Lens | eventually give a unified way

Here is a way using stack. First remove the _n from the columns names, then set_index the column id, mask the cell with empty string that would be remove when stacking the data. Then use reset_index and rename to fit the expected output.

Try with this recursive function:

Updated: As per comments, I've fixed some errors and added a few asides in [[double square brackets]].

Here's how/why your first mMistake works...

A prism is an optic that focus on a "part" that may or may not be present in the "whole". [[Technically, it focuses on the sort of part that can be used to reconstruct an entire whole, so it really pertains to a whole that can come in several alternative forms (as in the case of a sum type), with the "part" being one of those alternative forms. However, if you're only using a prism for viewing and not setting, this added functionality isn't too important.]]

In your example, both _StateRun and _Just are prisms. The _Just prism focuses on the a part of a Maybe a whole. Such an a may or may not be present. If the Maybe a value is Just x for some x :: a, the part a is present and has value x, and that's what _Just focuses on. If the Maybe a value is Nothing, then the part a is not present, and _Just doesn't focus on anything.

It's somewhat similar for your prism _StateRun. If the whole StateStep is a StateRun x y value, then _StateRun focuses on that "part", represented as a tuple of the fields of the StateRun constructor, namely (x, y) :: (Int, Maybe Text). On the other hand, if the whole StateStep is a StatePause, that part isn't present, and the prism doesn't focus on anything.

When you compose prisms, like _StateRun and _Just, and lenses, like stStep and _2, you create a new optic that combines the composed series of focusing operations.

[[As was pointed out in the comments, this new optic isn't a prism; it's "only" traversal. In fact, it's a specific kind of traversal, called an "affine traversal". A run-of-the-mill traversal can focus on zero or more parts, while an affine traversal focuses on exactly zero (part not present) or one (unique part present). The lens library doesn't make the distinction between affine traversals and other sorts of traversals, though. The reason the new optic is "only" an affine traversal instead of a prism relates to that earlier technical point. Once you add lenses, you remove your ability to reconstruct the entire "whole" from a single "part". Again, if you're only using the optics for viewing, not setting, it won't really matter.]]

Anyway, consider the optic (affine traversal):

ix 0 doesn't produce a lens, but a traversal.¹

Informally, a lens is a "path" that will definitively reach a single value (if you follow it within a hypothetical larger value). A traversal is a path to zero or more values. You can set or view the single target of a lens. And you can set the zero or more targets of a traversal (this simply updates all of them that are present, which is a no-op if there are zero present). But viewing the targets of a traversal is less straightforward.

If view simply took a traversal, and an outer structure, and gave you the target value, then it would have a problem. If there are multiple targets, how should it decide which to return? And if there are zero targets, it can't return anything; it would have to be partial. What it needs is a way of condensing zero-or-more values into a single value, so it can return that. And the Monoid class provides exactly the facilities to do that; mempty for if there aren't any targets at all, and <> to condense multiple values to a single one. So view with a traversal² actually requires a Monoid constraint on the returned type, and that's why you're getting the complaint about No instance for (Monoid Int) arising from a use of `ix'.

And in case it isn't clear, you can often compose (with .) different types of optics (the general term for "lens-ish things", including lenses, traversals, and several others). But the result has the capabilities of the least capable of the two inputs. So even though your inner and w are full lenses, composing them with a traversal produced by ix results in a traversal, not a lens.

But in this case you know that you're using ix. The specific kind of traversals ix makes end up having zero or one target, rather than the zero or more targets that traversals have in general. So you could use preview instead of view; for a traversal it will produce a Maybe containing Just the first target of the traversal, or Nothing if there weren't any. A Maybe is exactly what the type system deems appropriate here, since ix can't guarantee there will be a target value, but there won't be more than one.

In my experience, when I try to view something and get this Monoid instance error, it almost always means I have an optic that can't guarantee a result and I should actually be using preview to get a Maybe.

Simple example:

You might rotate the lens in the opposite direction (-180deg) and inverse background position too:

Side note: you don't want to apply background-image on every mousemove, move it to the lens init.

If you are sure that the key is present then you can use fromJust to turn the Maybe User into a User:

The data structure you have for lens is like a multiset, also available as Counter. The part of your algorithm that is the bottle neck in terms of time complexity, is this:

Not much of a standard approach, perhaps, but anyway: alaf can handle the Compose wrapping. For instance: