[chriswarbo]

Nobody's mentioned dependent typing yet, but languages like Idris and Agda will "narrow types based on control flow" (in fact, since they're pure-functional, control-flow is the same as data-flow). For example, zipping two vectors of the same length:

    zip: Vec n t1 -> Vec n t2 -> Vec n (t1, t2)
    zip Nil Nil = Nil
    zip (Cons x xs) (Cons y ys) = Cons (x, y) (zip xs ys)

Here the 'Vec' type has two constructors, Nil and Cons. Since their types specify the same length, the type-checker knows we can ignore the 'zip Nil Cons' or 'zip Cons Nil' cases.

[alduin32]

This is amazing, but I don't understand the justification :

> Since their types specify the same length, the type-checker knows we can ignore the 'zip Nil Cons' or 'zip Cons Nil' cases.

Specifically, I have trouble understanding "their types specify the same length". Whose types ?

[masklinn]

The types of the vectors: the length is a generic parameter to the type. So a Vec 4 Int and a Vec 5 Int are different types.

[alduin32]

Oh right, the output is parametrized by the input. I suppose this is what dependent types are.

That's really awesome. Thanks for the explanation.

[masklinn]

> Oh right, the output is parametrized by the input. I suppose this is what dependent types are.

Dependent types is really about the ability to parameterise types over values, and reason on those values-dependent types.

[earleybird]

You might read the Vector type constructor 'Vector N T' as "this is a Vector of T's of length N'.