diff --git a/narwhals/_arrow/expr.py b/narwhals/_arrow/expr.py
index d3378ea8eb..baeb9a9a40 100644
--- a/narwhals/_arrow/expr.py
+++ b/narwhals/_arrow/expr.py
@@ -30,7 +30,7 @@
     from narwhals.utils import Version
 
 
-class ArrowExpr(CompliantExpr[ArrowSeries]):
+class ArrowExpr(CompliantExpr["ArrowDataFrame", ArrowSeries]):
     _implementation: Implementation = Implementation.PYARROW
 
     def __init__(
diff --git a/narwhals/_arrow/namespace.py b/narwhals/_arrow/namespace.py
index f11e69af8e..4ae03060d7 100644
--- a/narwhals/_arrow/namespace.py
+++ b/narwhals/_arrow/namespace.py
@@ -40,7 +40,7 @@
     from narwhals.utils import Version
 
 
-class ArrowNamespace(CompliantNamespace[ArrowSeries]):
+class ArrowNamespace(CompliantNamespace[ArrowDataFrame, ArrowSeries]):
     def _create_expr_from_callable(
         self: Self,
         func: Callable[[ArrowDataFrame], Sequence[ArrowSeries]],
diff --git a/narwhals/_dask/expr.py b/narwhals/_dask/expr.py
index a0af9e64e0..434eac540a 100644
--- a/narwhals/_dask/expr.py
+++ b/narwhals/_dask/expr.py
@@ -35,7 +35,7 @@
     from narwhals.utils import Version
 
 
-class DaskExpr(CompliantExpr["dx.Series"]):
+class DaskExpr(CompliantExpr["DaskLazyFrame", "dx.Series"]):
     _implementation: Implementation = Implementation.DASK
 
     def __init__(
diff --git a/narwhals/_dask/group_by.py b/narwhals/_dask/group_by.py
index 39f79145e3..13b57796a2 100644
--- a/narwhals/_dask/group_by.py
+++ b/narwhals/_dask/group_by.py
@@ -107,7 +107,7 @@ def _from_native_frame(self: Self, df: DaskLazyFrame) -> DaskLazyFrame:
 def agg_dask(
     df: DaskLazyFrame,
     grouped: Any,
-    exprs: Sequence[CompliantExpr[dx.Series]],
+    exprs: Sequence[CompliantExpr[DaskLazyFrame, dx.Series]],
     keys: list[str],
     from_dataframe: Callable[[Any], DaskLazyFrame],
 ) -> DaskLazyFrame:
diff --git a/narwhals/_dask/namespace.py b/narwhals/_dask/namespace.py
index 1ef2d7e843..53ef7dbc8b 100644
--- a/narwhals/_dask/namespace.py
+++ b/narwhals/_dask/namespace.py
@@ -38,7 +38,7 @@
         import dask_expr as dx
 
 
-class DaskNamespace(CompliantNamespace["dx.Series"]):
+class DaskNamespace(CompliantNamespace[DaskLazyFrame, "dx.Series"]):
     @property
     def selectors(self: Self) -> DaskSelectorNamespace:
         return DaskSelectorNamespace(self)
diff --git a/narwhals/_duckdb/expr.py b/narwhals/_duckdb/expr.py
index 0dc9aab63f..45f614489a 100644
--- a/narwhals/_duckdb/expr.py
+++ b/narwhals/_duckdb/expr.py
@@ -33,7 +33,7 @@
     from narwhals.utils import Version
 
 
-class DuckDBExpr(CompliantExpr["duckdb.Expression"]):  # type: ignore[type-var]
+class DuckDBExpr(CompliantExpr["DuckDBLazyFrame", "duckdb.Expression"]):  # type: ignore[type-var]
     _implementation = Implementation.DUCKDB
     _depth = 0  # Unused, just for compatibility with CompliantExpr
 
diff --git a/narwhals/_duckdb/namespace.py b/narwhals/_duckdb/namespace.py
index 2f50a70724..bc5de2fd2c 100644
--- a/narwhals/_duckdb/namespace.py
+++ b/narwhals/_duckdb/namespace.py
@@ -34,7 +34,7 @@
     from narwhals.utils import Version
 
