From 3288afd8d933e6f899aae25c2028a05d0ffe84c1 Mon Sep 17 00:00:00 2001
From: Nick Crews <nicholas.b.crews@gmail.com>
Date: Thu, 20 Nov 2025 10:42:08 -0700
Subject: [PATCH] feat(typing): make types more precise for many common Values

---
 ibis/expr/types/generic.py |  82 +++++++-
 ibis/expr/types/logical.py |  40 +++-
 ibis/expr/types/numeric.py | 371 ++++++++++++++++++++++++++++++++-----
 ibis/expr/types/strings.py | 166 +++++++++++++++--
 4 files changed, 576 insertions(+), 83 deletions(-)

diff --git a/ibis/expr/types/generic.py b/ibis/expr/types/generic.py
index 7257feab5834..c1c4fde2c396 100644
--- a/ibis/expr/types/generic.py
+++ b/ibis/expr/types/generic.py
@@ -42,7 +42,7 @@
 class Value(Expr):
     """Base class for a data generating expression having a known type."""
 
-    def name(self, name: str, /) -> Value:
+    def name(self, name: str, /) -> Self:
         """Rename an expression to `name`.
 
         Parameters
@@ -121,6 +121,10 @@ def type(self) -> dt.DataType:
         """
         return self.op().dtype
 
+    @overload
+    def hash(self: Scalar) -> ir.IntegerScalar: ...
+    @overload
+    def hash(self: Column) -> ir.IntegerColumn: ...
     def hash(self) -> ir.IntegerValue:
         """Compute an integer hash value.
 
@@ -297,6 +301,10 @@ def cast(self, target_type: Any, /) -> Value:
 
         return op.to_expr()
 
+    @overload
+    def try_cast(self: Scalar, target_type: Any, /) -> Scalar: ...
+    @overload
+    def try_cast(self: Column, target_type: Any, /) -> Column: ...
     def try_cast(self, target_type: Any, /) -> Value:
         """Try cast expression to indicated data type.
 
@@ -383,6 +391,10 @@ def coalesce(self, /, *args: Value) -> Value:
         """
         return ops.Coalesce((self, *args)).to_expr()
 
+    @overload
+    def typeof(self: Scalar) -> ir.StringScalar: ...
+    @overload
+    def typeof(self: Column) -> ir.StringColumn: ...
     def typeof(self) -> ir.StringValue:
         """Return the string name of the datatype of self.
 
@@ -923,6 +935,10 @@ def bind(table):
         except com.IbisInputError:
             return bind(_)
 
+    @overload
+    def isnull(self: Scalar) -> ir.BooleanScalar: ...
+    @overload
+    def isnull(self: Column) -> ir.BooleanColumn: ...
     def isnull(self) -> ir.BooleanValue:
         """Whether this expression is `NULL`. Does NOT detect `NaN` and `inf` values.
 
@@ -960,6 +976,10 @@ def isnull(self) -> ir.BooleanValue:
         """
         return ops.IsNull(self).to_expr()
 
+    @overload
+    def notnull(self: Scalar) -> ir.BooleanScalar: ...
+    @overload
+    def notnull(self: Column) -> ir.BooleanColumn: ...
     def notnull(self) -> ir.BooleanValue:
         """Return whether this expression is not NULL.
 
@@ -1291,6 +1311,14 @@ def group_concat(
     def __hash__(self) -> int:
         return super().__hash__()
 
+    @overload
+    def __eq__(self: Scalar, other: Scalar) -> ir.BooleanScalar: ...
+    @overload
+    def __eq__(self: Scalar, other: Column) -> ir.BooleanColumn: ...
+    @overload
+    def __eq__(self: Column, other: Scalar) -> ir.BooleanColumn: ...
+    @overload
+    def __eq__(self: Column, other: Column) -> ir.BooleanColumn: ...
     def __eq__(self, other: Value) -> ir.BooleanValue:
         if _is_null_literal(other):
             return self.isnull()
@@ -1298,6 +1326,14 @@ def __eq__(self, other: Value) -> ir.BooleanValue:
             return other.isnull()
         return _binop(ops.Equals, self, other)
 
+    @overload
+    def __ne__(self: Scalar, other: Scalar) -> ir.BooleanScalar: ...
+    @overload
+    def __ne__(self: Scalar, other: Column) -> ir.BooleanColumn: ...
+    @overload
+    def __ne__(self: Column, other: Scalar) -> ir.BooleanColumn: ...
+    @overload
+    def __ne__(self: Column, other: Column) -> ir.BooleanColumn: ...
     def __ne__(self, other: Value) -> ir.BooleanValue:
         if _is_null_literal(other):
             return self.notnull()
@@ -1305,15 +1341,47 @@ def __ne__(self, other: Value) -> ir.BooleanValue:
             return other.notnull()
         return _binop(ops.NotEquals, self, other)
 
+    @overload
+    def __ge__(self: Scalar, other: Scalar) -> ir.BooleanScalar: ...
+    @overload
+    def __ge__(self: Scalar, other: Column) -> ir.BooleanColumn: ...
+    @overload
+    def __ge__(self: Column, other: Scalar) -> ir.BooleanColumn: ...
+    @overload
+    def __ge__(self: Column, other: Column) -> ir.BooleanColumn: ...
     def __ge__(self, other: Value) -> ir.BooleanValue:
         return _binop(ops.GreaterEqual, self, other)
 
+    @overload
+    def __gt__(self: Scalar, other: Scalar) -> ir.BooleanScalar: ...
+    @overload
+    def __gt__(self: Scalar, other: Column) -> ir.BooleanColumn: ...
+    @overload
+    def __gt__(self: Column, other: Scalar) -> ir.BooleanColumn: ...
+    @overload
+    def __gt__(self: Column, other: Column) -> ir.BooleanColumn: ...
     def __gt__(self, other: Value) -> ir.BooleanValue:
         return _binop(ops.Greater, self, other)
 
+    @overload
+    def __le__(self: Scalar, other: Scalar) -> ir.BooleanScalar: ...
+    @overload
+    def __le__(self: Scalar, other: Column) -> ir.BooleanColumn: ...
+    @overload
+    def __le__(self: Column, other: Scalar) -> ir.BooleanColumn: ...
+    @overload
+    def __le__(self: Column, other: Column) -> ir.BooleanColumn: ...
     def __le__(self, other: Value) -> ir.BooleanValue:
         return _binop(ops.LessEqual, self, other)
 
+    @overload
+    def __lt__(self: Scalar, other: Scalar) -> ir.BooleanScalar: ...
+    @overload
+    def __lt__(self: Scalar, other: Column) -> ir.BooleanColumn: ...
+    @overload
+    def __lt__(self: Column, other: Scalar) -> ir.BooleanColumn: ...
+    @overload
+    def __lt__(self: Column, other: Column) -> ir.BooleanColumn: ...
     def __lt__(self, other: Value) -> ir.BooleanValue:
         return _binop(ops.Less, self, other)
 
@@ -1484,7 +1552,7 @@ def __polars_result__(self, df: pl.DataFrame) -> Any:
 
         return PolarsData.convert_scalar(df, self.type())
 
-    def as_scalar(self):
+    def as_scalar(self) -> Self:
         """Inform ibis that the expression should be treated as a scalar.
 
