Use Lens as `map`

Question

I want to convert this line of code map (^?! ix 0) [[0, 1], [4, 5], [9, 1]] to entirely use lenses, so something like [[0, 1], [4, 5], [9, 1]] & each . ix 0. However, the types don't match up. What is the correct way to do this?

Joey

Answer 1

Use folded:

Prelude Control.Lens> [[0, 1], [4, 5], [9, 1]] ^.. folded . ix 0
[0,4,9]

Works on any Foldable.

Also, if you plan to always extract the first element, perhaps it would be clearer to use the _head traversal from Control.Lens.Cons instead of ix.

[[0, 1], [4, 5], [9, 1]] ^.. folded . _head

Grainy

Answer 2

You can use either of

Prelude Control.Lens> [[0, 1], [4, 5], [9, 1]] & each %~ (^?! ix 0)
[0,4,9]
Prelude Control.Lens> [[0, 1], [4, 5], [9, 1]] ^.. each . ix 0
[0,4,9]

The first corresponds to precisely what you wrote, using the unsafe (^?!) operator, which means that it can give an error. The second is safer by leaving out empty lists.

They work in somewhat different ways: The first creates a modified version of your original structure, which corresponds more to what map does, and it can be used on structures that aren't lists.

The second creates a list summary of your structure using the lens fold provided; although it can be used with many kinds of structures, the result is always a list.

You can also replace each by traverse (or, as @danidiaz points out, the slightly more general traversed) in this. The former works for many special things like tuples, while the latter works for any Traversable.

Kleeman

Perhaps you mean traversed from Control.Lens.Traversal, instead of traverse? – Grainy

@Grainy Nope, I mean traverse. Although it isn't from lens, it's considered an essential part of it. – Landsman

@Grainy Oh I see, both work here. It seems traversed is more general, allowing indices. – Landsman

I wasn't aware that one could use traverse directly. But looking at the type, I should have been. – Grainy