 
-class DuckDBNamespace(CompliantNamespace["duckdb.Expression"]):  # type: ignore[type-var]
+class DuckDBNamespace(CompliantNamespace["DuckDBLazyFrame", "duckdb.Expression"]):  # type: ignore[type-var]
     def __init__(
         self: Self, *, backend_version: tuple[int, ...], version: Version
     ) -> None:
diff --git a/narwhals/_expression_parsing.py b/narwhals/_expression_parsing.py
index ba0c81f9cb..0e91c02d09 100644
--- a/narwhals/_expression_parsing.py
+++ b/narwhals/_expression_parsing.py
@@ -12,7 +12,6 @@
 from typing import Sequence
 from typing import TypedDict
 from typing import TypeVar
-from typing import Union
 from typing import overload
 
 from narwhals.dependencies import is_narwhals_series
@@ -30,6 +29,7 @@
     from narwhals.expr import Expr
     from narwhals.typing import CompliantDataFrame
     from narwhals.typing import CompliantExpr
+    from narwhals.typing import CompliantFrameT_contra
     from narwhals.typing import CompliantLazyFrame
     from narwhals.typing import CompliantNamespace
     from narwhals.typing import CompliantSeries
@@ -37,9 +37,6 @@
     from narwhals.typing import IntoExpr
     from narwhals.typing import _1DArray
 
-    ArrowOrPandasLikeExpr = TypeVar(
-        "ArrowOrPandasLikeExpr", bound=Union[ArrowExpr, PandasLikeExpr]
-    )
     PandasLikeExprT = TypeVar("PandasLikeExprT", bound=PandasLikeExpr)
     ArrowExprT = TypeVar("ArrowExprT", bound=ArrowExpr)
 
@@ -54,8 +51,8 @@ def is_expr(obj: Any) -> TypeIs[Expr]:
 
 
 def evaluate_into_expr(
-    df: CompliantDataFrame | CompliantLazyFrame,
-    expr: CompliantExpr[CompliantSeriesT_co],
+    df: CompliantFrameT_contra,
+    expr: CompliantExpr[CompliantFrameT_contra, CompliantSeriesT_co],
 ) -> Sequence[CompliantSeriesT_co]:
     """Return list of raw columns.
 
@@ -75,7 +72,9 @@ def evaluate_into_expr(
 
 
 def evaluate_into_exprs(
-    df: CompliantDataFrame, /, *exprs: CompliantExpr[CompliantSeriesT_co]
+    df: CompliantFrameT_contra,
+    /,
+    *exprs: CompliantExpr[CompliantFrameT_contra, CompliantSeriesT_co],
 ) -> list[CompliantSeriesT_co]:
     """Evaluate each expr into Series."""
     return [
@@ -87,7 +86,8 @@ def evaluate_into_exprs(
 
 @overload
 def maybe_evaluate_expr(
-    df: CompliantDataFrame, expr: CompliantExpr[CompliantSeriesT_co]
+    df: CompliantFrameT_contra,
+    expr: CompliantExpr[CompliantFrameT_contra, CompliantSeriesT_co],
 ) -> CompliantSeriesT_co: ...
 
 
@@ -96,7 +96,7 @@ def maybe_evaluate_expr(df: CompliantDataFrame, expr: T) -> T: ...
 
 
 def maybe_evaluate_expr(
-    df: CompliantDataFrame, expr: CompliantExpr[CompliantSeriesT_co] | T
+    df: Any, expr: CompliantExpr[Any, CompliantSeriesT_co] | T
 ) -> CompliantSeriesT_co | T:
     """Evaluate `expr` if it's an expression, otherwise return it as is."""
     if is_compliant_expr(expr):
@@ -234,7 +234,7 @@ def reuse_series_namespace_implementation(
     )
 
 
-def is_simple_aggregation(expr: CompliantExpr[Any]) -> bool:
+def is_simple_aggregation(expr: CompliantExpr[Any, Any]) -> bool:
     """Check if expr is a very simple one.
 