         If the expression is a literal, it will be returned as is. If it depends
@@ -2461,7 +2529,7 @@ def first(
         where: ir.BooleanValue | None = None,
         order_by: Any = None,
         include_null: bool = False,
-    ) -> Value:
+    ) -> Scalar:
         """Return the first value of a column.
 
         Parameters
@@ -2515,7 +2583,7 @@ def last(
         where: ir.BooleanValue | None = None,
         order_by: Any = None,
         include_null: bool = False,
-    ) -> Value:
+    ) -> Scalar:
         """Return the last value of a column.
 
         Parameters
@@ -2627,7 +2695,7 @@ def dense_rank(self) -> ir.IntegerColumn:
         """
         return ibis.dense_rank().over(order_by=self)
 
-    def percent_rank(self) -> Column:
+    def percent_rank(self) -> ir.IntegerColumn:
         """Return the relative rank of the values in the column.
 
         Examples
@@ -2651,7 +2719,7 @@ def percent_rank(self) -> Column:
         """
         return ibis.percent_rank().over(order_by=self)
 
-    def cume_dist(self) -> Column:
+    def cume_dist(self) -> ir.FloatingColumn:
         """Return the cumulative distribution over a window.
 
         Examples
@@ -2995,7 +3063,7 @@ class NullColumn(Column, NullValue):
 
 @public
 @deferrable
-def null(type: dt.DataType | str | None = None, /) -> Value:
+def null(type: dt.DataType | str | None = None, /) -> Scalar:
     """Create a NULL scalar.
 
     `NULL`s with an unspecified type are castable and comparable to values,
diff --git a/ibis/expr/types/logical.py b/ibis/expr/types/logical.py
index b921621187c2..b40141067d14 100644
--- a/ibis/expr/types/logical.py
+++ b/ibis/expr/types/logical.py
@@ -1,6 +1,6 @@
 from __future__ import annotations
 
-from typing import TYPE_CHECKING
+from typing import TYPE_CHECKING, overload
 
 from public import public
 
@@ -11,11 +11,19 @@
 from ibis.expr.types.numeric import NumericColumn, NumericScalar, NumericValue
 
 if TYPE_CHECKING:
+    from typing_extensions import Self
+
     import ibis.expr.types as ir
 
 
 @public
 class BooleanValue(NumericValue):
+    @overload
+    def ifelse(
+        self: ir.BooleanScalar, true_expr: ir.Scalar, false_expr: ir.Scalar, /
+    ) -> ir.Scalar: ...
+    @overload
+    def ifelse(self, true_expr: ir.Value, false_expr: ir.Value, /) -> ir.Column: ...
     def ifelse(self, true_expr: ir.Value, false_expr: ir.Value, /) -> ir.Value:
         """Construct a ternary conditional expression.
 
@@ -53,7 +61,11 @@ def ifelse(self, true_expr: ir.Value, false_expr: ir.Value, /) -> ir.Value:
         # must be used.
         return ops.IfElse(self, true_expr, false_expr).to_expr()
 
-    def __and__(self, other: BooleanValue) -> BooleanValue:
+    @overload
+    def __and__(self: BooleanScalar, other: bool | BooleanScalar) -> BooleanScalar: ...
+    @overload
+    def __and__(self, other: bool | BooleanValue) -> BooleanColumn: ...
+    def __and__(self, other: bool | BooleanValue) -> BooleanValue:
         """Construct a binary AND conditional expression with `self` and `other`.
 
         Parameters
@@ -101,7 +113,11 @@ def __and__(self, other: BooleanValue) -> BooleanValue:
 
     __rand__ = __and__
 
-    def __or__(self, other: BooleanValue) -> BooleanValue:
+    @overload
+    def __or__(self: BooleanScalar, other: bool | BooleanScalar) -> BooleanScalar: ...
+    @overload
+    def __or__(self, other: bool | BooleanValue) -> BooleanColumn: ...
+    def __or__(self, other: bool | BooleanValue) -> BooleanValue:
         """Construct a binary OR conditional expression with `self` and `other`.
 
         Parameters
@@ -137,7 +153,11 @@ def __or__(self, other: BooleanValue) -> BooleanValue:
 
     __ror__ = __or__
 
-    def __xor__(self, other: BooleanValue) -> BooleanValue:
+    @overload
+    def __xor__(self: BooleanScalar, other: bool | BooleanScalar) -> BooleanScalar: ...
+    @overload
+    def __xor__(self, other: bool | BooleanValue) -> BooleanColumn: ...
+    def __xor__(self, other: bool | BooleanValue) -> BooleanValue:
         """Construct a binary XOR conditional expression with `self` and `other`.
 
         Parameters
@@ -198,7 +218,7 @@ def __xor__(self, other: BooleanValue) -> BooleanValue:
 
     __rxor__ = __xor__
 
-    def __invert__(self) -> BooleanValue:
+    def __invert__(self) -> Self:
         """Construct a unary NOT conditional expression with `self`.
 
         Parameters
@@ -230,7 +250,7 @@ def __invert__(self) -> BooleanValue:
         """
         return ops.Not(self).to_expr()
 
-    def negate(self) -> BooleanValue:
+    def negate(self) -> Self:
         """DEPRECATED."""
         util.warn_deprecated(
             "`-bool_val`/`bool_val.negate()`",
@@ -247,7 +267,7 @@ class BooleanScalar(NumericScalar, BooleanValue):
 
 @public
 class BooleanColumn(NumericColumn, BooleanValue):
-    def any(self, *, where: BooleanValue | None = None) -> BooleanValue:
+    def any(self, *, where: bool | BooleanValue | None = None) -> BooleanScalar:
         """Return whether at least one element is `True`.
 
         If the expression does not reference any foreign tables, the result
@@ -339,7 +359,7 @@ def resolve_exists_subquery(outer):
 
         return op.to_expr()
 
-    def notany(self, *, where: BooleanValue | None = None) -> BooleanValue:
+    def notany(self, *, where: bool | BooleanValue | None = None) -> BooleanScalar:
         """Return whether no elements are `True`.
 
         Parameters
@@ -373,7 +393,7 @@ def notany(self, *, where: BooleanValue | None = None) -> BooleanValue:
         """
         return ~self.any(where=where)
 
-    def all(self, *, where: BooleanValue | None = None) -> BooleanScalar:
+    def all(self, *, where: bool | BooleanValue | None = None) -> BooleanScalar:
         """Return whether all elements are `True`.
 
         Parameters
@@ -410,7 +430,7 @@ def all(self, *, where: BooleanValue | None = None) -> BooleanScalar:
         """
         return ops.All(self, where=self._bind_to_parent_table(where)).to_expr()
 
-    def notall(self, *, where: BooleanValue | None = None) -> BooleanScalar:
+    def notall(self, *, where: bool | BooleanValue | None = None) -> BooleanScalar:
         """Return whether not all elements are `True`.
 
