from __future__ import annotations

import math
from collections.abc import Iterable, Mapping, Sequence
from typing import TYPE_CHECKING, Any, Callable

from narwhals._expression_parsing import ExprKind, ExprNode, evaluate_nodes
from narwhals._utils import (
    _validate_rolling_arguments,
    ensure_type,
    flatten,
    no_default,
    unstable,
)
from narwhals.dtypes import _validate_dtype
from narwhals.exceptions import ComputeError, InvalidOperationError
from narwhals.expr_cat import ExprCatNamespace
from narwhals.expr_dt import ExprDateTimeNamespace
from narwhals.expr_list import ExprListNamespace
from narwhals.expr_name import ExprNameNamespace
from narwhals.expr_str import ExprStringNamespace
from narwhals.expr_struct import ExprStructNamespace
from narwhals.translate import to_native

if TYPE_CHECKING:
    from typing import NoReturn, TypeVar

    from typing_extensions import Concatenate, ParamSpec, Self

    from narwhals._compliant import CompliantExpr, CompliantNamespace
    from narwhals._typing import NoDefault
    from narwhals.dtypes import DType
    from narwhals.series import Series
    from narwhals.typing import (
        ClosedInterval,
        FillNullStrategy,
        IntoDType,
        IntoExpr,
        ModeKeepStrategy,
        NonNestedLiteral,
        NumericLiteral,
        RankMethod,
        RollingInterpolationMethod,
        TemporalLiteral,
    )

    PS = ParamSpec("PS")
    R = TypeVar("R")


class Expr:
    def __init__(self, *nodes: ExprNode) -> None:
        self._nodes = nodes

    def _to_compliant_expr(
        self, ns: CompliantNamespace[Any, Any]
    ) -> CompliantExpr[Any, Any]:
        return evaluate_nodes(self._nodes, ns)

    def _append_node(self, node: ExprNode) -> Self:
        return self.__class__(*self._nodes, node)

    def _with_over_node(self, node: ExprNode) -> Self:
        # insert `over` before any elementwise operations.
        # check "how it works" page in docs for why we do this.
        new_nodes = list(self._nodes)
        kwargs_no_order_by = {
            key: value if key != "order_by" else []
            for (key, value) in node.kwargs.items()
        }
        node_without_order_by = node._with_kwargs(**kwargs_no_order_by)
        n = len(new_nodes)
        i = n
        while i > 0 and (_node := new_nodes[i - 1]).kind is ExprKind.ELEMENTWISE:
            i -= 1
            _node._push_down_over_node_in_place(node, node_without_order_by)
        if i == n:
            # node could not be pushed down, just append as-is
            new_nodes.append(node)
            return self.__class__(*new_nodes)
        if node.kwargs["order_by"] and any(node.is_orderable() for node in new_nodes[:i]):
            new_nodes.insert(i, node)
        elif node.kwargs["partition_by"] and any(
            not node.is_elementwise() for node in new_nodes[:i]
        ):
            new_nodes.insert(i, node_without_order_by)
        elif all(node.is_elementwise() for node in new_nodes):
            msg = "Cannot apply `over` to elementwise expression."
            raise InvalidOperationError(msg)
        return self.__class__(*new_nodes)

    def __repr__(self) -> str:
        """Pretty-print the expression by combining all nodes in the metadata."""
        return ".".join(repr(node) for node in self._nodes)

    def __bool__(self) -> NoReturn:
        msg = (
            f"the truth value of {type(self)} is ambiguous"
            "\n\n"
            "You probably got here by using a Python standard library function instead "
            "of the native expressions API.\n"
            "Here are some things you might want to try:\n"
            "- instead of `nw.col('a') and nw.col('b')`, use `nw.col('a') & nw.col('b')`\n"
            "- instead of `nw.col('a') in [y, z]`, use `nw.col('a').is_in([y, z])`\n"
            "- instead of `max(nw.col('a'), nw.col('b'))`, use `nw.max_horizontal(nw.col('a'), nw.col('b'))`\n"
        )
        raise TypeError(msg)

    def _taxicab_norm(self) -> Self:
        # This is just used to test out the stable api feature in a realistic-ish way.
        # It's not intended to be used.
        return self.abs().sum()

    # --- convert ---
    def alias(self, name: str) -> Self:
        """Rename the expression.

        Arguments:
            name: The new name.

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> df_native = pd.DataFrame({"a": [1, 2], "b": [4, 5]})
            >>> df = nw.from_native(df_native)
            >>> df.select((nw.col("b") + 10).alias("c"))
            ┌──────────────────┐
            |Narwhals DataFrame|
            |------------------|
            |          c       |
            |      0  14       |
            |      1  15       |
            └──────────────────┘
        """
        return self._append_node(ExprNode(ExprKind.ELEMENTWISE, "alias", name=name))

    def pipe(
        self,
        function: Callable[Concatenate[Self, PS], R],
        *args: PS.args,
        **kwargs: PS.kwargs,
    ) -> R:
        """Pipe function call.

        Arguments:
            function: Function to apply.
            args: Positional arguments to pass to function.
            kwargs: Keyword arguments to pass to function.

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> df_native = pd.DataFrame({"a": [1, 2, 3, 4]})
            >>> df = nw.from_native(df_native)
            >>> df.with_columns(a_piped=nw.col("a").pipe(lambda x: x + 1))
            ┌──────────────────┐
            |Narwhals DataFrame|
            |------------------|
            |     a  a_piped   |
            |  0  1        2   |
            |  1  2        3   |
            |  2  3        4   |
            |  3  4        5   |
            └──────────────────┘
        """
        return function(self, *args, **kwargs)

    def cast(self, dtype: IntoDType) -> Self:
        """Redefine an object's data type.

        Arguments:
            dtype: Data type that the object will be cast into.

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> df_native = pd.DataFrame({"foo": [1, 2, 3], "bar": [6.0, 7.0, 8.0]})
            >>> df = nw.from_native(df_native)
            >>> df.select(nw.col("foo").cast(nw.Float32), nw.col("bar").cast(nw.UInt8))
            ┌──────────────────┐
            |Narwhals DataFrame|
            |------------------|
            |      foo  bar    |
            |   0  1.0    6    |
            |   1  2.0    7    |
            |   2  3.0    8    |
            └──────────────────┘
        """
        _validate_dtype(dtype)
        return self._append_node(ExprNode(ExprKind.ELEMENTWISE, "cast", dtype=dtype))

    # --- binary ---
    def _with_binary(self, attr: str, other: Self | Any) -> Self:
        node = ExprNode(ExprKind.ELEMENTWISE, attr, exprs=(other,), str_as_lit=True)
        return self._append_node(node)

    def __eq__(self, other: Self | Any) -> Self:  # type: ignore[override]
        return self._with_binary("__eq__", other)

    def __ne__(self, other: Self | Any) -> Self:  # type: ignore[override]
        return self._with_binary("__ne__", other)

    def __and__(self, other: Any) -> Self:
        return self._with_binary("__and__", other)

    def __rand__(self, other: Any) -> Self:
        return (self & other).alias("literal")  # type: ignore[no-any-return]

    def __or__(self, other: Any) -> Self:
        return self._with_binary("__or__", other)

    def __ror__(self, other: Any) -> Self:
        return (self | other).alias("literal")  # type: ignore[no-any-return]

    def __add__(self, other: Any) -> Self:
        return self._with_binary("__add__", other)

    def __radd__(self, other: Any) -> Self:
        return (self + other).alias("literal")  # type: ignore[no-any-return]

    def __sub__(self, other: Any) -> Self:
        return self._with_binary("__sub__", other)

    def __rsub__(self, other: Any) -> Self:
        return self._with_binary("__rsub__", other)

    def __truediv__(self, other: Any) -> Self:
        return self._with_binary("__truediv__", other)

    def __rtruediv__(self, other: Any) -> Self:
        return self._with_binary("__rtruediv__", other)

    def __mul__(self, other: Any) -> Self:
        return self._with_binary("__mul__", other)

    def __rmul__(self, other: Any) -> Self:
        return (self * other).alias("literal")  # type: ignore[no-any-return]

    def __le__(self, other: Any) -> Self:
        return self._with_binary("__le__", other)

    def __lt__(self, other: Any) -> Self:
        return self._with_binary("__lt__", other)

    def __gt__(self, other: Any) -> Self:
        return self._with_binary("__gt__", other)

    def __ge__(self, other: Any) -> Self:
        return self._with_binary("__ge__", other)

    def __pow__(self, other: Any) -> Self:
        return self._with_binary("__pow__", other)

    def __rpow__(self, other: Any) -> Self:
        return self._with_binary("__rpow__", other)

    def __floordiv__(self, other: Any) -> Self:
        return self._with_binary("__floordiv__", other)

    def __rfloordiv__(self, other: Any) -> Self:
        return self._with_binary("__rfloordiv__", other)

    def __mod__(self, other: Any) -> Self:
        return self._with_binary("__mod__", other)

    def __rmod__(self, other: Any) -> Self:
        return self._with_binary("__rmod__", other)

    # --- unary ---
    def __invert__(self) -> Self:
        return self._append_node(ExprNode(ExprKind.ELEMENTWISE, "__invert__"))

    def any(self) -> Self:
        """Return whether any of the values in the column are `True`.

        If there are no non-null elements, the result is `False`.

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> df_native = pd.DataFrame({"a": [True, False], "b": [True, True]})
            >>> df = nw.from_native(df_native)
            >>> df.select(nw.col("a", "b").any())
            ┌──────────────────┐
            |Narwhals DataFrame|
            |------------------|
            |        a     b   |
            |  0  True  True   |
            └──────────────────┘
        """
        return self._append_node(ExprNode(ExprKind.AGGREGATION, "any"))

    def all(self) -> Self:
        """Return whether all values in the column are `True`.

        If there are no non-null elements, the result is `True`.

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> df_native = pd.DataFrame({"a": [True, False], "b": [True, True]})
            >>> df = nw.from_native(df_native)
            >>> df.select(nw.col("a", "b").all())
            ┌──────────────────┐
            |Narwhals DataFrame|
            |------------------|
            |         a     b  |
            |  0  False  True  |
            └──────────────────┘
        """
        return self._append_node(ExprNode(ExprKind.AGGREGATION, "all"))

    def ewm_mean(
        self,
        *,
        com: float | None = None,
        span: float | None = None,
        half_life: float | None = None,
        alpha: float | None = None,
        adjust: bool = True,
        min_samples: int = 1,
        ignore_nulls: bool = False,
    ) -> Self:
        r"""Compute exponentially-weighted moving average.