     Examples:
@@ -252,24 +252,22 @@ def is_simple_aggregation(expr: CompliantExpr[Any]) -> bool:
 
 
 def combine_evaluate_output_names(
-    *exprs: CompliantExpr[Any],
-) -> Callable[[CompliantDataFrame | CompliantLazyFrame], Sequence[str]]:
+    *exprs: CompliantExpr[CompliantFrameT_contra, Any],
+) -> Callable[[CompliantFrameT_contra], Sequence[str]]:
     # Follow left-hand-rule for naming. E.g. `nw.sum_horizontal(expr1, expr2)` takes the
     # first name of `expr1`.
     if not is_compliant_expr(exprs[0]):  # pragma: no cover
         msg = f"Safety assertion failed, expected expression, got: {type(exprs[0])}. Please report a bug."
         raise AssertionError(msg)
 
-    def evaluate_output_names(
-        df: CompliantDataFrame | CompliantLazyFrame,
-    ) -> Sequence[str]:
+    def evaluate_output_names(df: CompliantFrameT_contra) -> Sequence[str]:
         return exprs[0]._evaluate_output_names(df)[:1]
 
     return evaluate_output_names
 
 
 def combine_alias_output_names(
-    *exprs: CompliantExpr[Any],
+    *exprs: CompliantExpr[Any, Any],
 ) -> Callable[[Sequence[str]], Sequence[str]] | None:
     # Follow left-hand-rule for naming. E.g. `nw.sum_horizontal(expr1.alias(alias), expr2)` takes the
     # aliasing function of `expr1` and apply it to the first output name of `expr1`.
@@ -283,11 +281,11 @@ def alias_output_names(names: Sequence[str]) -> Sequence[str]:
 
 
 def extract_compliant(
-    plx: CompliantNamespace[CompliantSeriesT_co],
+    plx: CompliantNamespace[CompliantFrameT_contra, CompliantSeriesT_co],
     other: Any,
     *,
     str_as_lit: bool,
-) -> CompliantExpr[CompliantSeriesT_co] | object:
+) -> CompliantExpr[CompliantFrameT_contra, CompliantSeriesT_co] | object:
     if is_expr(other):
         return other._to_compliant_expr(plx)
     if isinstance(other, str) and not str_as_lit:
@@ -301,7 +299,7 @@ def extract_compliant(
 
 
 def evaluate_output_names_and_aliases(
-    expr: CompliantExpr[Any],
+    expr: CompliantExpr[Any, Any],
     df: CompliantDataFrame | CompliantLazyFrame,
     exclude: Sequence[str],
 ) -> tuple[Sequence[str], Sequence[str]]:
@@ -446,7 +444,7 @@ def apply_n_ary_operation(
     function: Any,
     *comparands: IntoExpr,
     str_as_lit: bool,
-) -> CompliantExpr[Any]:
+) -> CompliantExpr[Any, Any]:
     compliant_exprs = (
         extract_compliant(plx, comparand, str_as_lit=str_as_lit)
         for comparand in comparands
@@ -463,3 +461,4 @@ def apply_n_ary_operation(
         for compliant_expr, kind in zip(compliant_exprs, kinds)
     )
     return function(*compliant_exprs)
+    return function(*compliant_exprs)
diff --git a/narwhals/_pandas_like/expr.py b/narwhals/_pandas_like/expr.py
index f9694c0777..1bf5ffd592 100644
--- a/narwhals/_pandas_like/expr.py
+++ b/narwhals/_pandas_like/expr.py
@@ -46,7 +46,7 @@
 }
 
 
-class PandasLikeExpr(CompliantExpr[PandasLikeSeries]):
+class PandasLikeExpr(CompliantExpr["PandasLikeDataFrame", PandasLikeSeries]):
     def __init__(
         self: Self,
         call: Callable[[PandasLikeDataFrame], Sequence[PandasLikeSeries]],
diff --git a/narwhals/_pandas_like/namespace.py b/narwhals/_pandas_like/namespace.py
index d930630e38..c5275d2d4a 100644
--- a/narwhals/_pandas_like/namespace.py
+++ b/narwhals/_pandas_like/namespace.py
@@ -33,7 +33,7 @@
     from narwhals.utils import Version
 