         Parameters
diff --git a/ibis/expr/types/numeric.py b/ibis/expr/types/numeric.py
index 44d68297cb72..c0ef35954a2a 100644
--- a/ibis/expr/types/numeric.py
+++ b/ibis/expr/types/numeric.py
@@ -1,7 +1,7 @@
 from __future__ import annotations
 
 from collections.abc import Sequence
-from typing import TYPE_CHECKING, Literal
+from typing import TYPE_CHECKING, Literal, overload
 
 from public import public
 
@@ -11,12 +11,19 @@
 from ibis.expr.types.generic import Column, Scalar, Value, _binop
 
 if TYPE_CHECKING:
+    from decimal import Decimal
+    from typing import Union
+
+    from typing_extensions import Self
+
     import ibis.expr.types as ir
 
+    Number = Union[int, float, Decimal]
+
 
 @public
 class NumericValue(Value):
-    def negate(self) -> NumericValue:
+    def negate(self) -> Self:
         """Negate a numeric expression.
 
         Returns
@@ -42,7 +49,7 @@ def negate(self) -> NumericValue:
         """
         return ops.Negate(self).to_expr()
 
-    def __neg__(self) -> NumericValue:
+    def __neg__(self) -> Self:
         """Negate `self`.
 
         Returns
@@ -52,6 +59,12 @@ def __neg__(self) -> NumericValue:
         """
         return self.negate()
 
+    @overload
+    def round(self: NumericScalar, digits: int | IntegerScalar, /) -> NumericScalar: ...
+    @overload
+    def round(self: NumericScalar, digits: IntegerColumn, /) -> NumericColumn: ...
+    @overload
+    def round(self: NumericColumn, digits: int | IntegerValue, /) -> NumericColumn: ...
     def round(self, digits: int | IntegerValue = 0, /) -> NumericValue:
         """Round values to an indicated number of decimal places.
 
@@ -114,7 +127,17 @@ def round(self, digits: int | IntegerValue = 0, /) -> NumericValue:
         """
         return ops.Round(self, digits).to_expr()
 
-    def log(self, base: NumericValue | None = None, /) -> NumericValue:
+    @overload
+    def log(
+        self: NumericScalar, base: Number | NumericScalar | None, /
+    ) -> FloatingScalar: ...
+    @overload
+    def log(self: NumericScalar, base: NumericColumn, /) -> FloatingColumn: ...
+    @overload
+    def log(
+        self: NumericColumn, base: Number | NumericValue | None, /
+    ) -> FloatingColumn: ...
+    def log(self, base: Number | NumericValue | None = None, /) -> NumericValue:
         r"""Compute $\log_{\texttt{base}}\left(\texttt{self}\right)$.
 
         Parameters
@@ -163,9 +186,9 @@ def log(self, base: NumericValue | None = None, /) -> NumericValue:
 
     def clip(
         self,
-        lower: NumericValue | None = None,
-        upper: NumericValue | None = None,
-    ) -> NumericValue:
+        lower: Number | NumericValue | None = None,
+        upper: Number | NumericValue | None = None,
+    ) -> Self:
         """Trim values outside of `lower` and `upper` bounds.
 
         `NULL` values are preserved and are not replaced with bounds.
@@ -211,7 +234,7 @@ def clip(
 
         return ops.Clip(self, lower, upper).to_expr()
 
-    def abs(self) -> NumericValue:
+    def abs(self) -> Self:
         """Return the absolute value of `self`.
 
         Examples
@@ -233,6 +256,14 @@ def abs(self) -> NumericValue:
         """
         return ops.Abs(self).to_expr()
 
+    @overload
+    def ceil(self: DecimalScalar) -> DecimalScalar: ...
+    @overload
+    def ceil(self: DecimalColumn) -> DecimalColumn: ...
+    @overload
+    def ceil(self: NumericScalar) -> IntegerScalar: ...
+    @overload
+    def ceil(self: NumericColumn) -> IntegerColumn: ...
     def ceil(self) -> DecimalValue | IntegerValue:
         """Return the ceiling of `self`.
 
@@ -256,6 +287,14 @@ def ceil(self) -> DecimalValue | IntegerValue:
         """
         return ops.Ceil(self).to_expr()
 
+    @overload
+    def degrees(self: NumericScalar) -> FloatingScalar: ...
+    @overload
+    def degrees(self: NumericColumn) -> FloatingColumn: ...
+    @overload
+    def degrees(self: DecimalScalar) -> DecimalScalar: ...
+    @overload
+    def degrees(self: DecimalColumn) -> DecimalColumn: ...
     def degrees(self) -> NumericValue:
         """Compute the degrees of `self` radians.
 
@@ -282,7 +321,15 @@ def degrees(self) -> NumericValue:
 
     rad2deg = degrees
 
-    def exp(self) -> NumericValue:
+    @overload
+    def exp(self: NumericScalar) -> FloatingScalar: ...
+    @overload
+    def exp(self: NumericColumn) -> FloatingColumn: ...
+    @overload
+    def exp(self: DecimalScalar) -> DecimalScalar: ...
+    @overload
+    def exp(self: DecimalColumn) -> DecimalColumn: ...
+    def exp(self) -> FloatingValue:
         r"""Compute $e^\texttt{self}$.
 
         Returns
@@ -309,6 +356,14 @@ def exp(self) -> NumericValue:
         """
         return ops.Exp(self).to_expr()
 
+    @overload
+    def floor(self: DecimalScalar) -> DecimalScalar: ...
+    @overload
+    def floor(self: DecimalColumn) -> DecimalColumn: ...
+    @overload
+    def floor(self: NumericScalar) -> IntegerScalar: ...
+    @overload
+    def floor(self: NumericColumn) -> IntegerColumn: ...
     def floor(self) -> DecimalValue | IntegerValue:
         """Return the floor of an expression.
 
@@ -333,7 +388,11 @@ def floor(self) -> DecimalValue | IntegerValue:
         """
         return ops.Floor(self).to_expr()
 
-    def log2(self) -> NumericValue:
+    @overload
+    def log2(self: NumericScalar) -> FloatingScalar: ...
+    @overload
+    def log2(self: NumericColumn) -> FloatingColumn: ...
+    def log2(self) -> FloatingValue:
         r"""Compute $\log_{2}\left(\texttt{self}\right)$.
 
         Examples
@@ -355,7 +414,11 @@ def log2(self) -> NumericValue:
         """
         return ops.Log2(self).to_expr()
 
-    def log10(self) -> NumericValue:
+    @overload
+    def log10(self: NumericScalar) -> FloatingScalar: ...
+    @overload
+    def log10(self: NumericColumn) -> FloatingColumn: ...
+    def log10(self) -> FloatingValue:
         r"""Compute $\log_{10}\left(\texttt{self}\right)$.
 
         Examples
@@ -376,7 +439,11 @@ def log10(self) -> NumericValue:
         """
         return ops.Log10(self).to_expr()
 
-    def ln(self) -> NumericValue:
+    @overload
+    def ln(self: NumericScalar) -> FloatingScalar: ...
+    @overload
+    def ln(self: NumericColumn) -> FloatingColumn: ...
+    def ln(self) -> FloatingValue:
         r"""Compute $\ln\left(\texttt{self}\right)$.
 
