# 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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