        Arguments:
            com: Specify decay in terms of center of mass, $\gamma$, with <br> $\alpha = \frac{1}{1+\gamma}\forall\gamma\geq0$
            span: Specify decay in terms of span, $\theta$, with <br> $\alpha = \frac{2}{\theta + 1} \forall \theta \geq 1$
            half_life: Specify decay in terms of half-life, $\tau$, with <br> $\alpha = 1 - \exp \left\{ \frac{ -\ln(2) }{ \tau } \right\} \forall \tau > 0$
            alpha: Specify smoothing factor alpha directly, $0 < \alpha \leq 1$.
            adjust: Divide by decaying adjustment factor in beginning periods to account for imbalance in relative weightings

                - When `adjust=True` (the default) the EW function is calculated
                  using weights $w_i = (1 - \alpha)^i$
                - When `adjust=False` the EW function is calculated recursively by
                  $$
                  y_0=x_0
                  $$
                  $$
                  y_t = (1 - \alpha)y_{t - 1} + \alpha x_t
                  $$
            min_samples: Minimum number of observations in window required to have a value, (otherwise result is null).
            ignore_nulls: Ignore missing values when calculating weights.

                - When `ignore_nulls=False` (default), weights are based on absolute
                  positions.
                  For example, the weights of $x_0$ and $x_2$ used in
                  calculating the final weighted average of $[x_0, None, x_2]$ are
                  $(1-\alpha)^2$ and $1$ if `adjust=True`, and
                  $(1-\alpha)^2$ and $\alpha$ if `adjust=False`.
                - When `ignore_nulls=True`, weights are based
                  on relative positions. For example, the weights of
                  $x_0$ and $x_2$ used in calculating the final weighted
                  average of $[x_0, None, x_2]$ are
                  $1-\alpha$ and $1$ if `adjust=True`,
                  and $1-\alpha$ and $\alpha$ if `adjust=False`.

        Examples:
            >>> import pandas as pd
            >>> import polars as pl
            >>> import narwhals as nw
            >>> from narwhals.typing import IntoFrameT
            >>>
            >>> data = {"a": [1, 2, 3]}
            >>> df_pd = pd.DataFrame(data)
            >>> df_pl = pl.DataFrame(data)

            We define a library agnostic function:

            >>> def agnostic_ewm_mean(df_native: IntoFrameT) -> IntoFrameT:
            ...     df = nw.from_native(df_native)
            ...     return df.select(
            ...         nw.col("a").ewm_mean(com=1, ignore_nulls=False)
            ...     ).to_native()

            We can then pass either pandas or Polars to `agnostic_ewm_mean`:

            >>> agnostic_ewm_mean(df_pd)
                      a
            0  1.000000
            1  1.666667
            2  2.428571

            >>> agnostic_ewm_mean(df_pl)  # doctest: +NORMALIZE_WHITESPACE
            shape: (3, 1)
            ┌──────────┐
            │ a        │
            │ ---      │
            │ f64      │
            ╞══════════╡
            │ 1.0      │
            │ 1.666667 │
            │ 2.428571 │
            └──────────┘
        """
        return self._append_node(
            ExprNode(
                ExprKind.ORDERABLE_WINDOW,
                "ewm_mean",
                com=com,
                span=span,
                half_life=half_life,
                alpha=alpha,
                adjust=adjust,
                min_samples=min_samples,
                ignore_nulls=ignore_nulls,
            )
        )

    def mean(self) -> Self:
        """Get mean value.

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> df_native = pd.DataFrame({"a": [-1, 0, 1], "b": [2, 4, 6]})
            >>> df = nw.from_native(df_native)
            >>> df.select(nw.col("a", "b").mean())
            ┌──────────────────┐
            |Narwhals DataFrame|
            |------------------|
            |        a    b    |
            |   0  0.0  4.0    |
            └──────────────────┘
        """
        return self._append_node(ExprNode(ExprKind.AGGREGATION, "mean"))

    def median(self) -> Self:
        """Get median value.

        Notes:
            Results might slightly differ across backends due to differences in the underlying algorithms used to compute the median.

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> df_native = pd.DataFrame({"a": [1, 8, 3], "b": [4, 5, 2]})
            >>> df = nw.from_native(df_native)
            >>> df.select(nw.col("a", "b").median())
            ┌──────────────────┐
            |Narwhals DataFrame|
            |------------------|
            |        a    b    |
            |   0  3.0  4.0    |
            └──────────────────┘
        """
        return self._append_node(ExprNode(ExprKind.AGGREGATION, "median"))

    def std(self, *, ddof: int = 1) -> Self:
        """Get standard deviation.

        Arguments:
            ddof: "Delta Degrees of Freedom": the divisor used in the calculation is N - ddof,
                where N represents the number of elements. By default ddof is 1.

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> df_native = pd.DataFrame({"a": [20, 25, 60], "b": [1.5, 1, -1.4]})
            >>> df = nw.from_native(df_native)
            >>> df.select(nw.col("a", "b").std(ddof=0))
            ┌─────────────────────┐
            | Narwhals DataFrame  |
            |---------------------|
            |          a         b|
            |0  17.79513  1.265789|
            └─────────────────────┘
        """
        return self._append_node(ExprNode(ExprKind.AGGREGATION, "std", ddof=ddof))

    def var(self, *, ddof: int = 1) -> Self:
        """Get variance.

        Arguments:
            ddof: "Delta Degrees of Freedom": the divisor used in the calculation is N - ddof,
                     where N represents the number of elements. By default ddof is 1.

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> df_native = pd.DataFrame({"a": [20, 25, 60], "b": [1.5, 1, -1.4]})
            >>> df = nw.from_native(df_native)
            >>> df.select(nw.col("a", "b").var(ddof=0))
            ┌───────────────────────┐
            |  Narwhals DataFrame   |
            |-----------------------|
            |            a         b|
            |0  316.666667  1.602222|
            └───────────────────────┘
        """
        return self._append_node(ExprNode(ExprKind.AGGREGATION, "var", ddof=ddof))

    def map_batches(
        self,
        function: Callable[[Any], CompliantExpr[Any, Any]],
        return_dtype: DType | None = None,
        *,
        returns_scalar: bool = False,
    ) -> Self:
        """Apply a custom python function to a whole Series or sequence of Series.

        The output of this custom function is presumed to be either a Series,
        or a NumPy array (in which case it will be automatically converted into
        a Series).

        Arguments:
            function: Function to apply to Series.
            return_dtype: Dtype of the output Series.
                If not set, the dtype will be inferred based on the first non-null value
                that is returned by the function.
            returns_scalar: If the function returns a scalar, by default it will be wrapped
                in a list in the output, since the assumption is that the function always
                returns something Series-like.
                If you want to keep the result as a scalar, set this argument to True.

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> df_native = pd.DataFrame({"a": [1, 2, 3], "b": [4, 5, 6]})
            >>> df = nw.from_native(df_native)
            >>> df.with_columns(
            ...     nw.col("a", "b")
            ...     .map_batches(lambda s: s.to_numpy() + 1, return_dtype=nw.Float64)
            ...     .name.suffix("_mapped")
            ... )
            ┌───────────────────────────┐
            |    Narwhals DataFrame     |
            |---------------------------|
            |   a  b  a_mapped  b_mapped|
            |0  1  4       2.0       5.0|
            |1  2  5       3.0       6.0|
            |2  3  6       4.0       7.0|
            └───────────────────────────┘
        """
        kind = (
            ExprKind.ORDERABLE_AGGREGATION
            if returns_scalar
            else ExprKind.ORDERABLE_FILTRATION
        )
        return self._append_node(
            ExprNode(
                kind,
                "map_batches",
                function=function,
                return_dtype=return_dtype,
                returns_scalar=returns_scalar,
            )
        )

    def skew(self) -> Self:
        """Calculate the sample skewness of a column.

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> df_native = pd.DataFrame({"a": [1, 2, 3, 4, 5], "b": [1, 1, 2, 10, 100]})
            >>> df = nw.from_native(df_native)
            >>> df.select(nw.col("a", "b").skew())
            ┌──────────────────┐
            |Narwhals DataFrame|
            |------------------|
            |      a         b |
            | 0  0.0  1.472427 |
            └──────────────────┘
        """
        return self._append_node(ExprNode(ExprKind.AGGREGATION, "skew"))

    def kurtosis(self) -> Self:
        """Compute the kurtosis (Fisher's definition) without bias correction.

        Kurtosis is the fourth central moment divided by the square of the variance.
        The Fisher's definition is used where 3.0 is subtracted from the result to give 0.0 for a normal distribution.

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> df_native = pd.DataFrame({"a": [1, 2, 3, 4, 5], "b": [1, 1, 2, 10, 100]})
            >>> df = nw.from_native(df_native)
            >>> df.select(nw.col("a", "b").kurtosis())
            ┌──────────────────┐
            |Narwhals DataFrame|
            |------------------|
            |      a         b |
            | 0 -1.3  0.210657 |
            └──────────────────┘
        """
        return self._append_node(ExprNode(ExprKind.AGGREGATION, "kurtosis"))

    def sum(self) -> Self:
        """Return the sum value.

        If there are no non-null elements, the result is zero.

        Examples:
            >>> import duckdb
            >>> import narwhals as nw
            >>> df_native = duckdb.sql("SELECT * FROM VALUES (5, 50), (10, 100) df(a, b)")
            >>> df = nw.from_native(df_native)
            >>> df.select(nw.col("a", "b").sum())
            ┌───────────────────┐
            |Narwhals LazyFrame |
            |-------------------|
            |┌────────┬────────┐|
            |│   a    │   b    │|
            |│ int128 │ int128 │|
            |├────────┼────────┤|
            |│     15 │    150 │|
            |└────────┴────────┘|
            └───────────────────┘
        """
        return self._append_node(ExprNode(ExprKind.AGGREGATION, "sum"))

    def min(self) -> Self:
        """Returns the minimum value(s) from a column(s).

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> df_native = pd.DataFrame({"a": [1, 2], "b": [4, 3]})
            >>> df = nw.from_native(df_native)
            >>> df.select(nw.min("a", "b"))
            ┌──────────────────┐
            |Narwhals DataFrame|
            |------------------|
            |        a  b      |
            |     0  1  3      |
            └──────────────────┘
        """
        return self._append_node(ExprNode(ExprKind.AGGREGATION, "min"))

    def max(self) -> Self:
        """Returns the maximum value(s) from a column(s).

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> df_native = pd.DataFrame({"a": [10, 20], "b": [50, 100]})
            >>> df = nw.from_native(df_native)
            >>> df.select(nw.max("a", "b"))
            ┌──────────────────┐
            |Narwhals DataFrame|
            |------------------|
            |        a    b    |
            |    0  20  100    |
            └──────────────────┘
        """
        return self._append_node(ExprNode(ExprKind.AGGREGATION, "max"))

    def count(self) -> Self:
        """Returns the number of non-null elements in the column.