         Examples
@@ -397,7 +464,11 @@ def ln(self) -> NumericValue:
         """
         return ops.Ln(self).to_expr()
 
-    def radians(self) -> NumericValue:
+    @overload
+    def radians(self: NumericScalar) -> FloatingScalar: ...
+    @overload
+    def radians(self: NumericColumn) -> FloatingColumn: ...
+    def radians(self) -> FloatingValue:
         """Compute radians from `self` degrees.
 
         Examples
@@ -422,7 +493,7 @@ def radians(self) -> NumericValue:
 
     deg2rad = radians
 
-    def sign(self) -> NumericValue:
+    def sign(self) -> Self:
         """Return the sign of the input.
 
         Examples
@@ -444,7 +515,11 @@ def sign(self) -> NumericValue:
         """
         return ops.Sign(self).to_expr()
 
-    def sqrt(self) -> NumericValue:
+    @overload
+    def sqrt(self: NumericScalar) -> FloatingScalar: ...
+    @overload
+    def sqrt(self: NumericColumn) -> FloatingColumn: ...
+    def sqrt(self) -> FloatingValue:
         """Compute the square root of `self`.
 
         Examples
@@ -466,7 +541,11 @@ def sqrt(self) -> NumericValue:
         """
         return ops.Sqrt(self).to_expr()
 
-    def acos(self) -> NumericValue:
+    @overload
+    def acos(self: NumericScalar) -> FloatingScalar: ...
+    @overload
+    def acos(self: NumericColumn) -> FloatingColumn: ...
+    def acos(self) -> FloatingValue:
         """Compute the arc cosine of `self`.
 
         Examples
@@ -488,7 +567,11 @@ def acos(self) -> NumericValue:
         """
         return ops.Acos(self).to_expr()
 
-    def asin(self) -> NumericValue:
+    @overload
+    def asin(self: NumericScalar) -> FloatingScalar: ...
+    @overload
+    def asin(self: NumericColumn) -> FloatingColumn: ...
+    def asin(self) -> FloatingValue:
         """Compute the arc sine of `self`.
 
         Examples
@@ -509,7 +592,11 @@ def asin(self) -> NumericValue:
         """
         return ops.Asin(self).to_expr()
 
-    def atan(self) -> NumericValue:
+    @overload
+    def atan(self: NumericScalar) -> FloatingScalar: ...
+    @overload
+    def atan(self: NumericColumn) -> FloatingColumn: ...
+    def atan(self) -> FloatingValue:
         """Compute the arc tangent of `self`.
 
         Examples
@@ -530,7 +617,17 @@ def atan(self) -> NumericValue:
         """
         return ops.Atan(self).to_expr()
 
-    def atan2(self, other: NumericValue, /) -> NumericValue:
+    @overload
+    def atan2(
+        self: NumericScalar, other: Number | NumericScalar, /
+    ) -> FloatingScalar: ...
+    @overload
+    def atan2(self: NumericScalar, other: NumericColumn, /) -> FloatingColumn: ...
+    @overload
+    def atan2(
+        self: NumericColumn, other: Number | NumericValue, /
+    ) -> FloatingColumn: ...
+    def atan2(self, other: NumericValue, /) -> FloatingValue:
         """Compute the two-argument version of arc tangent.
 
         Examples
@@ -551,7 +648,11 @@ def atan2(self, other: NumericValue, /) -> NumericValue:
         """
         return ops.Atan2(self, other).to_expr()
 
-    def cos(self) -> NumericValue:
+    @overload
+    def cos(self: NumericScalar) -> FloatingScalar: ...
+    @overload
+    def cos(self: NumericColumn) -> FloatingColumn: ...
+    def cos(self) -> FloatingValue:
         """Compute the cosine of `self`.
 
         Examples
@@ -572,7 +673,11 @@ def cos(self) -> NumericValue:
         """
         return ops.Cos(self).to_expr()
 
-    def cot(self) -> NumericValue:
+    @overload
+    def cot(self: NumericScalar) -> FloatingScalar: ...
+    @overload
+    def cot(self: NumericColumn) -> FloatingColumn: ...
+    def cot(self) -> FloatingValue:
         """Compute the cotangent of `self`.
 
         Examples
@@ -593,7 +698,11 @@ def cot(self) -> NumericValue:
         """
         return ops.Cot(self).to_expr()
 
-    def sin(self) -> NumericValue:
+    @overload
+    def sin(self: NumericScalar) -> FloatingScalar: ...
+    @overload
+    def sin(self: NumericColumn) -> FloatingColumn: ...
+    def sin(self) -> FloatingValue:
         """Compute the sine of `self`.
 
         Examples
@@ -614,7 +723,11 @@ def sin(self) -> NumericValue:
         """
         return ops.Sin(self).to_expr()
 
-    def tan(self) -> NumericValue:
+    @overload
+    def tan(self: NumericScalar) -> FloatingScalar: ...
+    @overload
+    def tan(self: NumericColumn) -> FloatingColumn: ...
+    def tan(self) -> FloatingValue:
         """Compute the tangent of `self`.
 
         Examples
@@ -635,51 +748,112 @@ def tan(self) -> NumericValue:
         """
         return ops.Tan(self).to_expr()
 
-    def __add__(self, other: NumericValue) -> NumericValue:
+    @overload
+    def __add__(
+        self: NumericScalar, other: Number | NumericScalar
+    ) -> NumericScalar: ...
+    @overload
+    def __add__(self: NumericScalar, other: NumericColumn) -> NumericColumn: ...
+    @overload
+    def __add__(self, other: Number | NumericValue) -> NumericColumn: ...
+    def __add__(self, other: Number | NumericValue) -> NumericValue:
         """Add `self` with `other`."""
         return _binop(ops.Add, self, other)
 
     add = radd = __radd__ = __add__
 
-    def __sub__(self, other: NumericValue) -> NumericValue:
+    @overload
+    def __sub__(
+        self: NumericScalar, other: Number | NumericScalar
+    ) -> NumericScalar: ...
+    @overload
+    def __sub__(self: NumericScalar, other: NumericColumn) -> NumericColumn: ...
+    @overload
+    def __sub__(self, other: Number | NumericValue) -> NumericColumn: ...
+    def __sub__(self, other: Number | NumericValue) -> NumericValue:
         """Subtract `other` from `self`."""
         return _binop(ops.Subtract, self, other)
 
     sub = __sub__
 
-    def __rsub__(self, other: NumericValue) -> NumericValue:
+    @overload
+    def __rsub__(
+        self: NumericScalar, other: Number | NumericScalar
+    ) -> NumericScalar: ...
+    @overload
+    def __rsub__(self: NumericScalar, other: NumericColumn) -> NumericColumn: ...
+    @overload
+    def __rsub__(self, other: Number | NumericValue) -> NumericColumn: ...
+    def __rsub__(self, other: Number | NumericValue) -> NumericValue:
         """Subtract `self` from `other`."""
         return _binop(ops.Subtract, other, self)
 
     rsub = __rsub__
 
-    def __mul__(self, other: NumericValue) -> NumericValue:
+    @overload
+    def __mul__(
+        self: NumericScalar, other: Number | NumericScalar
+    ) -> NumericScalar: ...
+    @overload
+    def __mul__(self: NumericScalar, other: NumericColumn) -> NumericColumn: ...
+    @overload
+    def __mul__(self, other: Number | NumericValue) -> NumericColumn: ...
+    def __mul__(self, other: Number | NumericValue) -> NumericValue:
         """Multiply `self` and `other`."""
         return _binop(ops.Multiply, self, other)
 
