Type aliasing

Type aliasing is something that’s been included in most languages for a while now. Basically, if you have a type Foo, aliasing Bar to Foo means that you introduce a new symbol Bar that refers to Foo. It’s not a new type, it’s just an alias, a binding.

In Haskell, we do aliasing with the keyword type, which is a bit stupid since we won’t necessarily alias a type (we could alias a function, a typeclass constraint, and so on and so forth).

Aliasing is great and useful in many ways. For instance, there’s a Haskell package I love called linear. That package is used to deal with linear algebra, and you can find common math types in there among vectors (Vec) and low-algebra vectors (V2, V3, V4). There are the same things for matrices (M22 for 2x2 matrices, M33, M44).

If you come up with using 4x4 floating matrices a lot, you might end up with a lot of M44 Float everywhere in your code. So that would be sane aliasing it. Like so:

type V4F = V4 Float

This is a perfect aliasing use to me as V4F is straight-forward for graphics people. Furthermore, linear is pretty a standard now in Haskell linear algebra application, so V4 should be familiar to you.

However, there is a drawback with type aliasing.

Why has type aliasing almost killed me

I spent more than a day crawling for a bug. I was refactoring code, a lot of code. Nothing fancy though, just some code cleaning. Nevertheless, I created a brand new git branch to make my cleaning. On the initial branch, the application behavior was normal. After having cleaned the code, I got a black screen.

After a long investigation, I found out that the bug was due to a mismatch between two matrices – i.e. M44 Float. One matrix is used as a camera projection and the other one is used as a light projection. In term of code, both matrices are placed in a type. I simplified (a lot), but this is the idea:

data Foo = Foo {
    -- […]
  , cameraProjection :: M44 Float
  , lightProjection :: M44 Float
  }

What makes those matrices different in term of compilation? Nothing. M44 Float and M44 Float are the same type. Swapping matrices is then silently compiled, since it’s not an error to the compiler. And such a swapping result in a terrible and hard to find bug.

Yeah, so we could have simply aliased those matrices to two different names!

Remember what I said earlier. Aliased types are not new types. They’re bindings in the type system:

type CameraProjection = M44 Float
type LightProjection = M44 Float

Here, both CameraProjection and LightProjection are the same type. If a function expects a CameraProjection, it actually expects a M44 Float. You could then pass a value of type M44 Float or even LightProjection, that would be legit.

Is there a solution yet?

Yes, there is. Haskell has several keywords to create types:

• type, which is, as we’ve already seen, a way to alias types;
• data, which is used to create data types;
• newtype, which is used as a type wrapper to introduce a data type.

newtype is the most important keyword for us here. Basically, it has the same semantic as data except that newtype introduces a type with a single field; it can’t have none nor several. newtype is often used to express the same thing that the inner type, but adding / removing some properties.

For instance, Bool can’t be an instance of Monoid since we could define a lot of instances. mempty could be True if we consider the monoid of booleans with AND but it would be False if we consider the monoid of booleans with OR. Well, we could write those, actually:

newtype And = And { getAnd :: Bool } deriving WhateverYouWant
newtype Or = Or { getOr :: Bool } deriving WhateverYouWant

instance Monoid And where
  mempty = True
  And a `mappend` And b = And (a && b)

instance Monoid Or where
  mempty = False
  Or a `mappend` Or b = Or (a || b)

Those two types are defined in Data.Monoid as All and Any.

Back to our problem. We could use newtype to add M44 Float the correct semantic, and disable us to mix them:

newtype CameraProjection = CameraProjection { getCameraProjection :: M44 Float }
newtype LightProjection = LightProjection { getLightProjection :: M44 Float }

And here, CameraProjection ≠ LightProjection. If a function expects a CameraProjection, you can’t pass anything else than a CameraProjection.

However, be careful. You’ll have to wrap a M44 Float into your CameraProjection. Such a function, like the CameraProjection constructor, is not semantic safe since you could still pass a light representation. Nevertheless, it’s better than the initial design since once wrapped, you can’t make confusions anymore.

Final words

To sum up, use aliasing when it’s handy but don’t use it if it could break semantics or add confusion. If you have several types that use the same type (e.g. colors and positions could use the same V3 Float type), don’t use aliases! Create proper types to prevent confusion later on. Your compiler will reward you, then you don’t get nasty runtime bugs ;).