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> df_native = pd.DataFrame({"a": [1, 2, 3], "b": [None, 4, 4]})
            >>> df = nw.from_native(df_native)
            >>> df.select(nw.all().count())
            ┌──────────────────┐
            |Narwhals DataFrame|
            |------------------|
            |        a  b      |
            |     0  3  2      |
            └──────────────────┘
        """
        return self._append_node(ExprNode(ExprKind.AGGREGATION, "count"))

    def n_unique(self) -> Self:
        """Returns count of unique values.

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> df_native = pd.DataFrame({"a": [1, 2, 3, 4, 5], "b": [1, 1, 3, 3, 5]})
            >>> df = nw.from_native(df_native)
            >>> df.select(nw.col("a", "b").n_unique())
            ┌──────────────────┐
            |Narwhals DataFrame|
            |------------------|
            |        a  b      |
            |     0  5  3      |
            └──────────────────┘
        """
        return self._append_node(ExprNode(ExprKind.AGGREGATION, "n_unique"))

    def unique(self) -> Self:
        """Return unique values of this expression.

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> df_native = pd.DataFrame({"a": [1, 1, 3, 5, 5], "b": [2, 4, 4, 6, 6]})
            >>> df = nw.from_native(df_native)
            >>> df.select(nw.col("a", "b").unique().sum())
            ┌──────────────────┐
            |Narwhals DataFrame|
            |------------------|
            |        a   b     |
            |     0  9  12     |
            └──────────────────┘
        """
        return self._append_node(ExprNode(ExprKind.FILTRATION, "unique"))

    def abs(self) -> Self:
        """Return absolute value of each element.

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> df_native = pd.DataFrame({"a": [1, -2], "b": [-3, 4]})
            >>> df = nw.from_native(df_native)
            >>> df.with_columns(nw.col("a", "b").abs().name.suffix("_abs"))
            ┌─────────────────────┐
            | Narwhals DataFrame  |
            |---------------------|
            |   a  b  a_abs  b_abs|
            |0  1 -3      1      3|
            |1 -2  4      2      4|
            └─────────────────────┘
        """
        return self._append_node(ExprNode(ExprKind.ELEMENTWISE, "abs"))

    def cum_sum(self, *, reverse: bool = False) -> Self:
        """Return cumulative sum.

        Info:
            For lazy backends, this operation must be followed by `Expr.over` with
            `order_by` specified, see [order-dependence](../concepts/order_dependence.md).

        Arguments:
            reverse: reverse the operation

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> df_native = pd.DataFrame({"a": [1, 1, 3, 5, 5], "b": [2, 4, 4, 6, 6]})
            >>> df = nw.from_native(df_native)
            >>> df.with_columns(a_cum_sum=nw.col("a").cum_sum())
            ┌──────────────────┐
            |Narwhals DataFrame|
            |------------------|
            |   a  b  a_cum_sum|
            |0  1  2          1|
            |1  1  4          2|
            |2  3  4          5|
            |3  5  6         10|
            |4  5  6         15|
            └──────────────────┘
        """
        return self._append_node(
            ExprNode(ExprKind.ORDERABLE_WINDOW, "cum_sum", reverse=reverse)
        )

    def diff(self) -> Self:
        """Returns the difference between each element and the previous one.

        Info:
            For lazy backends, this operation must be followed by `Expr.over` with
            `order_by` specified, see [order-dependence](../concepts/order_dependence.md).

        Notes:
            pandas may change the dtype here, for example when introducing missing
            values in an integer column. To ensure, that the dtype doesn't change,
            you may want to use `fill_null` and `cast`. For example, to calculate
            the diff and fill missing values with `0` in a Int64 column, you could
            do:

                nw.col("a").diff().fill_null(0).cast(nw.Int64)

        Examples:
            >>> import polars as pl
            >>> import narwhals as nw
            >>> df_native = pl.DataFrame({"a": [1, 1, 3, 5, 5]})
            >>> df = nw.from_native(df_native)
            >>> df.with_columns(a_diff=nw.col("a").diff())
            ┌──────────────────┐
            |Narwhals DataFrame|
            |------------------|
            | shape: (5, 2)    |
            | ┌─────┬────────┐ |
            | │ a   ┆ a_diff │ |
            | │ --- ┆ ---    │ |
            | │ i64 ┆ i64    │ |
            | ╞═════╪════════╡ |
            | │ 1   ┆ null   │ |
            | │ 1   ┆ 0      │ |
            | │ 3   ┆ 2      │ |
            | │ 5   ┆ 2      │ |
            | │ 5   ┆ 0      │ |
            | └─────┴────────┘ |
            └──────────────────┘
        """
        return self._append_node(ExprNode(ExprKind.ORDERABLE_WINDOW, "diff"))

    def shift(self, n: int) -> Self:
        """Shift values by `n` positions.

        Info:
            For lazy backends, this operation must be followed by `Expr.over` with
            `order_by` specified, see [order-dependence](../concepts/order_dependence.md).

        Arguments:
            n: Number of positions to shift values by.

        Notes:
            pandas may change the dtype here, for example when introducing missing
            values in an integer column. To ensure, that the dtype doesn't change,
            you may want to use `fill_null` and `cast`. For example, to shift
            and fill missing values with `0` in a Int64 column, you could
            do:

                nw.col("a").shift(1).fill_null(0).cast(nw.Int64)

        Examples:
            >>> import polars as pl
            >>> import narwhals as nw
            >>> df_native = pl.DataFrame({"a": [1, 1, 3, 5, 5]})
            >>> df = nw.from_native(df_native)
            >>> df.with_columns(a_shift=nw.col("a").shift(n=1))
            ┌──────────────────┐
            |Narwhals DataFrame|
            |------------------|
            |shape: (5, 2)     |
            |┌─────┬─────────┐ |
            |│ a   ┆ a_shift │ |
            |│ --- ┆ ---     │ |
            |│ i64 ┆ i64     │ |
            |╞═════╪═════════╡ |
            |│ 1   ┆ null    │ |
            |│ 1   ┆ 1       │ |
            |│ 3   ┆ 1       │ |
            |│ 5   ┆ 3       │ |
            |│ 5   ┆ 5       │ |
            |└─────┴─────────┘ |
            └──────────────────┘
        """
        ensure_type(n, int, param_name="n")
        return self._append_node(ExprNode(ExprKind.ORDERABLE_WINDOW, "shift", n=n))

    def replace_strict(
        self,
        old: Sequence[Any] | Mapping[Any, Any],
        new: Sequence[Any] | None = None,
        *,
        default: Any | NoDefault = no_default,
        return_dtype: IntoDType | None = None,
    ) -> Self:
        """Replace all values by different values.

        Arguments:
            old: Sequence of values to replace. It also accepts a mapping of values to
                their replacement as syntactic sugar for
                `replace_strict(old=list(mapping.keys()), new=list(mapping.values()))`.
            new: Sequence of values to replace by. Length must match the length of `old`.
            default: Set values that were not replaced to this value. If no default is
                specified, (default), an error is raised if any values were not replaced.
                Accepts expression input. Non-expression inputs are parsed as literals.
            return_dtype: The data type of the resulting expression. If set to `None`
                (default), the data type is determined automatically based on the other
                inputs.

        Raises:
            InvalidOperationError: If any non-null values in the original column were not
                replaced, and no default was specified.

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> df_native = pd.DataFrame({"a": [3, 0, 1, 2]})
            >>> df = nw.from_native(df_native)
            >>> df.with_columns(
            ...     b=nw.col("a").replace_strict(
            ...         [0, 1, 2, 3],
            ...         ["zero", "one", "two", "three"],
            ...         return_dtype=nw.String,
            ...     )
            ... )
            ┌──────────────────┐
            |Narwhals DataFrame|
            |------------------|
            |      a      b    |
            |   0  3  three    |
            |   1  0   zero    |
            |   2  1    one    |
            |   3  2    two    |
            └──────────────────┘

            Replace values and set a default for values not in the mapping:

            >>> data = {"a": [1, 2, 3, 4], "b": ["beluga", "narwhal", "orca", "vaquita"]}
            >>> df = nw.from_native(pd.DataFrame(data))
            >>> df.with_columns(
            ...     a_replaced=nw.col("a").replace_strict(
            ...         {1: "one", 2: "two"},
            ...         default=nw.concat_str(nw.lit("default_"), nw.col("b")),
            ...         return_dtype=nw.String,
            ...     )
            ... )
            ┌──────────────────────────────┐
            |      Narwhals DataFrame      |
            |------------------------------|
            |   a        b       a_replaced|
            |0  1   beluga              one|
            |1  2  narwhal              two|
            |2  3     orca     default_orca|
            |3  4  vaquita  default_vaquita|
            └──────────────────────────────┘
        """
        if new is None:
            if not isinstance(old, Mapping):
                msg = "`new` argument is required if `old` argument is not a Mapping type"
                raise TypeError(msg)

            new = list(old.values())
            old = list(old.keys())

        if default is no_default:
            node = ExprNode(
                ExprKind.ELEMENTWISE,
                "replace_strict",
                default=default,
                old=old,
                new=new,
                return_dtype=return_dtype,
            )
        else:
            node = ExprNode(
                ExprKind.ELEMENTWISE,
                "replace_strict",
                exprs=(default,),
                old=old,
                new=new,
                return_dtype=return_dtype,
                str_as_lit=True,
            )
        return self._append_node(node)

    # --- transform ---
    def is_between(
        self,
        lower_bound: Any | IntoExpr,
        upper_bound: Any | IntoExpr,
        closed: ClosedInterval = "both",
    ) -> Self:
        """Check if this expression is between the given lower and upper bounds.

        Arguments:
            lower_bound: Lower bound value. String literals are interpreted as column names.
            upper_bound: Upper bound value. String literals are interpreted as column names.
            closed: Define which sides of the interval are closed (inclusive). Options are {"left", "right", "none", "both"}.

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> df_native = pd.DataFrame({"a": [1, 2, 3, 4, 5]})
            >>> df = nw.from_native(df_native)
            >>> df.with_columns(b=nw.col("a").is_between(2, 4, "right"))
            ┌──────────────────┐
            |Narwhals DataFrame|
            |------------------|
            |      a      b    |
            |   0  1  False    |
            |   1  2  False    |
            |   2  3   True    |
            |   3  4   True    |
            |   4  5  False    |
            └──────────────────┘
        """
        node = ExprNode(
            ExprKind.ELEMENTWISE,
            "is_between",
            exprs=(lower_bound, upper_bound),
            closed=closed,
        )
        return self._append_node(node)

    def is_in(self, other: Any) -> Self:
        """Check if elements of this expression are present in the other iterable.