     mul = rmul = __rmul__ = __mul__
 
-    def __truediv__(self, other):
+    @overload
+    def __truediv__(
+        self: NumericScalar, other: Number | NumericScalar
+    ) -> FloatingScalar: ...
+    @overload
+    def __truediv__(self: NumericScalar, other: NumericColumn) -> FloatingColumn: ...
+    @overload
+    def __truediv__(self, other: Number | NumericValue) -> FloatingColumn: ...
+    def __truediv__(self, other: Number | NumericValue) -> FloatingValue:
         """Divide `self` by `other`."""
         return _binop(ops.Divide, self, other)
 
     div = __div__ = __truediv__
 
-    def __rtruediv__(self, other: NumericValue) -> NumericValue:
+    @overload
+    def __rtruediv__(
+        self: NumericScalar, other: Number | NumericScalar
+    ) -> FloatingScalar: ...
+    @overload
+    def __rtruediv__(self: NumericScalar, other: NumericColumn) -> FloatingColumn: ...
+    @overload
+    def __rtruediv__(self, other: Number | NumericValue) -> FloatingColumn: ...
+    def __rtruediv__(self, other: Number | NumericValue) -> NumericValue:
         """Divide `other` by `self`."""
         return _binop(ops.Divide, other, self)
 
     rdiv = __rdiv__ = __rtruediv__
 
+    @overload
     def __floordiv__(
-        self,
-        other: NumericValue,
-    ) -> NumericValue:
+        self: NumericScalar, other: Number | NumericScalar
+    ) -> IntegerScalar: ...
+    @overload
+    def __floordiv__(self: NumericScalar, other: NumericColumn) -> IntegerColumn: ...
+    @overload
+    def __floordiv__(self, other: Number | NumericValue) -> IntegerColumn: ...
+    def __floordiv__(self, other: Number | NumericValue) -> IntegerValue:
         """Floor divide `self` by `other`."""
         return _binop(ops.FloorDivide, self, other)
 
     floordiv = __floordiv__
 
+    @overload
+    def __rfloordiv__(
+        self: NumericScalar, other: Number | NumericScalar
+    ) -> IntegerScalar: ...
+    @overload
+    def __rfloordiv__(self: NumericScalar, other: NumericColumn) -> IntegerColumn: ...
+    @overload
+    def __rfloordiv__(self, other: Number | NumericValue) -> IntegerColumn: ...
     def __rfloordiv__(
         self,
         other: NumericValue,
@@ -714,7 +888,17 @@ def __rmod__(self, other: NumericValue) -> NumericValue:
 
     rmod = __rmod__
 
-    def point(self, right: int | float | NumericValue, /) -> ir.PointValue:
+    @overload
+    def point(
+        self: NumericScalar, right: Number | NumericScalar, /
+    ) -> ir.PointScalar: ...
+    @overload
+    def point(self: NumericScalar, right: NumericColumn, /) -> ir.PointColumn: ...
+    @overload
+    def point(
+        self: NumericColumn, right: Number | NumericValue, /
+    ) -> ir.PointColumn: ...
+    def point(self, right: Number | NumericValue, /) -> ir.PointValue:
         """Return a point constructed from the coordinate values.
 
         Constant coordinates result in construction of a `POINT` literal or
@@ -764,12 +948,26 @@ class NumericScalar(Scalar, NumericValue):
 
 @public
 class NumericColumn(Column, NumericValue):
+    @overload
+    def kurtosis(
+        self: DecimalColumn,
+        *,
+        where: ir.BooleanValue | None = None,
+        how: Literal["sample", "pop"] = "sample",
+    ) -> DecimalScalar: ...
+    @overload
+    def kurtosis(
+        self: NumericColumn,
+        *,
+        where: ir.BooleanValue | None = None,
+        how: Literal["sample", "pop"] = "sample",
+    ) -> FloatingScalar: ...
     def kurtosis(
         self,
         *,
         where: ir.BooleanValue | None = None,
         how: Literal["sample", "pop"] = "sample",
-    ) -> NumericScalar:
+    ) -> FloatingScalar | DecimalScalar:
         """Return the kurtosis of a numeric column.
 
         Parameters
@@ -813,12 +1011,26 @@ def kurtosis(
             self, how=how, where=self._bind_to_parent_table(where)
         ).to_expr()
 
+    @overload
+    def std(
+        self: DecimalColumn,
+        *,
+        where: ir.BooleanValue | None = None,
+        how: Literal["sample", "pop"] = "sample",
+    ) -> DecimalScalar: ...
+    @overload
+    def std(
+        self: NumericColumn,
+        *,
+        where: ir.BooleanValue | None = None,
+        how: Literal["sample", "pop"] = "sample",
+    ) -> FloatingScalar: ...
     def std(
         self,
         *,
         where: ir.BooleanValue | None = None,
         how: Literal["sample", "pop"] = "sample",
-    ) -> NumericScalar:
+    ) -> FloatingScalar | DecimalScalar:
         """Return the standard deviation of a numeric column.
 
         Parameters
@@ -864,12 +1076,26 @@ def std(
             self, how=how, where=self._bind_to_parent_table(where)
         ).to_expr()
 
+    @overload
+    def var(
+        self: DecimalColumn,
+        *,
+        where: ir.BooleanValue | None = None,
+        how: Literal["sample", "pop"] = "sample",
+    ) -> DecimalScalar: ...
+    @overload
+    def var(
+        self: NumericColumn,
+        *,
+        where: ir.BooleanValue | None = None,
+        how: Literal["sample", "pop"] = "sample",
+    ) -> FloatingScalar: ...
     def var(
         self,
         *,
         where: ir.BooleanValue | None = None,
         how: Literal["sample", "pop"] = "sample",
-    ) -> NumericScalar:
+    ) -> FloatingScalar | DecimalScalar:
         """Return the variance of a numeric column.
 
         Parameters
@@ -922,7 +1148,7 @@ def corr(
         *,
         where: ir.BooleanValue | None = None,
         how: Literal["sample", "pop"] = "sample",
-    ) -> NumericScalar:
+    ) -> FloatingScalar:
         """Return the correlation of two numeric columns.
 
         Parameters
@@ -981,7 +1207,7 @@ def cov(
         *,
         where: ir.BooleanValue | None = None,
         how: Literal["sample", "pop"] = "sample",
-    ) -> NumericScalar:
+    ) -> FloatingScalar:
         """Return the covariance of two numeric columns.
 
         Parameters
@@ -1037,7 +1263,7 @@ def cov(
             where=self._bind_to_parent_table(where),
         ).to_expr()
 
-    def mean(self, *, where: ir.BooleanValue | None = None) -> NumericScalar:
+    def mean(self, *, where: ir.BooleanValue | None = None) -> FloatingScalar:
         """Return the mean of a numeric column.
 
