Question

I wrote a mathematical Vector module in Haskell.

So I started out with:

data Vector a = Vector !a !a !a deriving (Eq, Show)

Fine—this lets me use any numerical data type I want. The problem is that I don’t want to be writing Double and Vector Double everywhere for the simple reason that I shouldn’t have to. So I add:

type Scalar = Double
type Vector = Vector Scalar

But of course that second line is wrong, since there are now two declarations of Vector. So what should I change it to? I think to myself, no, I’m going to be writing this all over my code, so I want to leave the type alias simply as Vector. Which means I have to change the data type name. But if I change that, then I feel like I should also change the constructor, which makes everything more confusing. But if it feels awkward making the constructor have the same name as the type alias this way.

Right now I have this:

type Scalar = Double
type Vector = VectorT Scalar

data VectorT a = Vector !a !a !a deriving (Eq, Show)

I picked T arbitrarily (I guess it stands for “type”) but I’m not so sure about this. Normally when I document functions I would say -- Calculate the magnitude of a Vector, but with VectorT I feel like I should really be using that type name. So I resort to just referring to them as vectors (not capitalized)—except then I feel like I have to apply this convention to every comment for every data type.

Has anyone been in a similar situation? Can anyone think of a more elegant solution in this case?

Answer 1

One solution to your particular problem would be to have the data type in a different module from the type synonym. That is, have a Math.Vector module which contains the data declaration and some generic functions (that is, functions working for all numeric types). Then, when you actually use Vector Double in your code a lot, just create the type synonym using a qualified import:

import qualified Math.Vector as MV

type Scalar = Double
type Vector = MV.Vector Scalar

I think this makes sense from a code organization standpoint. Particularly, if you’ve defined your Vector type to work on all numeric types, I expect the functions in that module to also work on all numeric types. The fact that you use Vector Double a lot in some other part of the code should not affect the module where Vector is actually defined. After all, it’s completely reasonable to imagine using Vector Int a lot in yet another part of your program.

As an aside, I’m not sure calling it Vector is the best idea. A vector does not necessarily have to have three dimensions, so I would call your data type something like Vector3D. This is actually the name used in some other APIs (like the Java 3D API), so it’s probably a good choice.