 
-class PandasLikeNamespace(CompliantNamespace[PandasLikeSeries]):
+class PandasLikeNamespace(CompliantNamespace[PandasLikeDataFrame, PandasLikeSeries]):
     @property
     def selectors(self: Self) -> PandasSelectorNamespace:
         return PandasSelectorNamespace(self)
diff --git a/narwhals/_spark_like/expr.py b/narwhals/_spark_like/expr.py
index 97c176061f..046755de95 100644
--- a/narwhals/_spark_like/expr.py
+++ b/narwhals/_spark_like/expr.py
@@ -27,7 +27,7 @@
     from narwhals.utils import Version
 
 
-class SparkLikeExpr(CompliantExpr["Column"]):
+class SparkLikeExpr(CompliantExpr["SparkLikeLazyFrame", "Column"]):
     _depth = 0  # Unused, just for compatibility with CompliantExpr
 
     def __init__(
diff --git a/narwhals/_spark_like/namespace.py b/narwhals/_spark_like/namespace.py
index b6f51a60f8..6946e1ff85 100644
--- a/narwhals/_spark_like/namespace.py
+++ b/narwhals/_spark_like/namespace.py
@@ -28,7 +28,7 @@
     from narwhals.utils import Version
 
 
-class SparkLikeNamespace(CompliantNamespace["Column"]):
+class SparkLikeNamespace(CompliantNamespace["SparkLikeLazyFrame", "Column"]):
     def __init__(
         self: Self,
         *,
diff --git a/narwhals/dataframe.py b/narwhals/dataframe.py
index 90a18935a8..c22125b679 100644
--- a/narwhals/dataframe.py
+++ b/narwhals/dataframe.py
@@ -82,7 +82,7 @@ def _from_compliant_dataframe(self: Self, df: Any) -> Self:
 
     def _flatten_and_extract(
         self, *exprs: IntoExpr | Iterable[IntoExpr], **named_exprs: IntoExpr
-    ) -> tuple[list[IntoCompliantExpr[Any]], list[ExprKind]]:
+    ) -> tuple[list[IntoCompliantExpr[Any, Any]], list[ExprKind]]:
         """Process `args` and `kwargs`, extracting underlying objects as we go, interpreting strings as column names."""
         out_exprs = []
         out_kinds = []
diff --git a/narwhals/expr.py b/narwhals/expr.py
index 2c323329bc..d628456aa8 100644
--- a/narwhals/expr.py
+++ b/narwhals/expr.py
@@ -1189,10 +1189,10 @@ def is_between(
         """
 
         def func(
-            compliant_expr: CompliantExpr[Any],
-            lb: CompliantExpr[Any],
-            ub: CompliantExpr[Any],
-        ) -> CompliantExpr[Any]:
+            compliant_expr: CompliantExpr[Any, Any],
+            lb: CompliantExpr[Any, Any],
+            ub: CompliantExpr[Any, Any],
+        ) -> CompliantExpr[Any, Any]:
             if closed == "left":
                 return (compliant_expr >= lb) & (compliant_expr < ub)  # type: ignore[no-any-return]
             elif closed == "right":
diff --git a/narwhals/functions.py b/narwhals/functions.py
index 22634f9847..2cd172ae0c 100644
--- a/narwhals/functions.py
+++ b/narwhals/functions.py
@@ -1458,7 +1458,7 @@ class Then(Expr):
     def otherwise(self: Self, value: IntoExpr | Any) -> Expr:
         kind = infer_kind(value, str_as_lit=False)
 
-        def func(plx: CompliantNamespace[Any]) -> CompliantExpr[Any]:
+        def func(plx: CompliantNamespace[Any, Any]) -> CompliantExpr[Any, Any]:
             compliant_expr = self._to_compliant_expr(plx)
             compliant_value = extract_compliant(plx, value, str_as_lit=False)
             if (
diff --git a/narwhals/typing.py b/narwhals/typing.py
index 4923bbed7b..98457fab71 100644
--- a/narwhals/typing.py
+++ b/narwhals/typing.py
@@ -72,25 +72,30 @@ def aggregate(self, *exprs: Any) -> Self:
         # (so, no broadcasting is necessary).
 
