# Haskell/Phantom types

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Phantom types are a way to embed a language with a stronger type system than Haskell's.

## Phantom types[edit]

An ordinary type

data T = TI Int | TS String plus :: T -> T -> T concat :: T -> T -> T

its phantom type version

data T a = TI Int | TS String

Nothing's changed - just a new argument `a`

that we don't touch. But magic!

plus :: T Int -> T Int -> T Int concat :: T String -> T String -> T String

Now we can enforce a little bit more!

This is useful if you want to increase the type-safety of your code, but not impose additional runtime overhead:

-- Peano numbers at the type level. data Zero = Zero data Succ a = Succ a -- Example: 3 can be modeled as the type -- Succ (Succ (Succ Zero))) type D2 = Succ (Succ Zero) type D3 = Succ (Succ (Succ Zero)) data Vector n a = Vector [a] deriving (Eq, Show) vector2d :: Vector D2 Int vector2d = Vector [1,2] vector3d :: Vector D3 Int vector3d = Vector [1,2,3] -- vector2d == vector3d raises a type error -- at compile-time: -- Couldn't match expected type `Zero' -- with actual type `Succ Zero' -- Expected type: Vector D2 Int -- Actual type: Vector D3 Int -- In the second argument of `(==)', namely `vector3d' -- In the expression: vector2d == vector3d -- while vector2d == Vector [1,2,3] works

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