        Arguments:
            other: iterable

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> df_native = pd.DataFrame({"a": [1, 2, 9, 10]})
            >>> df = nw.from_native(df_native)
            >>> df.with_columns(b=nw.col("a").is_in([1, 2]))
            ┌──────────────────┐
            |Narwhals DataFrame|
            |------------------|
            |       a      b   |
            |   0   1   True   |
            |   1   2   True   |
            |   2   9  False   |
            |   3  10  False   |
            └──────────────────┘
        """
        if isinstance(other, Iterable) and not isinstance(other, (str, bytes)):
            return self._append_node(
                ExprNode(
                    ExprKind.ELEMENTWISE,
                    "is_in",
                    other=to_native(other, pass_through=True),
                )
            )
        msg = "Narwhals `is_in` doesn't accept expressions as an argument, as opposed to Polars. You should provide an iterable instead."
        raise NotImplementedError(msg)

    def filter(self, *predicates: Any) -> Self:
        """Filters elements based on a condition, returning a new expression.

        Arguments:
            predicates: Conditions to filter by (which get AND-ed together).

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> df_native = pd.DataFrame(
            ...     {"a": [2, 3, 4, 5, 6, 7], "b": [10, 11, 12, 13, 14, 15]}
            ... )
            >>> df = nw.from_native(df_native)
            >>> df.select(
            ...     nw.col("a").filter(nw.col("a") > 4),
            ...     nw.col("b").filter(nw.col("b") < 13),
            ... )
            ┌──────────────────┐
            |Narwhals DataFrame|
            |------------------|
            |        a   b     |
            |     3  5  10     |
            |     4  6  11     |
            |     5  7  12     |
            └──────────────────┘
        """
        return self._append_node(
            ExprNode(ExprKind.FILTRATION, "filter", exprs=predicates)
        )

    def is_null(self) -> Self:
        """Returns a boolean Series indicating which values are null.

        Notes:
            pandas handles null values differently from Polars and PyArrow.
            See [null_handling](../concepts/null_handling.md/) for reference.

        Examples:
            >>> import duckdb
            >>> import narwhals as nw
            >>> df_native = duckdb.sql(
            ...     "SELECT * FROM VALUES (null, CAST('NaN' AS DOUBLE)), (2, 2.) df(a, b)"
            ... )
            >>> df = nw.from_native(df_native)
            >>> df.with_columns(
            ...     a_is_null=nw.col("a").is_null(), b_is_null=nw.col("b").is_null()
            ... )
            ┌──────────────────────────────────────────┐
            |            Narwhals LazyFrame            |
            |------------------------------------------|
            |┌───────┬────────┬───────────┬───────────┐|
            |│   a   │   b    │ a_is_null │ b_is_null │|
            |│ int32 │ double │  boolean  │  boolean  │|
            |├───────┼────────┼───────────┼───────────┤|
            |│  NULL │    nan │ true      │ false     │|
            |│     2 │    2.0 │ false     │ false     │|
            |└───────┴────────┴───────────┴───────────┘|
            └──────────────────────────────────────────┘
        """
        return self._append_node(ExprNode(ExprKind.ELEMENTWISE, "is_null"))

    def is_nan(self) -> Self:
        """Indicate which values are NaN.

        Notes:
            pandas handles null values differently from Polars and PyArrow.
            See [null_handling](../concepts/null_handling.md/) for reference.

        Examples:
            >>> import duckdb
            >>> import narwhals as nw
            >>> df_native = duckdb.sql(
            ...     "SELECT * FROM VALUES (null, CAST('NaN' AS DOUBLE)), (2, 2.) df(a, b)"
            ... )
            >>> df = nw.from_native(df_native)
            >>> df.with_columns(
            ...     a_is_nan=nw.col("a").is_nan(), b_is_nan=nw.col("b").is_nan()
            ... )
            ┌────────────────────────────────────────┐
            |           Narwhals LazyFrame           |
            |----------------------------------------|
            |┌───────┬────────┬──────────┬──────────┐|
            |│   a   │   b    │ a_is_nan │ b_is_nan │|
            |│ int32 │ double │ boolean  │ boolean  │|
            |├───────┼────────┼──────────┼──────────┤|
            |│  NULL │    nan │ NULL     │ true     │|
            |│     2 │    2.0 │ false    │ false    │|
            |└───────┴────────┴──────────┴──────────┘|
            └────────────────────────────────────────┘
        """
        return self._append_node(ExprNode(ExprKind.ELEMENTWISE, "is_nan"))

    def fill_null(
        self,
        value: Expr | NonNestedLiteral = None,
        strategy: FillNullStrategy | None = None,
        limit: int | None = None,
    ) -> Self:
        """Fill null values with given value.

        Arguments:
            value: Value or expression used to fill null values.
            strategy: Strategy used to fill null values.
            limit: Number of consecutive null values to fill when using the 'forward' or 'backward' strategy.

        Notes:
            - pandas handles null values differently from other libraries.
              See [null_handling](../concepts/null_handling.md/)
              for reference.
            - For pandas Series of `object` dtype, `fill_null` will not automatically change the
              Series' dtype as pandas used to do. Explicitly call `cast` if you want the dtype to change.

        Examples:
            >>> import polars as pl
            >>> import narwhals as nw
            >>> df_native = pl.DataFrame(
            ...     {
            ...         "a": [2, None, None, 3],
            ...         "b": [2.0, float("nan"), float("nan"), 3.0],
            ...         "c": [1, 2, 3, 4],
            ...     }
            ... )
            >>> df = nw.from_native(df_native)
            >>> df.with_columns(
            ...     nw.col("a", "b").fill_null(0).name.suffix("_filled"),
            ...     nw.col("a").fill_null(nw.col("c")).name.suffix("_filled_with_c"),
            ... )
            ┌────────────────────────────────────────────────────────────┐
            |                     Narwhals DataFrame                     |
            |------------------------------------------------------------|
            |shape: (4, 6)                                               |
            |┌──────┬─────┬─────┬──────────┬──────────┬─────────────────┐|
            |│ a    ┆ b   ┆ c   ┆ a_filled ┆ b_filled ┆ a_filled_with_c │|
            |│ ---  ┆ --- ┆ --- ┆ ---      ┆ ---      ┆ ---             │|
            |│ i64  ┆ f64 ┆ i64 ┆ i64      ┆ f64      ┆ i64             │|
            |╞══════╪═════╪═════╪══════════╪══════════╪═════════════════╡|
            |│ 2    ┆ 2.0 ┆ 1   ┆ 2        ┆ 2.0      ┆ 2               │|
            |│ null ┆ NaN ┆ 2   ┆ 0        ┆ NaN      ┆ 2               │|
            |│ null ┆ NaN ┆ 3   ┆ 0        ┆ NaN      ┆ 3               │|
            |│ 3    ┆ 3.0 ┆ 4   ┆ 3        ┆ 3.0      ┆ 3               │|
            |└──────┴─────┴─────┴──────────┴──────────┴─────────────────┘|
            └────────────────────────────────────────────────────────────┘

            Using a strategy:

            >>> df.select(
            ...     nw.col("a", "b"),
            ...     nw.col("a", "b")
            ...     .fill_null(strategy="forward", limit=1)
            ...     .name.suffix("_nulls_forward_filled"),
            ... )
            ┌────────────────────────────────────────────────────────────────┐
            |                       Narwhals DataFrame                       |
            |----------------------------------------------------------------|
            |shape: (4, 4)                                                   |
            |┌──────┬─────┬────────────────────────┬────────────────────────┐|
            |│ a    ┆ b   ┆ a_nulls_forward_filled ┆ b_nulls_forward_filled │|
            |│ ---  ┆ --- ┆ ---                    ┆ ---                    │|
            |│ i64  ┆ f64 ┆ i64                    ┆ f64                    │|
            |╞══════╪═════╪════════════════════════╪════════════════════════╡|
            |│ 2    ┆ 2.0 ┆ 2                      ┆ 2.0                    │|
            |│ null ┆ NaN ┆ 2                      ┆ NaN                    │|
            |│ null ┆ NaN ┆ null                   ┆ NaN                    │|
            |│ 3    ┆ 3.0 ┆ 3                      ┆ 3.0                    │|
            |└──────┴─────┴────────────────────────┴────────────────────────┘|
            └────────────────────────────────────────────────────────────────┘
        """
        if value is not None and strategy is not None:
            msg = "cannot specify both `value` and `strategy`"
            raise ValueError(msg)
        if value is None and strategy is None:
            msg = "must specify either a fill `value` or `strategy`"
            raise ValueError(msg)
        if strategy is not None and strategy not in {"forward", "backward"}:
            msg = f"strategy not supported: {strategy}"
            raise ValueError(msg)

        if strategy is not None:
            node = ExprNode(
                ExprKind.ORDERABLE_WINDOW,
                "fill_null",
                value=value,
                strategy=strategy,
                limit=limit,
            )
        else:
            node = ExprNode(
                ExprKind.ELEMENTWISE,
                "fill_null",
                exprs=(value,),
                strategy=strategy,
                limit=limit,
                str_as_lit=True,
            )
        return self._append_node(node)

    def fill_nan(self, value: float | None) -> Self:
        """Fill floating point NaN values with given value.

        Arguments:
            value: Value used to fill NaN values.

        Notes:
            This function only fills `'NaN'` values, not null ones, except for pandas
            which doesn't distinguish between them.
            See [null_handling](../concepts/null_handling.md/) for reference.

        Examples:
            >>> import duckdb
            >>> import narwhals as nw
            >>> df_native = duckdb.sql(
            ...     "SELECT * FROM VALUES (5.::DOUBLE, 50.::DOUBLE), ('NaN', null) df(a, b)"
            ... )
            >>> df = nw.from_native(df_native)
            >>> df.with_columns(nw.col("a", "b").fill_nan(0).name.suffix("_nans_filled"))
            ┌───────────────────────────────────────────────────┐
            |                Narwhals LazyFrame                 |
            |---------------------------------------------------|
            |┌────────┬────────┬───────────────┬───────────────┐|
            |│   a    │   b    │ a_nans_filled │ b_nans_filled │|
            |│ double │ double │    double     │    double     │|
            |├────────┼────────┼───────────────┼───────────────┤|
            |│    5.0 │   50.0 │           5.0 │          50.0 │|
            |│    nan │   NULL │           0.0 │          NULL │|
            |└────────┴────────┴───────────────┴───────────────┘|
            └───────────────────────────────────────────────────┘
        """
        return self._append_node(ExprNode(ExprKind.ELEMENTWISE, "fill_nan", value=value))

    # --- partial reduction ---
    def drop_nulls(self) -> Self:
        """Drop null values.

        Notes:
            pandas handles null values differently from Polars and PyArrow.
            See [null_handling](../concepts/null_handling.md/) for reference.

