diff --git a/Lib/fontParts/base/annotations.py b/Lib/fontParts/base/annotations.py
index 11908339..a02df1ee 100644
--- a/Lib/fontParts/base/annotations.py
+++ b/Lib/fontParts/base/annotations.py
@@ -54,8 +54,14 @@
 class Interpolatable(Protocol):
     """Represent a protocol for interpolatable types."""
 
-    def __add__(self, other: InterpolatableType) -> InterpolatableType: ...
+    def __add__(
+        self: InterpolatableType, other: InterpolatableType
+    ) -> InterpolatableType: ...
 
-    def __sub__(self, other: InterpolatableType) -> InterpolatableType: ...
+    def __sub__(
+        self: InterpolatableType, other: InterpolatableType
+    ) -> InterpolatableType: ...
 
-    def __mul__(self, other: TransformationType) -> InterpolatableType: ...
+    def __mul__(
+        self: InterpolatableType, other: TransformationType
+    ) -> InterpolatableType: ...
diff --git a/Lib/fontParts/base/bPoint.py b/Lib/fontParts/base/bPoint.py
index 0fa173e5..525a3448 100644
--- a/Lib/fontParts/base/bPoint.py
+++ b/Lib/fontParts/base/bPoint.py
@@ -1,5 +1,5 @@
 from __future__ import annotations
-from typing import TYPE_CHECKING, Any, List, Optional
+from typing import TYPE_CHECKING, Any, Callable, List, Optional, Union
 from fontTools.misc import transform
 
 from fontParts.base.base import (
@@ -59,7 +59,7 @@ def __eq__(self, other):
     # this class should not be used in hashable
     # collections since it is dynamically generated.
 
-    __hash__ = None
+    __hash__ = None  # type: ignore[assignment]
 
     # -------
     # Parents
@@ -126,7 +126,7 @@ def _get_base_nextSegment(self) -> Optional[BaseSegment]:
 
     # Contour
 
-    _contour: Optional[BaseContour] = None
+    _contour: Optional[Callable[[], BaseContour]] = None
 
     contour = dynamicProperty(
         "contour",
@@ -151,7 +151,9 @@ def _get_contour(self) -> Optional[BaseContour]:
             return None
         return self._contour()
 
-    def _set_contour(self, contour: Optional[BaseContour]) -> None:
+    def _set_contour(
+        self, contour: Optional[Union[BaseContour, Callable[[], BaseContour]]]
+    ) -> None:
         if self._contour is not None:
             raise AssertionError("contour for bPoint already set")
         if contour is not None:
diff --git a/Lib/fontParts/base/base.py b/Lib/fontParts/base/base.py
index a0b6da74..e355e166 100644
--- a/Lib/fontParts/base/base.py
+++ b/Lib/fontParts/base/base.py
@@ -1631,7 +1631,7 @@ def raiseNotImplementedError(self):
         pass
 
 
-def reference(obj: Callable[[], Any]) -> Callable[[], Any]:
+def reference(obj: Any) -> Callable[[], Any]:
     """
     This code returns a simple function that returns the given object.
     This is a backwards compatibility function that is under review (see issue #749).
diff --git a/Lib/fontParts/base/component.py b/Lib/fontParts/base/component.py
index 14f584bf..f8f1d6d3 100644
--- a/Lib/fontParts/base/component.py
+++ b/Lib/fontParts/base/component.py
@@ -1,5 +1,5 @@
 from __future__ import annotations
-from typing import TYPE_CHECKING, Any, List, Optional, Tuple
+from typing import TYPE_CHECKING, Any, Callable, List, Optional, Tuple, Union
 
 from fontTools.misc import transform
 from fontTools.pens.pointInsidePen import PointInsidePen
@@ -68,7 +68,7 @@ def _reprContents(self) -> List[str]:
 
     # Glyph
 
-    _glyph = None
+    _glyph: Optional[Callable[[], BaseGlyph]] = None
 
     glyph: dynamicProperty = dynamicProperty(
         "glyph",
@@ -93,7 +93,9 @@ def _get_glyph(self) -> Optional[BaseGlyph]:
             return None
         return self._glyph()
 
