr a -> Expr a
Eq :: Expr a -> Expr a -> Expr a
So, when looking at the pattern (I n), since I :: Int -> Expr a we know
that n :: Int and that (I n) :: Expr a.
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