        Examples:
            >>> import polars as pl
            >>> import narwhals as nw
            >>> df_native = pl.DataFrame({"a": [2.0, 4.0, float("nan"), 3.0, None, 5.0]})
            >>> df = nw.from_native(df_native)
            >>> df.select(nw.col("a").drop_nulls())
            ┌──────────────────┐
            |Narwhals DataFrame|
            |------------------|
            |  shape: (5, 1)   |
            |  ┌─────┐         |
            |  │ a   │         |
            |  │ --- │         |
            |  │ f64 │         |
            |  ╞═════╡         |
            |  │ 2.0 │         |
            |  │ 4.0 │         |
            |  │ NaN │         |
            |  │ 3.0 │         |
            |  │ 5.0 │         |
            |  └─────┘         |
            └──────────────────┘
        """
        return self._append_node(ExprNode(ExprKind.FILTRATION, "drop_nulls"))

    def over(
        self,
        *partition_by: str | Sequence[str],
        order_by: str | Sequence[str] | None = None,
    ) -> Self:
        """Compute expressions over the given groups (optionally with given order).

        Arguments:
            partition_by: Names of columns to compute window expression over.
                Must be names of columns, as opposed to expressions -
                so, this is a bit less flexible than Polars' `Expr.over`.
            order_by: Column(s) to order window functions by.
                For lazy backends, this argument is required when `over` is applied
                to order-dependent functions, see [order-dependence](../concepts/order_dependence.md).

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> df_native = pd.DataFrame({"a": [1, 2, 4], "b": ["x", "x", "y"]})
            >>> df = nw.from_native(df_native)
            >>> df.with_columns(a_min_per_group=nw.col("a").min().over("b"))
            ┌────────────────────────┐
            |   Narwhals DataFrame   |
            |------------------------|
            |   a  b  a_min_per_group|
            |0  1  x                1|
            |1  2  x                1|
            |2  4  y                4|
            └────────────────────────┘

            Cumulative operations are also supported, but (currently) only for
            pandas and Polars:

            >>> df.with_columns(a_cum_sum_per_group=nw.col("a").cum_sum().over("b"))
            ┌────────────────────────────┐
            |     Narwhals DataFrame     |
            |----------------------------|
            |   a  b  a_cum_sum_per_group|
            |0  1  x                    1|
            |1  2  x                    3|
            |2  4  y                    4|
            └────────────────────────────┘
        """
        flat_partition_by = flatten(partition_by)
        flat_order_by = [order_by] if isinstance(order_by, str) else (order_by or [])
        if not flat_partition_by and not flat_order_by:  # pragma: no cover
            msg = "At least one of `partition_by` or `order_by` must be specified."
            raise ValueError(msg)
        node = ExprNode(
            ExprKind.OVER, "over", partition_by=flat_partition_by, order_by=flat_order_by
        )
        return self._with_over_node(node)

    def is_duplicated(self) -> Self:
        r"""Return a boolean mask indicating duplicated values.

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> df_native = pd.DataFrame({"a": [1, 2, 3, 1], "b": ["a", "a", "b", "c"]})
            >>> df = nw.from_native(df_native)
            >>> df.with_columns(nw.all().is_duplicated().name.suffix("_is_duplicated"))
            ┌─────────────────────────────────────────┐
            |           Narwhals DataFrame            |
            |-----------------------------------------|
            |   a  b  a_is_duplicated  b_is_duplicated|
            |0  1  a             True             True|
            |1  2  a            False             True|
            |2  3  b            False            False|
            |3  1  c             True            False|
            └─────────────────────────────────────────┘
        """
        return self._append_node(ExprNode(ExprKind.WINDOW, "is_duplicated"))

    def is_unique(self) -> Self:
        r"""Return a boolean mask indicating unique values.

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> df_native = pd.DataFrame({"a": [1, 2, 3, 1], "b": ["a", "a", "b", "c"]})
            >>> df = nw.from_native(df_native)
            >>> df.with_columns(nw.all().is_unique().name.suffix("_is_unique"))
            ┌─────────────────────────────────┐
            |       Narwhals DataFrame        |
            |---------------------------------|
            |   a  b  a_is_unique  b_is_unique|
            |0  1  a        False        False|
            |1  2  a         True        False|
            |2  3  b         True         True|
            |3  1  c        False         True|
            └─────────────────────────────────┘
        """
        return self._append_node(ExprNode(ExprKind.WINDOW, "is_unique"))

    def null_count(self) -> Self:
        r"""Count null values.

        Notes:
            pandas handles null values differently from Polars and PyArrow.
            See [null_handling](../concepts/null_handling.md/) for reference.

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> df_native = pd.DataFrame(
            ...     {"a": [1, 2, None, 1], "b": ["a", None, "b", None]}
            ... )
            >>> df = nw.from_native(df_native)
            >>> df.select(nw.all().null_count())
            ┌──────────────────┐
            |Narwhals DataFrame|
            |------------------|
            |        a  b      |
            |     0  1  2      |
            └──────────────────┘
        """
        return self._append_node(ExprNode(ExprKind.AGGREGATION, "null_count"))

    def is_first_distinct(self) -> Self:
        r"""Return a boolean mask indicating the first occurrence of each distinct value.

        Info:
            For lazy backends, this operation must be followed by `Expr.over` with
            `order_by` specified, see [order-dependence](../concepts/order_dependence.md).

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> df_native = pd.DataFrame({"a": [1, 2, 3, 1], "b": ["a", "a", "b", "c"]})
            >>> df = nw.from_native(df_native)
            >>> df.with_columns(
            ...     nw.all().is_first_distinct().name.suffix("_is_first_distinct")
            ... )
            ┌─────────────────────────────────────────────────┐
            |               Narwhals DataFrame                |
            |-------------------------------------------------|
            |   a  b  a_is_first_distinct  b_is_first_distinct|
            |0  1  a                 True                 True|
            |1  2  a                 True                False|
            |2  3  b                 True                 True|
            |3  1  c                False                 True|
            └─────────────────────────────────────────────────┘
        """
        return self._append_node(ExprNode(ExprKind.ORDERABLE_WINDOW, "is_first_distinct"))

    def is_last_distinct(self) -> Self:
        r"""Return a boolean mask indicating the last occurrence of each distinct value.

        Info:
            For lazy backends, this operation must be followed by `Expr.over` with
            `order_by` specified, see [order-dependence](../concepts/order_dependence.md).

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> df_native = pd.DataFrame({"a": [1, 2, 3, 1], "b": ["a", "a", "b", "c"]})
            >>> df = nw.from_native(df_native)
            >>> df.with_columns(
            ...     nw.all().is_last_distinct().name.suffix("_is_last_distinct")
            ... )
            ┌───────────────────────────────────────────────┐
            |              Narwhals DataFrame               |
            |-----------------------------------------------|
            |   a  b  a_is_last_distinct  b_is_last_distinct|
            |0  1  a               False               False|
            |1  2  a                True                True|
            |2  3  b                True                True|
            |3  1  c                True                True|
            └───────────────────────────────────────────────┘
        """
        return self._append_node(ExprNode(ExprKind.ORDERABLE_WINDOW, "is_last_distinct"))

    def quantile(
        self, quantile: float, interpolation: RollingInterpolationMethod
    ) -> Self:
        r"""Get quantile value.

        Arguments:
            quantile: Quantile between 0.0 and 1.0.
            interpolation: Interpolation method.

        Note:
            - pandas and Polars may have implementation differences for a given interpolation method.
            - [dask](https://docs.dask.org/en/stable/generated/dask.dataframe.Series.quantile.html) has
                its own method to approximate quantile and it doesn't implement 'nearest', 'higher',
                'lower', 'midpoint' as interpolation method - use 'linear' which is closest to the
                native 'dask' - method.

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> df_native = pd.DataFrame(
            ...     {"a": list(range(50)), "b": list(range(50, 100))}
            ... )
            >>> df = nw.from_native(df_native)
            >>> df.select(nw.col("a", "b").quantile(0.5, interpolation="linear"))
            ┌──────────────────┐
            |Narwhals DataFrame|
            |------------------|
            |        a     b   |
            |  0  24.5  74.5   |
            └──────────────────┘
        """
        return self._append_node(
            ExprNode(
                ExprKind.AGGREGATION,
                "quantile",
                quantile=quantile,
                interpolation=interpolation,
            )
        )

    def round(self, decimals: int = 0) -> Self:
        r"""Round underlying floating point data by `decimals` digits.

        Arguments:
            decimals: Number of decimals to round by.


        Notes:
            For values exactly halfway between rounded decimal values pandas behaves differently than Polars and Arrow.

            pandas rounds to the nearest even value (e.g. -0.5 and 0.5 round to 0.0, 1.5 and 2.5 round to 2.0, 3.5 and
            4.5 to 4.0, etc..).

            Polars and Arrow round away from 0 (e.g. -0.5 to -1.0, 0.5 to 1.0, 1.5 to 2.0, 2.5 to 3.0, etc..).

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> df_native = pd.DataFrame({"a": [1.12345, 2.56789, 3.901234]})
            >>> df = nw.from_native(df_native)
            >>> df.with_columns(a_rounded=nw.col("a").round(1))
            ┌──────────────────────┐
            |  Narwhals DataFrame  |
            |----------------------|
            |          a  a_rounded|
            |0  1.123450        1.1|
            |1  2.567890        2.6|
            |2  3.901234        3.9|
            └──────────────────────┘
        """
        return self._append_node(
            ExprNode(ExprKind.ELEMENTWISE, "round", decimals=decimals)
        )

    def floor(self) -> Self:
        r"""Compute the numerical floor.

        Examples:
            >>> import pyarrow as pa
            >>> import narwhals as nw
            >>> df_native = pa.table({"values": [1.1, 4.3, -1.3]})
            >>> df = nw.from_native(df_native)
            >>> result = df.with_columns(floor=nw.col("values").floor())
            >>> result
            ┌────────────────────────┐
            |   Narwhals DataFrame   |
            |------------------------|
            |pyarrow.Table           |
            |values: double          |
            |floor: double           |
            |----                    |
            |values: [[1.1,4.3,-1.3]]|
            |floor: [[1,4,-2]]       |
            └────────────────────────┘
        """
        return self._append_node(ExprNode(ExprKind.ELEMENTWISE, "floor"))

    def ceil(self) -> Self:
        r"""Compute the numerical ceiling.

        Examples:
            >>> import pyarrow as pa
            >>> import narwhals as nw
            >>> df_native = pa.table({"values": [1.1, 4.3, -1.3]})
            >>> df = nw.from_native(df_native)
            >>> result = df.with_columns(ceil=nw.col("values").ceil())
            >>> result
            ┌────────────────────────┐
            |   Narwhals DataFrame   |
            |------------------------|
            |pyarrow.Table           |
            |values: double          |
            |ceil: double            |
            |----                    |
            |values: [[1.1,4.3,-1.3]]|
            |ceil: [[2,5,-1]]        |
            └────────────────────────┘
        """
        return self._append_node(ExprNode(ExprKind.ELEMENTWISE, "ceil"))

    def len(self) -> Self:
        r"""Return the number of elements in the column.

