Array functor uglified

gistfile1.md

Let us make the array functor slightly uglier.

According to Functor's definition, for every type a, we first need to define the type F(a), the set of all admissible values for our Functor.

For the array Functor Array, that would be the set [a] of all arrays with entries of type a.

We now define a new Functor F, where we slightly change the set of values F(a): Namely, we say that an array arr is of type F(a) if either

(1) arr.length !== 1

or

(2) arr === [0]

In other words, any array is allowed apart from length 1, where only the array [0] is allowed.

Now define the map:

// (a -> b) -> F(a) -> F(b)
const map = f => arr => 
    (arr.length === 1) ? [0] : arr.map(f)

I think this provides a Functor, because all the functor laws can be checked independently for arrays of a fixed lengh.

The type definition of such an array would have to be

data ModifiedList a = Nil | SingleZeroList | Cons a (Array a)

So it's a list with a fixed special case. I think, in terms of encoding, this is actually just an obfuscated Maybe List - the list itself is still unbreakable, hah :)