Make a Product adapter for the Itertools trait

[alexchandel]

In addition to iproduct!(iter_a, iter_b), Itertools should have something like iter_a.times(iter_b) or iter_a.cartesian_product(iter_b). This would let you take the product of iterators inline, functional style.

Maybe a method like this:

pub trait Itertools: Iterator {
    ...
    fn cartesian_product<U: Iterator>(self, other: U) -> Product<Item, Self, U> 

This would allow you to do much better inline operations, like:

oranges.iter().map(apple_for_orange).filter(is_granny_smith).cartesian_product(
    guests.iter().map(favorite_desert)
).map(more_nonsense).etc()

This shouldn't require higher-kinded types either.

[bluss]

An adaptor for product is a good idea, I guess it's the most natural way to use it. Not sure if we can make it expand tuples like the iproduct macro does (((x, y), z) → (x, y, z)).

[alexchandel]

That would be preferable, but I think it requires variadic generics, or at minimum having two impls, one for Item=A and one for Item=(A,B).

I'd be satisfied with the basics for now. I can always map(|((x,y),z)| (x,y,z)) until then.

[bluss]

Is there any reason to prefer the long name cartesian_product? I.e. are there other products we might want to add?

[alexchandel]

@bluss Can't think of any others (not that there aren't any), but we want to avoid product() because it's taken by MultiplicativeIterator. times() would work too, though it's less specific.

[FranklinChen]

Something else very useful is a Cartesian product without a hardcoded length, i.e., concretely something like taking a vector of iterators and returning a iterator of vectors: a form of Haskell's sequenceA, where

sequenceA [[0..2], [0..2], [0..2]] == [[0,0,0],[0,0,1],[0,0,2],[0,1,0],[0,1,1],[0,1,2],[0,2,0],[0,2,1],[0,2,2],[1,0,0],[1,0,1],[1,0,2],[1,1,0],[1,1,1],[1,1,2],[1,2,0],[1,2,1],[1,2,2],[2,0,0],[2,0,1],[2,0,2],[2,1,0],[2,1,1],[2,1,2],[2,2,0],[2,2,1],[2,2,2]]