        Null values count towards the total.

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> df_native = pd.DataFrame({"a": ["x", "y", "z"], "b": [1, 2, 1]})
            >>> df = nw.from_native(df_native)
            >>> df.select(
            ...     nw.col("a").filter(nw.col("b") == 1).len().alias("a1"),
            ...     nw.col("a").filter(nw.col("b") == 2).len().alias("a2"),
            ... )
            ┌──────────────────┐
            |Narwhals DataFrame|
            |------------------|
            |       a1  a2     |
            |    0   2   1     |
            └──────────────────┘
        """
        return self._append_node(ExprNode(ExprKind.AGGREGATION, "len"))

    def clip(
        self,
        lower_bound: IntoExpr | NumericLiteral | TemporalLiteral | None = None,
        upper_bound: IntoExpr | NumericLiteral | TemporalLiteral | None = None,
    ) -> Self:
        r"""Clip values in the Series.

        Arguments:
            lower_bound: Lower bound value. String literals are treated as column names.
            upper_bound: Upper bound value. String literals are treated as column names.

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> df_native = pd.DataFrame({"a": [1, 2, 3]})
            >>> df = nw.from_native(df_native)
            >>> df.with_columns(a_clipped=nw.col("a").clip(-1, 3))
            ┌──────────────────┐
            |Narwhals DataFrame|
            |------------------|
            |    a  a_clipped  |
            | 0  1          1  |
            | 1  2          2  |
            | 2  3          3  |
            └──────────────────┘
        """
        if upper_bound is None:
            return self._append_node(
                ExprNode(ExprKind.ELEMENTWISE, "clip_lower", exprs=(lower_bound,))
            )
        if lower_bound is None:
            return self._append_node(
                ExprNode(ExprKind.ELEMENTWISE, "clip_upper", exprs=(upper_bound,))
            )
        return self._append_node(
            ExprNode(ExprKind.ELEMENTWISE, "clip", exprs=(lower_bound, upper_bound))
        )

    def first(self, order_by: str | Iterable[str] | None = None) -> Self:
        """Get the first value.

        Notes:
            For lazy backends, this can only be used with `over` or with `order_by`.

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> data = {"a": [1, 1, 2, 2], "b": ["foo", None, None, "baz"]}
            >>> df_native = pd.DataFrame(data)
            >>> df = nw.from_native(df_native)
            >>> df.select(nw.all().first())
            ┌──────────────────┐
            |Narwhals DataFrame|
            |------------------|
            |       a    b     |
            |    0  1  foo     |
            └──────────────────┘

            >>> df.group_by("a").agg(nw.col("b").first())
            ┌──────────────────┐
            |Narwhals DataFrame|
            |------------------|
            |       a    b     |
            |    0  1  foo     |
            |    1  2  NaN     |
            └──────────────────┘
        """
        if order_by is None:
            return self._append_node(ExprNode(ExprKind.ORDERABLE_AGGREGATION, "first"))
        return self._append_node(
            ExprNode(
                ExprKind.AGGREGATION,
                "first",
                order_by=[order_by] if isinstance(order_by, str) else order_by,
            )
        )

    def last(self, order_by: str | Iterable[str] | None = None) -> Self:
        """Get the last value.

        Notes:
            For lazy backends, this can only be used with `over` or with `order_by`.

        Examples:
            >>> import pyarrow as pa
            >>> import narwhals as nw
            >>> data = {"a": [1, 1, 2, 2], "b": ["foo", None, None, "baz"]}
            >>> df_native = pa.table(data)
            >>> df = nw.from_native(df_native)
            >>> df.select(nw.all().last())
            ┌──────────────────┐
            |Narwhals DataFrame|
            |------------------|
            |  pyarrow.Table   |
            |  a: int64        |
            |  b: string       |
            |  ----            |
            |  a: [[2]]        |
            |  b: [["baz"]]    |
            └──────────────────┘

            >>> df.group_by("a").agg(nw.col("b").last())
            ┌──────────────────┐
            |Narwhals DataFrame|
            |------------------|
            |pyarrow.Table     |
            |a: int64          |
            |b: string         |
            |----              |
            |a: [[1,2]]        |
            |b: [[null,"baz"]] |
            └──────────────────┘
        """
        if order_by is None:
            return self._append_node(ExprNode(ExprKind.ORDERABLE_AGGREGATION, "last"))
        return self._append_node(
            ExprNode(
                ExprKind.AGGREGATION,
                "last",
                order_by=[order_by] if isinstance(order_by, str) else order_by,
            )
        )

    def mode(self, *, keep: ModeKeepStrategy = "all") -> Self:
        r"""Compute the most occurring value(s).

        Can return multiple values.

        Arguments:
            keep: Whether to keep all modes or any mode found. Remark that `keep='any'`
                is not deterministic for multimodal values.

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> df_native = pd.DataFrame({"a": [1, 1, 2, 3], "b": [1, 1, 2, 2]})
            >>> df = nw.from_native(df_native)
            >>> df.select(nw.col("a").mode()).sort("a")
            ┌──────────────────┐
            |Narwhals DataFrame|
            |------------------|
            |          a       |
            |       0  1       |
            └──────────────────┘
        """
        _supported_keep_values = ("all", "any")
        if keep not in _supported_keep_values:  # pragma: no cover
            msg = f"`keep` must be one of {_supported_keep_values}, found '{keep}'"
            raise ValueError(msg)
        kind = ExprKind.AGGREGATION if keep == "any" else ExprKind.FILTRATION
        return self._append_node(ExprNode(kind, "mode", keep=keep))

    def is_finite(self) -> Self:
        """Returns boolean values indicating which original values are finite.

        Warning:
            pandas handles null values differently from Polars and PyArrow.
            See [null_handling](../concepts/null_handling.md/) for reference.
            `is_finite` will return False for NaN and Null's in the Dask and
            pandas non-nullable backend, while for Polars, PyArrow and pandas
            nullable backends null values are kept as such.

        Examples:
            >>> import polars as pl
            >>> import narwhals as nw
            >>> df_native = pl.DataFrame({"a": [float("nan"), float("inf"), 2.0, None]})
            >>> df = nw.from_native(df_native)
            >>> df.with_columns(a_is_finite=nw.col("a").is_finite())
            ┌──────────────────────┐
            |  Narwhals DataFrame  |
            |----------------------|
            |shape: (4, 2)         |
            |┌──────┬─────────────┐|
            |│ a    ┆ a_is_finite │|
            |│ ---  ┆ ---         │|
            |│ f64  ┆ bool        │|
            |╞══════╪═════════════╡|
            |│ NaN  ┆ false       │|
            |│ inf  ┆ false       │|
            |│ 2.0  ┆ true        │|
            |│ null ┆ null        │|
            |└──────┴─────────────┘|
            └──────────────────────┘
        """
        return self._append_node(ExprNode(ExprKind.ELEMENTWISE, "is_finite"))

    def cum_count(self, *, reverse: bool = False) -> Self:
        r"""Return the cumulative count of the non-null values in the column.

        Info:
            For lazy backends, this operation must be followed by `Expr.over` with
            `order_by` specified, see [order-dependence](../concepts/order_dependence.md).

        Arguments:
            reverse: reverse the operation

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> df_native = pd.DataFrame({"a": ["x", "k", None, "d"]})
            >>> df = nw.from_native(df_native)
            >>> df.with_columns(
            ...     nw.col("a").cum_count().alias("a_cum_count"),
            ...     nw.col("a").cum_count(reverse=True).alias("a_cum_count_reverse"),
            ... )
            ┌────────────────────────────────────────┐
            |           Narwhals DataFrame           |
            |----------------------------------------|
            |     a  a_cum_count  a_cum_count_reverse|
            |0    x            1                    3|
            |1    k            2                    2|
            |2  NaN            2                    1|
            |3    d            3                    1|
            └────────────────────────────────────────┘
        """
        return self._append_node(
            ExprNode(ExprKind.ORDERABLE_WINDOW, "cum_count", reverse=reverse)
        )

    def cum_min(self, *, reverse: bool = False) -> Self:
        r"""Return the cumulative min of the non-null values in the column.

        Info:
            For lazy backends, this operation must be followed by `Expr.over` with
            `order_by` specified, see [order-dependence](../concepts/order_dependence.md).

        Arguments:
            reverse: reverse the operation

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> df_native = pd.DataFrame({"a": [3, 1, None, 2]})
            >>> df = nw.from_native(df_native)
            >>> df.with_columns(
            ...     nw.col("a").cum_min().alias("a_cum_min"),
            ...     nw.col("a").cum_min(reverse=True).alias("a_cum_min_reverse"),
            ... )
            ┌────────────────────────────────────┐
            |         Narwhals DataFrame         |
            |------------------------------------|
            |     a  a_cum_min  a_cum_min_reverse|
            |0  3.0        3.0                1.0|
            |1  1.0        1.0                1.0|
            |2  NaN        NaN                NaN|
            |3  2.0        1.0                2.0|
            └────────────────────────────────────┘
        """
        return self._append_node(
            ExprNode(ExprKind.ORDERABLE_WINDOW, "cum_min", reverse=reverse)
        )

    def cum_max(self, *, reverse: bool = False) -> Self:
        r"""Return the cumulative max of the non-null values in the column.

        Info:
            For lazy backends, this operation must be followed by `Expr.over` with
            `order_by` specified, see [order-dependence](../concepts/order_dependence.md).

        Arguments:
            reverse: reverse the operation

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> df_native = pd.DataFrame({"a": [1, 3, None, 2]})
            >>> df = nw.from_native(df_native)
            >>> df.with_columns(
            ...     nw.col("a").cum_max().alias("a_cum_max"),
            ...     nw.col("a").cum_max(reverse=True).alias("a_cum_max_reverse"),
            ... )
            ┌────────────────────────────────────┐
            |         Narwhals DataFrame         |
            |------------------------------------|
            |     a  a_cum_max  a_cum_max_reverse|
            |0  1.0        1.0                3.0|
            |1  3.0        3.0                3.0|
            |2  NaN        NaN                NaN|
            |3  2.0        3.0                2.0|
            └────────────────────────────────────┘
        """
        return self._append_node(
            ExprNode(ExprKind.ORDERABLE_WINDOW, "cum_max", reverse=reverse)
        )

    def cum_prod(self, *, reverse: bool = False) -> Self:
        r"""Return the cumulative product of the non-null values in the column.

        Info:
            For lazy backends, this operation must be followed by `Expr.over` with
            `order_by` specified, see [order-dependence](../concepts/order_dependence.md).