 
+CompliantFrameT_contra = TypeVar(
+    "CompliantFrameT_contra",
+    bound="CompliantDataFrame | CompliantLazyFrame",
+    contravariant=True,
+)
 CompliantSeriesT_co = TypeVar(
     "CompliantSeriesT_co", bound=CompliantSeries, covariant=True
 )
 
 
-class CompliantExpr(Protocol, Generic[CompliantSeriesT_co]):
+class CompliantExpr(Protocol, Generic[CompliantFrameT_contra, CompliantSeriesT_co]):
     _implementation: Implementation
     _backend_version: tuple[int, ...]
     _version: Version
-    _evaluate_output_names: Callable[
-        [CompliantDataFrame | CompliantLazyFrame], Sequence[str]
-    ]
+    _evaluate_output_names: Callable[[CompliantFrameT_contra], Sequence[str]]
     _alias_output_names: Callable[[Sequence[str]], Sequence[str]] | None
     _depth: int
     _function_name: str
 
     def __call__(self, df: Any) -> Sequence[CompliantSeriesT_co]: ...
     def __narwhals_expr__(self) -> None: ...
-    def __narwhals_namespace__(self) -> CompliantNamespace[CompliantSeriesT_co]: ...
+    def __narwhals_namespace__(
+        self,
+    ) -> CompliantNamespace[CompliantFrameT_contra, CompliantSeriesT_co]: ...
     def is_null(self) -> Self: ...
     def alias(self, name: str) -> Self: ...
     def cast(self, dtype: DType) -> Self: ...
@@ -112,11 +117,13 @@ def broadcast(
     ) -> Self: ...
 
 
-class CompliantNamespace(Protocol, Generic[CompliantSeriesT_co]):
-    def col(self, *column_names: str) -> CompliantExpr[CompliantSeriesT_co]: ...
+class CompliantNamespace(Protocol, Generic[CompliantFrameT_contra, CompliantSeriesT_co]):
+    def col(
+        self, *column_names: str
+    ) -> CompliantExpr[CompliantFrameT_contra, CompliantSeriesT_co]: ...
     def lit(
         self, value: Any, dtype: DType | None
-    ) -> CompliantExpr[CompliantSeriesT_co]: ...
+    ) -> CompliantExpr[CompliantFrameT_contra, CompliantSeriesT_co]: ...
 
 
 class SupportsNativeNamespace(Protocol):
@@ -316,7 +323,7 @@ class DTypes:
     # This one needs to be in TYPE_CHECKING to pass on 3.9,
     # and can only be defined after CompliantExpr has been defined
     IntoCompliantExpr: TypeAlias = (
-        CompliantExpr[CompliantSeriesT_co] | CompliantSeriesT_co
+        CompliantExpr[CompliantFrameT_contra, CompliantSeriesT_co] | CompliantSeriesT_co
     )
 
 
diff --git a/narwhals/utils.py b/narwhals/utils.py
index cb33a603d6..4b3183bf7e 100644
--- a/narwhals/utils.py
+++ b/narwhals/utils.py
@@ -53,6 +53,7 @@
     from narwhals.series import Series
     from narwhals.typing import CompliantDataFrame
     from narwhals.typing import CompliantExpr
+    from narwhals.typing import CompliantFrameT_contra
     from narwhals.typing import CompliantLazyFrame
     from narwhals.typing import CompliantSeries
     from narwhals.typing import CompliantSeriesT_co
@@ -1321,8 +1322,8 @@ def is_compliant_series(obj: Any) -> TypeIs[CompliantSeries]:
 
 
 def is_compliant_expr(
-    obj: CompliantExpr[CompliantSeriesT_co] | Any,
-) -> TypeIs[CompliantExpr[CompliantSeriesT_co]]:
+    obj: CompliantExpr[CompliantFrameT_contra, CompliantSeriesT_co] | Any,
+) -> TypeIs[CompliantExpr[CompliantFrameT_contra, CompliantSeriesT_co]]:
     return hasattr(obj, "__narwhals_expr__")