         Parameters
@@ -1093,7 +1319,7 @@ def mean(self, *, where: ir.BooleanValue | None = None) -> NumericScalar:
         # of default name generated by ops.Value operations
         return ops.Mean(self, where=self._bind_to_parent_table(where)).to_expr()
 
-    def cummean(self, *, where=None, group_by=None, order_by=None) -> NumericColumn:
+    def cummean(self, *, where=None, group_by=None, order_by=None) -> FloatingColumn:
         """Return the cumulative mean of the input.
 
         Examples
@@ -1322,7 +1548,7 @@ def histogram(
         binwidth: float | None = None,
         base: float | None = None,
         eps: float = 1e-13,
-    ):
+    ) -> IntegerColumn:
         """Compute a histogram with fixed width bins.
 
         Parameters
@@ -1467,6 +1693,14 @@ def approx_quantile(
 
 @public
 class IntegerValue(NumericValue):
+    @overload
+    def as_timestamp(
+        self: IntegerScalar, unit: Literal["s", "ms", "us"], /
+    ) -> ir.TimestampScalar: ...
+    @overload
+    def as_timestamp(
+        self: IntegerColumn, unit: Literal["s", "ms", "us"], /
+    ) -> ir.TimestampColumn: ...
     def as_timestamp(self, unit: Literal["s", "ms", "us"], /) -> ir.TimestampValue:
         """Convert an integral UNIX timestamp to a timestamp expression.
 
@@ -1498,6 +1732,18 @@ def as_timestamp(self, unit: Literal["s", "ms", "us"], /) -> ir.TimestampValue:
         """
         return ops.TimestampFromUNIX(self, unit).to_expr()
 
+    @overload
+    def as_interval(
+        self: IntegerScalar,
+        unit: Literal["Y", "M", "W", "D", "h", "m", "s", "ms", "us", "ns"] = "s",
+        /,
+    ) -> ir.IntervalScalar: ...
+    @overload
+    def as_interval(
+        self: IntegerColumn,
+        unit: Literal["Y", "M", "W", "D", "h", "m", "s", "ms", "us", "ns"] = "s",
+        /,
+    ) -> ir.IntervalColumn: ...
     def as_interval(
         self,
         unit: Literal["Y", "M", "W", "D", "h", "m", "s", "ms", "us", "ns"] = "s",
@@ -1554,11 +1800,36 @@ def as_interval(
         """
         return ops.IntervalFromInteger(self, unit).to_expr()
 
+    @overload
+    def convert_base(
+        self: IntegerScalar,
+        from_base: int | IntegerScalar,
+        to_base: int | IntegerScalar,
+    ) -> ir.StringScalar: ...
+
+    @overload
+    def convert_base(
+        self: IntegerScalar,
+        from_base: IntegerColumn,
+        to_base: int | IntegerScalar,
+    ) -> ir.StringColumn: ...
+    @overload
+    def convert_base(
+        self: IntegerScalar,
+        from_base: int | IntegerScalar,
+        to_base: IntegerColumn,
+    ) -> ir.StringColumn: ...
+    @overload
+    def convert_base(
+        self: IntegerColumn,
+        from_base: int | IntegerValue,
+        to_base: int | IntegerValue,
+    ) -> ir.StringColumn: ...
     def convert_base(
         self,
-        from_base: IntegerValue,
-        to_base: IntegerValue,
-    ) -> IntegerValue:
+        from_base: int | IntegerValue,
+        to_base: int | IntegerValue,
+    ) -> ir.StringColumn:
         """Convert an integer from one base to another.
 
         Parameters
@@ -1570,7 +1841,7 @@ def convert_base(
 
         Returns
         -------
-        IntegerValue
+        StringValue
             Converted expression
         """
         return ops.BaseConvert(self, from_base, to_base).to_expr()
@@ -1609,7 +1880,7 @@ def __rrshift__(self, other: IntegerValue) -> IntegerValue:
         """Bitwise right shift `self` with `other`."""
         return _binop(ops.BitwiseRightShift, other, self)
 
-    def __invert__(self) -> IntegerValue:
+    def __invert__(self) -> Self:
         """Bitwise not of `self`.
 
         Returns
@@ -1692,6 +1963,10 @@ def bit_xor(self, *, where: ir.BooleanValue | None = None) -> IntegerScalar:
 
 @public
 class FloatingValue(NumericValue):
+    @overload
+    def isnan(self: FloatingScalar) -> ir.BooleanScalar: ...
+    @overload
+    def isnan(self: FloatingColumn) -> ir.BooleanColumn: ...
     def isnan(self) -> ir.BooleanValue:
         """Return whether the value is NaN. Does NOT detect `NULL` and `inf` values.
 
@@ -1725,6 +2000,10 @@ def isnan(self) -> ir.BooleanValue:
         """
         return ops.IsNan(self).to_expr()
 
+    @overload
+    def isinf(self: FloatingScalar) -> ir.BooleanScalar: ...
+    @overload
+    def isinf(self: FloatingColumn) -> ir.BooleanColumn: ...
     def isinf(self) -> ir.BooleanValue:
         """Return whether the value is +/-inf. Does NOT detect `NULL` and `inf` values.
 
diff --git a/ibis/expr/types/strings.py b/ibis/expr/types/strings.py
index 3ad482b5c1ee..1f3d2e33a9e7 100644
--- a/ibis/expr/types/strings.py
+++ b/ibis/expr/types/strings.py
@@ -2,7 +2,7 @@
 
 import functools
 import operator
-from typing import TYPE_CHECKING, Any, Literal
+from typing import TYPE_CHECKING, Any, Literal, overload
 
 from public import public
 
@@ -13,12 +13,20 @@
 if TYPE_CHECKING:
     from collections.abc import Iterable, Sequence
 
+    from typing_extensions import Self
+
     import ibis.expr.types as ir
 
 
 @public
 class StringValue(Value):
-    def __getitem__(self, key: slice | int | ir.IntegerScalar) -> StringValue:
+    @overload
+    def __getitem__(
+        self: ir.StringScalar, key: slice | int | ir.IntegerScalar
+    ) -> ir.StringScalar: ...
+    @overload
+    def __getitem__(self, key: slice | int | ir.IntegerValue) -> ir.StringColumn: ...
+    def __getitem__(self, key: slice | int | ir.IntegerValue) -> StringValue:
         """Index or slice a string expression.
 
         Parameters
@@ -109,6 +117,10 @@ def __getitem__(self, key: slice | int | ir.IntegerScalar) -> StringValue:
             return self.substr(key, 1)
         raise NotImplementedError(f"string __getitem__[{key.__class__.__name__}]")
 
+    @overload
+    def length(self: ir.StringScalar) -> ir.IntegerScalar: ...
+    @overload
+    def length(self: ir.StringColumn) -> ir.IntegerColumn: ...
     def length(self) -> ir.IntegerValue:
         """Compute the length of a string.
 
@@ -135,7 +147,7 @@ def length(self) -> ir.IntegerValue:
         """
         return ops.StringLength(self).to_expr()
 
-    def lower(self) -> StringValue:
+    def lower(self) -> Self:
         """Convert string to all lowercase.
 
         Returns
@@ -171,7 +183,7 @@ def lower(self) -> StringValue:
         """
         return ops.Lowercase(self).to_expr()
 
-    def upper(self) -> StringValue:
+    def upper(self) -> Self:
         """Convert string to all uppercase.
 