        Arguments:
            reverse: reverse the operation

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> df_native = pd.DataFrame({"a": [1, 3, None, 2]})
            >>> df = nw.from_native(df_native)
            >>> df.with_columns(
            ...     nw.col("a").cum_prod().alias("a_cum_prod"),
            ...     nw.col("a").cum_prod(reverse=True).alias("a_cum_prod_reverse"),
            ... )
            ┌──────────────────────────────────────┐
            |          Narwhals DataFrame          |
            |--------------------------------------|
            |     a  a_cum_prod  a_cum_prod_reverse|
            |0  1.0         1.0                 6.0|
            |1  3.0         3.0                 6.0|
            |2  NaN         NaN                 NaN|
            |3  2.0         6.0                 2.0|
            └──────────────────────────────────────┘
        """
        return self._append_node(
            ExprNode(ExprKind.ORDERABLE_WINDOW, "cum_prod", reverse=reverse)
        )

    def rolling_sum(
        self, window_size: int, *, min_samples: int | None = None, center: bool = False
    ) -> Self:
        """Apply a rolling sum (moving sum) over the values.

        A window of length `window_size` will traverse the values. The resulting values
        will be aggregated to their sum.

        The window at a given row will include the row itself and the `window_size - 1`
        elements before it.

        Info:
            For lazy backends, this operation must be followed by `Expr.over` with
            `order_by` specified, see [order-dependence](../concepts/order_dependence.md).

        Arguments:
            window_size: The length of the window in number of elements. It must be a
                strictly positive integer.
            min_samples: The number of values in the window that should be non-null before
                computing a result. If set to `None` (default), it will be set equal to
                `window_size`. If provided, it must be a strictly positive integer, and
                less than or equal to `window_size`
            center: Set the labels at the center of the window.

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> df_native = pd.DataFrame({"a": [1.0, 2.0, None, 4.0]})
            >>> df = nw.from_native(df_native)
            >>> df.with_columns(
            ...     a_rolling_sum=nw.col("a").rolling_sum(window_size=3, min_samples=1)
            ... )
            ┌─────────────────────┐
            | Narwhals DataFrame  |
            |---------------------|
            |     a  a_rolling_sum|
            |0  1.0            1.0|
            |1  2.0            3.0|
            |2  NaN            3.0|
            |3  4.0            6.0|
            └─────────────────────┘
        """
        window_size, min_samples = _validate_rolling_arguments(
            window_size=window_size, min_samples=min_samples
        )
        return self._append_node(
            ExprNode(
                ExprKind.ORDERABLE_WINDOW,
                "rolling_sum",
                window_size=window_size,
                min_samples=min_samples,
                center=center,
            )
        )

    def rolling_mean(
        self, window_size: int, *, min_samples: int | None = None, center: bool = False
    ) -> Self:
        """Apply a rolling mean (moving mean) over the values.

        A window of length `window_size` will traverse the values. The resulting values
        will be aggregated to their mean.

        The window at a given row will include the row itself and the `window_size - 1`
        elements before it.

        Info:
            For lazy backends, this operation must be followed by `Expr.over` with
            `order_by` specified, see [order-dependence](../concepts/order_dependence.md).

        Arguments:
            window_size: The length of the window in number of elements. It must be a
                strictly positive integer.
            min_samples: The number of values in the window that should be non-null before
                computing a result. If set to `None` (default), it will be set equal to
                `window_size`. If provided, it must be a strictly positive integer, and
                less than or equal to `window_size`
            center: Set the labels at the center of the window.

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> df_native = pd.DataFrame({"a": [1.0, 2.0, None, 4.0]})
            >>> df = nw.from_native(df_native)
            >>> df.with_columns(
            ...     a_rolling_mean=nw.col("a").rolling_mean(window_size=3, min_samples=1)
            ... )
            ┌──────────────────────┐
            |  Narwhals DataFrame  |
            |----------------------|
            |     a  a_rolling_mean|
            |0  1.0             1.0|
            |1  2.0             1.5|
            |2  NaN             1.5|
            |3  4.0             3.0|
            └──────────────────────┘
        """
        window_size, min_samples = _validate_rolling_arguments(
            window_size=window_size, min_samples=min_samples
        )

        return self._append_node(
            ExprNode(
                ExprKind.ORDERABLE_WINDOW,
                "rolling_mean",
                window_size=window_size,
                min_samples=min_samples,
                center=center,
            )
        )

    def rolling_var(
        self,
        window_size: int,
        *,
        min_samples: int | None = None,
        center: bool = False,
        ddof: int = 1,
    ) -> Self:
        """Apply a rolling variance (moving variance) over the values.

        A window of length `window_size` will traverse the values. The resulting values
        will be aggregated to their variance.

        The window at a given row will include the row itself and the `window_size - 1`
        elements before it.

        Info:
            For lazy backends, this operation must be followed by `Expr.over` with
            `order_by` specified, see [order-dependence](../concepts/order_dependence.md).

        Arguments:
            window_size: The length of the window in number of elements. It must be a
                strictly positive integer.
            min_samples: The number of values in the window that should be non-null before
                computing a result. If set to `None` (default), it will be set equal to
                `window_size`. If provided, it must be a strictly positive integer, and
                less than or equal to `window_size`.
            center: Set the labels at the center of the window.
            ddof: Delta Degrees of Freedom; the divisor for a length N window is N - ddof.

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> df_native = pd.DataFrame({"a": [1.0, 2.0, None, 4.0]})
            >>> df = nw.from_native(df_native)
            >>> df.with_columns(
            ...     a_rolling_var=nw.col("a").rolling_var(window_size=3, min_samples=1)
            ... )
            ┌─────────────────────┐
            | Narwhals DataFrame  |
            |---------------------|
            |     a  a_rolling_var|
            |0  1.0            NaN|
            |1  2.0            0.5|
            |2  NaN            0.5|
            |3  4.0            2.0|
            └─────────────────────┘
        """
        window_size, min_samples = _validate_rolling_arguments(
            window_size=window_size, min_samples=min_samples
        )
        return self._append_node(
            ExprNode(
                ExprKind.ORDERABLE_WINDOW,
                "rolling_var",
                ddof=ddof,
                window_size=window_size,
                min_samples=min_samples,
                center=center,
            )
        )

    def rolling_std(
        self,
        window_size: int,
        *,
        min_samples: int | None = None,
        center: bool = False,
        ddof: int = 1,
    ) -> Self:
        """Apply a rolling standard deviation (moving standard deviation) over the values.

        A window of length `window_size` will traverse the values. The resulting values
        will be aggregated to their standard deviation.

        The window at a given row will include the row itself and the `window_size - 1`
        elements before it.

        Info:
            For lazy backends, this operation must be followed by `Expr.over` with
            `order_by` specified, see [order-dependence](../concepts/order_dependence.md).

        Arguments:
            window_size: The length of the window in number of elements. It must be a
                strictly positive integer.
            min_samples: The number of values in the window that should be non-null before
                computing a result. If set to `None` (default), it will be set equal to
                `window_size`. If provided, it must be a strictly positive integer, and
                less than or equal to `window_size`.
            center: Set the labels at the center of the window.
            ddof: Delta Degrees of Freedom; the divisor for a length N window is N - ddof.

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> df_native = pd.DataFrame({"a": [1.0, 2.0, None, 4.0]})
            >>> df = nw.from_native(df_native)
            >>> df.with_columns(
            ...     a_rolling_std=nw.col("a").rolling_std(window_size=3, min_samples=1)
            ... )
            ┌─────────────────────┐
            | Narwhals DataFrame  |
            |---------------------|
            |     a  a_rolling_std|
            |0  1.0            NaN|
            |1  2.0       0.707107|
            |2  NaN       0.707107|
            |3  4.0       1.414214|
            └─────────────────────┘
        """
        window_size, min_samples = _validate_rolling_arguments(
            window_size=window_size, min_samples=min_samples
        )
        return self._append_node(
            ExprNode(
                ExprKind.ORDERABLE_WINDOW,
                "rolling_std",
                ddof=ddof,
                window_size=window_size,
                min_samples=min_samples,
                center=center,
            )
        )

    def rank(self, method: RankMethod = "average", *, descending: bool = False) -> Self:
        """Assign ranks to data, dealing with ties appropriately.

        Notes:
            The resulting dtype may differ between backends.

        Info:
            For lazy backends, this operation must be followed by `Expr.over` with
            `order_by` specified, see [order-dependence](../concepts/order_dependence.md).

        Arguments:
            method: The method used to assign ranks to tied elements.
                The following methods are available (default is 'average')

                - *"average"*: The average of the ranks that would have been assigned to
                    all the tied values is assigned to each value.
                - *"min"*: The minimum of the ranks that would have been assigned to all
                    the tied values is assigned to each value. (This is also referred to
                    as "competition" ranking.)
                - *"max"*: The maximum of the ranks that would have been assigned to all
                    the tied values is assigned to each value.
                - *"dense"*: Like "min", but the rank of the next highest element is
                    assigned the rank immediately after those assigned to the tied elements.
                - *"ordinal"*: All values are given a distinct rank, corresponding to the
                    order that the values occur in the Series.

            descending: Rank in descending order.

        Examples:
            >>> import pandas as pd
            >>> import narwhals as nw
            >>> df_native = pd.DataFrame({"a": [3, 6, 1, 1, 6]})
            >>> df = nw.from_native(df_native)
            >>> result = df.with_columns(rank=nw.col("a").rank(method="dense"))
            >>> result
            ┌──────────────────┐
            |Narwhals DataFrame|
            |------------------|
            |       a  rank    |
            |    0  3   2.0    |
            |    1  6   3.0    |
            |    2  1   1.0    |
            |    3  1   1.0    |
            |    4  6   3.0    |
            └──────────────────┘
        """
        supported_rank_methods = {"average", "min", "max", "dense", "ordinal"}
        if method not in supported_rank_methods:
            msg = (
                "Ranking method must be one of {'average', 'min', 'max', 'dense', 'ordinal'}. "
                f"Found '{method}'"
            )
            raise ValueError(msg)

        return self._append_node(
            ExprNode(ExprKind.WINDOW, "rank", method=method, descending=descending)
        )

    def log(self, base: float = math.e) -> Self:
        r"""Compute the logarithm to a given base.

        Arguments:
            base: Given base, defaults to `e`

        Examples:
            >>> import pyarrow as pa
            >>> import narwhals as nw
            >>> df_native = pa.table({"values": [1, 2, 4]})
            >>> df = nw.from_native(df_native)
            >>> result = df.with_columns(
            ...     log=nw.col("values").log(), log_2=nw.col("values").log(base=2)
            ... )
            >>> result
            ┌────────────────────────────────────────────────┐
            |               Narwhals DataFrame               |
            |------------------------------------------------|
            |pyarrow.Table                                   |
            |values: int64                                   |
            |log: double                                     |
            |log_2: double                                   |
            |----                                            |
            |values: [[1,2,4]]                               |
            |log: [[0,0.6931471805599453,1.3862943611198906]]|
            |log_2: [[0,1,2]]                                |
            └────────────────────────────────────────────────┘
        """
        return self._append_node(ExprNode(ExprKind.ELEMENTWISE, "log", base=base))

    def exp(self) -> Self:
        r"""Compute the exponent.

