[Python] Python Polars copy on write

I come from C++ and R world and just started using Polars. This is a great library. I want to confirm my understanding of its copy-on-write principle:

import polars as pl
x = pl.DataFrame({'a': [1, 2, 3], 'b': [4, 5, 6]})

y = x # Here, y is semantically a copy of x and
# users shall treat y as a copy of x, but under the
# hood, y is currently still just a "reference" to x.

y = y.with_columns(
pl.Series([7, 8, 9]).alias('b')
) # Copy-on-write occurs, but only a new column 'b' are created.

z = y # Users shall treat z as a copy of y, but
# under the hood, z is currently still just a
# "reference" to y.

# Create row index for conditional operations
z = z.with_row_index("row_idx")

z = z.with_columns(
pl.when(pl.col("row_idx") == 0)
.then(10)
.otherwise(pl.col("b"))
.alias("b")
) # Copy-on-write kicks in. The entire
# column 'b' is copied and then the first element is
# changed to 10.

z = z.with_columns(
pl.when(pl.col("row_idx") == 1)
.then(11)
.otherwise(pl.col("b"))
.alias("b")
) # The 2nd element is changed in-place to 11.

# Remove the temporary row index column
z = z.drop("row_idx")


And at this point, x, y and z are semantically independent data frames, and users shall treat them as such. But under the hood, only one column 'a' exists right now. In other words, here are the data actually existing in memory:

[1, 2, 3]
[4, 5, 6]
[7, 8, 9]
[10, 11, 9]


Are all my statements and code comments correct? If not, what should be the correct ones?

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