-    def _set_glyph(self, glyph: Optional[BaseGlyph]) -> None:
+    def _set_glyph(
+        self, glyph: Optional[Union[BaseGlyph, Callable[[], BaseGlyph]]]
+    ) -> None:
         if self._glyph is not None:
             raise AssertionError("glyph for component already set")
         if glyph is not None:
@@ -432,9 +434,10 @@ def _set_base_index(self, value: int) -> None:
         glyph = self.glyph
         if glyph is None:
             raise FontPartsError("The component does not belong to a glyph.")
-        value = normalizers.normalizeIndex(value)
-        if value is None:
+        index = normalizers.normalizeIndex(value)
+        if index is None:
             return
+        value = index
         componentCount = len(glyph.components)
         if value < 0:
             value = -(value % componentCount)
diff --git a/Lib/fontParts/base/contour.py b/Lib/fontParts/base/contour.py
index 041bea4a..1f11c503 100644
--- a/Lib/fontParts/base/contour.py
+++ b/Lib/fontParts/base/contour.py
@@ -3,6 +3,7 @@
     TYPE_CHECKING,
     cast,
     Any,
+    Callable,
     Iterator,
     List,
     Optional,
@@ -105,7 +106,7 @@ def copyData(self, source: BaseContourType) -> None:
 
     # Glyph
 
-    _glyph = None
+    _glyph: Optional[Callable[[], BaseGlyph]] = None
 
     glyph: dynamicProperty = dynamicProperty(
         "glyph",
@@ -130,7 +131,9 @@ def _get_glyph(self) -> Optional[BaseGlyph]:
             return None
         return self._glyph()
 
-    def _set_glyph(self, glyph: Optional[BaseGlyph]) -> None:
+    def _set_glyph(
+        self, glyph: Optional[Union[BaseGlyph, Callable[[], BaseGlyph]]]
+    ) -> None:
         if self._glyph is not None:
             raise AssertionError("glyph for contour already set")
         if glyph is not None:
diff --git a/Lib/fontParts/base/groups.py b/Lib/fontParts/base/groups.py
index d35e7590..1ad554ff 100644
--- a/Lib/fontParts/base/groups.py
+++ b/Lib/fontParts/base/groups.py
@@ -7,6 +7,7 @@
     List,
     Optional,
     Tuple,
+    Union,
 )
 from collections.abc import MutableMapping
 
@@ -63,7 +64,7 @@ def _reprContents(self) -> List[str]:
 
     # Font
 
-    _font = None
+    _font: Optional[Callable[[], BaseFont]] = None
 
     font: dynamicProperty = dynamicProperty(
         "font",
@@ -89,7 +90,9 @@ def _get_font(self) -> Optional[BaseFont]:
             return None
         return self._font()
 
-    def _set_font(self, font: Optional[BaseFont]) -> None:
+    def _set_font(
+        self, font: Optional[Union[BaseFont, Callable[[], BaseFont]]]
+    ) -> None:
         if self._font is not None and self._font != font:
             raise AssertionError("font for groups already set and is not same as font")
         if font is not None:
diff --git a/Lib/fontParts/base/layer.py b/Lib/fontParts/base/layer.py
index 081e81eb..480bc146 100644
--- a/Lib/fontParts/base/layer.py
+++ b/Lib/fontParts/base/layer.py
@@ -9,6 +9,7 @@
     List,
     Optional,
     Tuple,
+    Union,
 )
 import collections
 
@@ -673,7 +674,7 @@ def copyData(self, source: BaseLayer) -> None:
 
     # Font
 
-    _font = None
+    _font: Optional[Callable[[], BaseFont]] = None
 
     font: dynamicProperty = dynamicProperty(
         "font",
@@ -698,7 +699,9 @@ def _get_font(self) -> Optional[BaseFont]:
             return None
         return self._font()
 
-    def _set_font(self, font: Optional[BaseFont]) -> None:
+    def _set_font(
+        self, font: Optional[Union[BaseFont, Callable[[], BaseFont]]]
+    ) -> None:
         if self._font is not None:
             raise AssertionError("font for layer already set")
         if font is not None:
diff --git a/Lib/fontParts/base/lib.py b/Lib/fontParts/base/lib.py
index 9f4efbb7..7f27652d 100644
--- a/Lib/fontParts/base/lib.py
+++ b/Lib/fontParts/base/lib.py
@@ -6,6 +6,7 @@
     Iterator,
     List,
     Optional,
+    Union,
 )
 from collections.abc import MutableMapping
 