        Examples:
            >>> import pyarrow as pa
            >>> import narwhals as nw
            >>> df_native = pa.table({"values": [-1, 0, 1]})
            >>> df = nw.from_native(df_native)
            >>> result = df.with_columns(exp=nw.col("values").exp())
            >>> result
            ┌────────────────────────────────────────────────┐
            |               Narwhals DataFrame               |
            |------------------------------------------------|
            |pyarrow.Table                                   |
            |values: int64                                   |
            |exp: double                                     |
            |----                                            |
            |values: [[-1,0,1]]                              |
            |exp: [[0.36787944117144233,1,2.718281828459045]]|
            └────────────────────────────────────────────────┘
        """
        return self._append_node(ExprNode(ExprKind.ELEMENTWISE, "exp"))

    def sin(self) -> Self:
        r"""Compute the element-wise value for the sine.

        Examples:
            >>> import pyarrow as pa
            >>> import narwhals as nw
            >>> from math import pi
            >>> df_native = pa.table({"values": [0, pi / 2, 3 * pi / 2]})
            >>> df = nw.from_native(df_native)
            >>> result = df.with_columns(sin=nw.col("values").sin())
            >>> result
            ┌─────────────────────────────────────────────────┐
            |               Narwhals DataFrame                |
            |-------------------------------------------------|
            |pyarrow.Table                                    |
            |values: double                                   |
            |sin: double                                      |
            |----                                             |
            |values: [[0,1.5707963267948966,4.71238898038469]]|
            |sin: [[0,1,-1]]                                  |
            └─────────────────────────────────────────────────┘
        """
        return self._append_node(ExprNode(ExprKind.ELEMENTWISE, "sin"))

    def cos(self) -> Self:
        r"""Compute the element-wise value for the cosine.

        Examples:
            >>> import pyarrow as pa
            >>> import narwhals as nw
            >>> from math import pi
            >>> df_native = pa.table({"values": [0, pi / 2, pi]})
            >>> df = nw.from_native(df_native)
            >>> result = df.with_columns(cos=nw.col("values").cos()).select(
            ...     nw.all().round(4)
            ... )
            >>> result
            ┌───────────────────────────┐
            |    Narwhals DataFrame     |
            |---------------------------|
            |pyarrow.Table              |
            |values: double             |
            |cos: double                |
            |----                       |
            |values: [[0,1.5708,3.1416]]|
            |cos: [[1,0,-1]]            |
            └───────────────────────────┘
        """
        return self._append_node(ExprNode(ExprKind.ELEMENTWISE, "cos"))

    def sqrt(self) -> Self:
        r"""Compute the square root of the elements.

        Examples:
            >>> import pyarrow as pa
            >>> import narwhals as nw
            >>> df_native = pa.table({"values": [1, 4, 9]})
            >>> df = nw.from_native(df_native)
            >>> result = df.with_columns(sqrt=nw.col("values").sqrt())
            >>> result
            ┌──────────────────┐
            |Narwhals DataFrame|
            |------------------|
            |pyarrow.Table     |
            |values: int64     |
            |sqrt: double      |
            |----              |
            |values: [[1,4,9]] |
            |sqrt: [[1,2,3]]   |
            └──────────────────┘
        """
        return self._append_node(ExprNode(ExprKind.ELEMENTWISE, "sqrt"))

    def is_close(  # noqa: PLR0914
        self,
        other: Expr | Series[Any] | NumericLiteral,
        *,
        abs_tol: float = 0.0,
        rel_tol: float = 1e-09,
        nans_equal: bool = False,
    ) -> Self:
        r"""Check if this expression is close, i.e. almost equal, to the other expression.

        Two values `a` and `b` are considered close if the following condition holds:

        $$
        |a-b| \le max \{ \text{rel\_tol} \cdot max \{ |a|, |b| \}, \text{abs\_tol} \}
        $$

        Arguments:
            other: Values to compare with.
            abs_tol: Absolute tolerance. This is the maximum allowed absolute difference
                between two values. Must be non-negative.
            rel_tol: Relative tolerance. This is the maximum allowed difference between
                two values, relative to the larger absolute value. Must be in the range
                [0, 1).
            nans_equal: Whether NaN values should be considered equal.

        Notes:
            The implementation of this method is symmetric and mirrors the behavior of
            `math.isclose`. Specifically note that this behavior is different to
            `numpy.isclose`.

        Examples:
            >>> import duckdb
            >>> import pyarrow as pa
            >>> import narwhals as nw
            >>>
            >>> data = {
            ...     "x": [1.0, float("inf"), 1.41, None, float("nan")],
            ...     "y": [1.2, float("inf"), 1.40, None, float("nan")],
            ... }
            >>> _table = pa.table(data)
            >>> df_native = duckdb.table("_table")
            >>> df = nw.from_native(df_native)
            >>> df.with_columns(
            ...     is_close=nw.col("x").is_close(
            ...         nw.col("y"), abs_tol=0.1, nans_equal=True
            ...     )
            ... )
            ┌──────────────────────────────┐
            |      Narwhals LazyFrame      |
            |------------------------------|
            |┌────────┬────────┬──────────┐|
            |│   x    │   y    │ is_close │|
            |│ double │ double │ boolean  │|
            |├────────┼────────┼──────────┤|
            |│    1.0 │    1.2 │ false    │|
            |│    inf │    inf │ true     │|
            |│   1.41 │    1.4 │ true     │|
            |│   NULL │   NULL │ NULL     │|
            |│    nan │    nan │ true     │|
            |└────────┴────────┴──────────┘|
            └──────────────────────────────┘
        """
        if abs_tol < 0:
            msg = f"`abs_tol` must be non-negative but got {abs_tol}"
            raise ComputeError(msg)

        if not (0 <= rel_tol < 1):
            msg = f"`rel_tol` must be in the range [0, 1) but got {rel_tol}"
            raise ComputeError(msg)

        from decimal import Decimal

        other_f: Expr | Series[Any] | NumericLiteral
        other_abs: Expr | Series[Any] | NumericLiteral
        other_is_nan: Expr | Series[Any] | bool
        other_is_inf: Expr | Series[Any] | bool
        other_is_not_inf: Expr | Series[Any] | bool

        # Promote to float to handle non-float numeric types (e.g. Decimal, integers).
        # Adding 0.0 lets each backend decide the appropriate float type.
        self_f = self + 0.0

        if isinstance(other, (float, int, Decimal)):
            from math import isinf, isnan

            other_f = float(other)
            # NOTE: See https://discuss.python.org/t/inferred-type-of-function-that-calls-dunder-abs-abs/101447
            other_abs = other_f.__abs__()
            other_is_nan = isnan(other_f)
            other_is_inf = isinf(other_f)

            # Define the other_is_not_inf variable to prevent triggering the following warning:
            # > DeprecationWarning: Bitwise inversion '~' on bool is deprecated and will be
            # >     removed in Python 3.16.
            other_is_not_inf = not other_is_inf

        else:
            other_f = other + 0.0
            other_abs, other_is_nan = other_f.abs(), other_f.is_nan()
            other_is_not_inf = other_f.is_finite() | other_is_nan
            other_is_inf = ~other_is_not_inf

        rel_threshold = (
            self_f.abs().clip(lower_bound=other_abs, upper_bound=None) * rel_tol
        )
        tolerance = rel_threshold.clip(lower_bound=abs_tol, upper_bound=None)

        self_is_nan = self_f.is_nan()
        self_is_not_inf = self_f.is_finite() | self_is_nan

        # Values are close if abs_diff <= tolerance, and both finite
        is_close = (
            ((self_f - other_f).abs() <= tolerance) & self_is_not_inf & other_is_not_inf
        )

        # Handle infinity cases: infinities are close/equal if they have the same sign
        self_sign, other_sign = self_f > 0, other_f > 0
        is_same_inf = (~self_is_not_inf) & other_is_inf & (self_sign == other_sign)

        # Handle nan cases:
        #   * If any value is NaN, then False (via `& ~either_nan`)
        #   * However, if `nans_equals = True` and if _both_ values are NaN, then True
        either_nan = self_is_nan | other_is_nan
        result = (is_close | is_same_inf) & ~either_nan

        if nans_equal:
            both_nan = self_is_nan & other_is_nan
            result = result | both_nan

        return result

    @unstable
    def any_value(self, *, ignore_nulls: bool = False) -> Self:
        """Get a random value from the column.

        Warning:
            This functionality is considered **unstable** as it diverges from the polars API.
            It may be changed at any point without it being considered a breaking change.

        Arguments:
            ignore_nulls: Whether to ignore null values or not.
                If `True` and there are no not-null elements, then `None` is returned.

        Examples:
            >>> import pyarrow as pa
            >>> import narwhals as nw
            >>> data = {"a": [1, 1, 2, 2], "b": [None, "foo", "baz", None]}
            >>> df_native = pa.table(data)
            >>> df = nw.from_native(df_native)
            >>> df.select(nw.all().any_value(ignore_nulls=False))
            ┌──────────────────┐
            |Narwhals DataFrame|
            |------------------|
            |  pyarrow.Table   |
            |  a: int64        |
            |  b: null         |
            |  ----            |
            |  a: [[1]]        |
            |  b: [1 nulls]    |
            └──────────────────┘

            >>> df.group_by("a").agg(nw.col("b").any_value(ignore_nulls=True))
            ┌──────────────────┐
            |Narwhals DataFrame|
            |------------------|
            |pyarrow.Table     |
            |a: int64          |
            |b: string         |
            |----              |
            |a: [[1,2]]        |
            |b: [["foo","baz"]]|
            └──────────────────┘

        """
        return self._append_node(
            ExprNode(ExprKind.AGGREGATION, "any_value", ignore_nulls=ignore_nulls)
        )

    @property
    def str(self) -> ExprStringNamespace[Self]:
        return ExprStringNamespace(self)

    @property
    def dt(self) -> ExprDateTimeNamespace[Self]:
        return ExprDateTimeNamespace(self)

    @property
    def cat(self) -> ExprCatNamespace[Self]:
        return ExprCatNamespace(self)

    @property
    def name(self) -> ExprNameNamespace[Self]:
        return ExprNameNamespace(self)

    @property
    def list(self) -> ExprListNamespace[Self]:
        return ExprListNamespace(self)

    @property
    def struct(self) -> ExprStructNamespace[Self]:
        return ExprStructNamespace(self)


__all__ = ["Expr"]
