feat: Support over expressions more freely, make expressions printable, rewrite internals (travelling pr 🌴 )

[MarcoGorelli]

I've been on holiday I had a bit of time while travelling recently, so I tried rewriting the internals (yes, again)

The general idea is that narwhals.Expr stores a list of expressions in ._nodes, rather than passing around a bunch of opaque lambdas

What this enables

Expressions are pretty-printable

For example:

In [2]: nw.col('a').abs().rank()
Out[2]: col(a).abs().rank(method=average, descending=False)

This is still quite basic, but we could make it more complex by introducing line breaks if it gets too long. Seems like the kind of thing @camriddell might be interested in?

We can do simple expression rewrites

Currently, (nw.col('a').mean() + 1).over('b') isn't supported:

• for pandas-like, it's a non-elementary operation in over
• for sql, (mean(a) + 1) over (partition by b) isn't valid syntax, it should be mean(a) over (partition by b) + 1

With this PR, however, it is!

What we do here is, when inserting an over node, we push it down before any elementwise operations (such as +, .abs(), sum_horizontal, ...) and apply it to all expressions. There's some more details in the expansion to "how it works"

So now, expressions like (nw.col('a').mean() + 1).over('b') can be supported for all backends

This rewrite is extremely simple and cheap, it's just a matter of inserting a node at some position i rather than at the end of a list. In general, query optimisation is out of scope for Narwhals. But, given that this enables more of Polars' flexibility for other backends, I think this can be in scope.

Per-group broadcasting

Previously, nw.col('a') - nw.col('a').mean() would be fine, but (nw.col('a') - nw.col('a').mean()).over('b') would raise for sql-like backends. Now, it works fine across all backends! Really useful for feature engineering

Simplified internals

• We can completely get rid of depth, function_name, scalar_kwargs
• Replace CompliantWhen / CompliantThen and their complicated interaction with just CompliantNamespace.when_then

In fact, this goes as far as reducing package size by almost 1%. Not that that was the objective with this work, but it's nice to see that it doesn't make the package bigger

What this may open the doors to

• serialisation / deserialisation of expressions. e.g. nw.Expr.from_json(expr.to_json())
• chained window functions, like nw.col('a').shift(7).rolling_mean(7).over('store', order_by='date')
• non-elementary group-by aggregations for pandas/pyarrow, like df.group_by('a').agg((nw.col('b')-nw.col('c')).mean())

Benchmarks

• https://www.kaggle.com/code/marcogorelli/plotly-timings?scriptVersionId=268524779
• https://www.kaggle.com/code/marcogorelli/narwhals-vs-ibis-overhead?scriptVersionId=268533320

I'm not seeing any meaningful impact on performance

[MarcoGorelli]

Unless there's objections, I'll do a careful read-though of everything and then will plan to ship this by the end of the week