         Returns
@@ -207,7 +219,7 @@ def upper(self) -> StringValue:
         """
         return ops.Uppercase(self).to_expr()
 
-    def reverse(self) -> StringValue:
+    def reverse(self) -> Self:
         """Reverse the characters of a string.
 
         Returns
@@ -243,6 +255,10 @@ def reverse(self) -> StringValue:
         """
         return ops.Reverse(self).to_expr()
 
+    @overload
+    def ascii_str(self: ir.StringScalar) -> ir.IntegerScalar: ...
+    @overload
+    def ascii_str(self: ir.StringColumn) -> ir.IntegerColumn: ...
     def ascii_str(self) -> ir.IntegerValue:
         """Return the numeric ASCII code of the first character of a string.
 
@@ -269,7 +285,7 @@ def ascii_str(self) -> ir.IntegerValue:
         """
         return ops.StringAscii(self).to_expr()
 
-    def strip(self) -> StringValue:
+    def strip(self) -> Self:
         r"""Remove whitespace from left and right sides of a string.
 
         Returns
@@ -305,7 +321,7 @@ def strip(self) -> StringValue:
         """
         return ops.Strip(self).to_expr()
 
-    def lstrip(self) -> StringValue:
+    def lstrip(self) -> Self:
         r"""Remove whitespace from the left side of string.
 
         Returns
@@ -341,7 +357,7 @@ def lstrip(self) -> StringValue:
         """
         return ops.LStrip(self).to_expr()
 
-    def rstrip(self) -> StringValue:
+    def rstrip(self) -> Self:
         r"""Remove whitespace from the right side of string.
 
         Returns
@@ -377,7 +393,7 @@ def rstrip(self) -> StringValue:
         """
         return ops.RStrip(self).to_expr()
 
-    def capitalize(self) -> StringValue:
+    def capitalize(self) -> Self:
         """Uppercase the first letter, lowercase the rest.
 
         This API matches the semantics of the Python [](`str.capitalize`)
@@ -410,6 +426,14 @@ def capitalize(self) -> StringValue:
     def __contains__(self, *_: Any) -> bool:
         raise TypeError("Use string_expr.contains(arg)")
 
+    @overload
+    def contains(
+        self: StringScalar, substr: str | StringScalar
+    ) -> ir.BooleanScalar: ...
+    @overload
+    def contains(self: StringScalar, substr: StringColumn) -> ir.BooleanColumn: ...
+    @overload
+    def contains(self: StringColumn, substr: str | StringValue) -> ir.BooleanColumn: ...
     def contains(self, substr: str | StringValue, /) -> ir.BooleanValue:
         """Return whether the expression contains `substr`.
 
@@ -441,6 +465,18 @@ def contains(self, substr: str | StringValue, /) -> ir.BooleanValue:
         """
         return ops.StringContains(self, substr).to_expr()
 
+    @overload
+    def hashbytes(
+        self: StringScalar,
+        how: Literal["md5", "sha1", "sha256", "sha512"] = "sha256",
+        /,
+    ) -> ir.BinaryScalar: ...
+    @overload
+    def hashbytes(
+        self: StringColumn,
+        how: Literal["md5", "sha1", "sha256", "sha512"] = "sha256",
+        /,
+    ) -> ir.BinaryColumn: ...
     def hashbytes(
         self, how: Literal["md5", "sha1", "sha256", "sha512"] = "sha256", /
     ) -> ir.BinaryValue:
@@ -466,7 +502,7 @@ def hashbytes(
 
     def hexdigest(
         self, how: Literal["md5", "sha1", "sha256", "sha512"] = "sha256", /
-    ) -> ir.StringValue:
+    ) -> Self:
         """Return the hash digest of the input as a hex encoded string.
 
         Parameters
@@ -497,6 +533,18 @@ def hexdigest(
         """
         return ops.HexDigest(self, how.lower()).to_expr()
 
+    @overload
+    def substr(
+        self: StringScalar,
+        start: int | ir.IntegerScalar,
+        length: int | ir.IntegerScalar | None = None,
+    ) -> StringScalar: ...
+    @overload
+    def substr(
+        self,
+        start: int | ir.IntegerValue,
+        length: int | ir.IntegerValue | None = None,
+    ) -> StringColumn: ...
     def substr(
         self, start: int | ir.IntegerValue, length: int | ir.IntegerValue | None = None
     ) -> StringValue:
@@ -533,6 +581,12 @@ def substr(
         """
         return ops.Substring(self, start, length).to_expr()
 
+    @overload
+    def left(self: StringScalar, nchars: int | ir.IntegerScalar, /) -> StringScalar: ...
+    @overload
+    def left(self: StringScalar, nchars: ir.IntegerColumn, /) -> StringColumn: ...
+    @overload
+    def left(self: StringColumn, nchars: int | ir.IntegerValue, /) -> StringColumn: ...
     def left(self, nchars: int | ir.IntegerValue, /) -> StringValue:
         """Return the `nchars` left-most characters.
 
@@ -564,6 +618,14 @@ def left(self, nchars: int | ir.IntegerValue, /) -> StringValue:
         """
         return self.substr(0, length=nchars)
 
+    @overload
+    def right(
+        self: StringScalar, nchars: int | ir.IntegerScalar, /
+    ) -> StringScalar: ...
+    @overload
+    def right(self: StringScalar, nchars: ir.IntegerColumn, /) -> StringColumn: ...
+    @overload
+    def right(self: StringColumn, nchars: int | ir.IntegerValue, /) -> StringColumn: ...
     def right(self, nchars: int | ir.IntegerValue, /) -> StringValue:
         """Return up to `nchars` from the end of each string.
 
@@ -595,6 +657,12 @@ def right(self, nchars: int | ir.IntegerValue, /) -> StringValue:
         """
         return ops.StrRight(self, nchars).to_expr()
 
+    @overload
+    def repeat(self: StringScalar, n: int | ir.IntegerScalar, /) -> StringScalar: ...
+    @overload
+    def repeat(self: StringScalar, n: ir.IntegerColumn, /) -> StringColumn: ...
+    @overload
+    def repeat(self: StringColumn, n: int | ir.IntegerValue, /) -> StringColumn: ...
     def repeat(self, n: int | ir.IntegerValue, /) -> StringValue:
         """Repeat a string `n` times.
 
@@ -626,7 +694,17 @@ def repeat(self, n: int | ir.IntegerValue, /) -> StringValue:
         """
         return ops.Repeat(self, n).to_expr()
 
-    def translate(self, from_str: StringValue, to_str: StringValue) -> StringValue:
+    @overload
+    def translate(
+        self: StringScalar, from_str: str | StringScalar, to_str: str | StringScalar
+    ) -> StringScalar: ...
+    @overload
+    def translate(
+        self, from_str: str | StringValue, to_str: str | StringValue
+    ) -> StringColumn: ...
+    def translate(
+        self, from_str: str | StringValue, to_str: str | StringValue
+    ) -> StringValue:
         """Replace `from_str` characters in `self` characters in `to_str`.
 
         To avoid unexpected behavior, `from_str` should be shorter than
@@ -857,6 +935,12 @@ def join(
             cls = ops.StringJoin
         return cls(strings, sep=self).to_expr()
 
+    @overload
+    def startswith(
+        self: StringScalar, start: str | StringScalar, /
+    ) -> ir.BooleanScalar: ...
+    @overload
+    def startswith(self, start: str | StringValue, /) -> ir.BooleanColumn: ...
     def startswith(self, start: str | StringValue, /) -> ir.BooleanValue:
         """Determine whether `self` starts with `start`.
 
@@ -887,6 +971,12 @@ def startswith(self, start: str | StringValue, /) -> ir.BooleanValue:
         """
         return ops.StartsWith(self, start).to_expr()
 
+    @overload
+    def endswith(
+        self: StringScalar, end: str | StringScalar, /
+    ) -> ir.BooleanScalar: ...
+    @overload
+    def endswith(self, end: str | StringValue, /) -> ir.BooleanColumn: ...
     def endswith(self, end: str | StringValue, /) -> ir.BooleanValue:
         """Determine if `self` ends with `end`.
 
@@ -1259,6 +1349,10 @@ def replace(self, pattern: StringValue, replacement: StringValue) -> StringValue
         """
         return ops.StringReplace(self, pattern, replacement).to_expr()
 
+    @overload
+    def as_timestamp(self: StringScalar, format_str: str, /) -> ir.TimestampScalar: ...
+    @overload
+    def as_timestamp(self: StringColumn, format_str: str, /) -> ir.TimestampColumn: ...
     def as_timestamp(self, format_str: str, /) -> ir.TimestampValue:
         """Parse a string and return a timestamp.
 
@@ -1288,6 +1382,10 @@ def as_timestamp(self, format_str: str, /) -> ir.TimestampValue:
         """
         return ops.StringToTimestamp(self, format_str).to_expr()
 
+    @overload
+    def as_date(self: StringScalar, format_str: str, /) -> ir.DateScalar: ...
+    @overload
+    def as_date(self: StringColumn, format_str: str, /) -> ir.DateColumn: ...
     def as_date(self, format_str: str, /) -> ir.DateValue:
         """Parse a string and return a date.
 
@@ -1317,6 +1415,10 @@ def as_date(self, format_str: str, /) -> ir.DateValue:
         """
         return ops.StringToDate(self, format_str).to_expr()
 
+    @overload
+    def as_time(self: StringScalar, format_str: str, /) -> ir.TimeScalar: ...
+    @overload
+    def as_time(self: StringColumn, format_str: str, /) -> ir.TimeColumn: ...
     def as_time(self, format_str: str, /) -> ir.TimeValue:
         """Parse a string and return a time.
 
@@ -1346,7 +1448,7 @@ def as_time(self, format_str: str, /) -> ir.TimeValue:
         """
         return ops.StringToTime(self, format_str).to_expr()
 
-    def protocol(self):
+    def protocol(self) -> Self:
         """Parse a URL and extract protocol.
 
         Examples
@@ -1362,7 +1464,7 @@ def protocol(self):
         """
         return ops.ExtractProtocol(self).to_expr()
 
-    def authority(self):
+    def authority(self) -> Self:
         """Parse a URL and extract authority.
 
         Examples
@@ -1378,7 +1480,7 @@ def authority(self):
         """
         return ops.ExtractAuthority(self).to_expr()
 
-    def userinfo(self):
+    def userinfo(self) -> Self:
         """Parse a URL and extract user info.
 
         Examples
@@ -1394,7 +1496,7 @@ def userinfo(self):
         """
         return ops.ExtractUserInfo(self).to_expr()
 
-    def host(self):
+    def host(self) -> Self:
         """Parse a URL and extract host.
 
         Examples
@@ -1410,7 +1512,7 @@ def host(self):
         """
         return ops.ExtractHost(self).to_expr()
 
-    def file(self):
+    def file(self) -> Self:
         """Parse a URL and extract file.
 
         Examples
@@ -1428,7 +1530,7 @@ def file(self):
         """
         return ops.ExtractFile(self).to_expr()
 
-    def path(self):
+    def path(self) -> Self:
         """Parse a URL and extract path.
 
         Examples
@@ -1446,6 +1548,12 @@ def path(self):
         """
         return ops.ExtractPath(self).to_expr()
 
+    @overload
+    def query(self: StringScalar, key: str | StringScalar, /) -> StringScalar: ...
+    @overload
+    def query(self, key: None, /) -> Self: ...
+    @overload
+    def query(self, key: str | StringValue, /) -> StringColumn: ...
     def query(self, key: str | StringValue | None = None, /):
         """Parse a URL and returns query string or query string parameter.
 
@@ -1473,7 +1581,7 @@ def query(self, key: str | StringValue | None = None, /):
         """
         return ops.ExtractQuery(self, key).to_expr()
 
-    def fragment(self):
+    def fragment(self) -> Self:
         """Parse a URL and extract fragment identifier.
 
         Examples
@@ -1579,6 +1687,10 @@ def concat(
         """
         return ops.StringConcat((self, other, *args)).to_expr()
 
+    @overload
+    def __add__(self: StringScalar, other: str | StringScalar) -> StringScalar: ...
+    @overload
+    def __add__(self, other: str | StringValue) -> StringColumn: ...
     def __add__(self, other: str | StringValue) -> StringValue:
         """Concatenate strings.
 
@@ -1630,6 +1742,10 @@ def __add__(self, other: str | StringValue) -> StringValue:
         """
         return self.concat(other)
 
+    @overload
+    def __radd__(self: StringScalar, other: str | StringScalar) -> StringScalar: ...
+    @overload
+    def __radd__(self, other: str | StringValue) -> StringColumn: ...
     def __radd__(self, other: str | StringValue) -> StringValue:
         """Concatenate strings.
 
@@ -1690,12 +1806,22 @@ def convert_base(
         """
         return ops.BaseConvert(self, from_base, to_base).to_expr()
 
+    @overload
+    def __mul__(self: StringScalar, n: int | ir.IntegerScalar) -> StringScalar: ...
+    @overload
+    def __mul__(self, n: int | ir.IntegerValue) -> StringColumn: ...
     def __mul__(self, n: int | ir.IntegerValue) -> StringValue:
         return _binop(ops.Repeat, self, n)
 
     __rmul__ = __mul__
 
-    def levenshtein(self, other: StringValue, /) -> ir.IntegerValue:
+    @overload
+    def levenshtein(
+        self: StringScalar, other: str | StringScalar, /
+    ) -> ir.IntegerScalar: ...
+    @overload
+    def levenshtein(self, other: str | StringValue, /) -> ir.IntegerColumn: ...
+    def levenshtein(self, other: str | StringValue, /) -> ir.IntegerValue:
         """Return the Levenshtein distance between two strings.
 
         Parameters
@@ -1728,5 +1854,5 @@ class StringScalar(Scalar, StringValue):
 
 @public
 class StringColumn(Column, StringValue):
-    def __getitem__(self, key: slice | int | ir.IntegerScalar) -> StringColumn:
+    def __getitem__(self, key: slice | int | ir.IntegerValue) -> StringColumn:
         return StringValue.__getitem__(self, key)