@@ -64,7 +65,7 @@ def _reprContents(self) -> List[str]:
 
     # Glyph
 
-    _glyph: Optional[BaseGlyph] = None
+    _glyph: Optional[Callable[[], BaseGlyph]] = None
 
     glyph: dynamicProperty = dynamicProperty(
         "glyph",
@@ -91,7 +92,9 @@ def _get_glyph(self) -> Optional[BaseGlyph]:
             return None
         return self._glyph()
 
-    def _set_glyph(self, glyph: Optional[BaseGlyph]) -> None:
+    def _set_glyph(
+        self, glyph: Optional[Union[BaseGlyph, Callable[[], BaseGlyph]]]
+    ) -> None:
         if self._font is not None:
             raise AssertionError("font for lib already set")
         if self._glyph is not None and self._glyph() != glyph:
@@ -102,7 +105,7 @@ def _set_glyph(self, glyph: Optional[BaseGlyph]) -> None:
 
     # Font
 
-    _font: Optional[BaseFont] = None
+    _font: Optional[Callable[[], BaseFont]] = None
 
     font: dynamicProperty = dynamicProperty(
         "font",
@@ -131,7 +134,9 @@ def _get_font(self) -> Optional[BaseFont]:
             return self.glyph.font
         return None
 
-    def _set_font(self, font: Optional[BaseFont]) -> None:
+    def _set_font(
+        self, font: Optional[Union[BaseFont, Callable[[], BaseFont]]]
+    ) -> None:
         if self._font is not None and self._font() != font:
             raise AssertionError("font for lib already set and is not same as font")
         if self._glyph is not None:
diff --git a/Lib/fontParts/base/point.py b/Lib/fontParts/base/point.py
index b32a2558..e6e35699 100644
--- a/Lib/fontParts/base/point.py
+++ b/Lib/fontParts/base/point.py
@@ -1,5 +1,5 @@
 from __future__ import annotations
-from typing import TYPE_CHECKING, Any, Optional, Union, Tuple
+from typing import TYPE_CHECKING, Any, Callable, Optional, Union, Tuple
 
 from fontTools.misc import transform
 from fontParts.base.base import (
@@ -66,7 +66,7 @@ def _reprContents(self) -> list[str]:
 
     # Contour
 
-    _contour: Optional[BaseContour] = None
+    _contour: Optional[Callable[[], BaseContour]] = None
 
     contour: dynamicProperty = dynamicProperty(
         "contour",
@@ -91,7 +91,9 @@ def _get_contour(self) -> Optional[BaseContour]:
             return None
         return self._contour()
 
-    def _set_contour(self, contour: Optional[BaseContour]) -> None:
+    def _set_contour(
+        self, contour: Optional[Union[BaseContour, Callable[[], BaseContour]]]
+    ) -> None:
         if self._contour is not None:
             raise AssertionError("contour for point already set")
         if contour is not None:
diff --git a/Lib/fontParts/base/segment.py b/Lib/fontParts/base/segment.py
index 5737c581..3cdbaaa7 100644
--- a/Lib/fontParts/base/segment.py
+++ b/Lib/fontParts/base/segment.py
@@ -1,5 +1,5 @@
 from __future__ import annotations
-from typing import TYPE_CHECKING, Any, Generator, List, Optional, Tuple
+from typing import TYPE_CHECKING, Any, Callable, Generator, List, Optional, Tuple, Union
 
 from fontParts.base.errors import FontPartsError
 from fontParts.base.base import (
@@ -61,7 +61,7 @@ def _reprContents(self) -> List[str]:
 
     # Contour
 
-    _contour: Optional[BaseContour] = None
+    _contour: Optional[Callable[[], BaseContour]] = None
 
     contour: dynamicProperty = dynamicProperty(
         "contour",
@@ -86,7 +86,9 @@ def _get_contour(self) -> Optional[BaseContour]:
             return None
         return self._contour()
 
-    def _set_contour(self, contour: Optional[BaseContour]) -> None:
+    def _set_contour(
+        self, contour: Optional[Union[BaseContour, Callable[[], BaseContour]]]
+    ) -> None:
         if self._contour is not None:
             raise AssertionError("contour for segment already set")
         if contour is not None: