diff --git a/aiida/engine/processes/functions.py b/aiida/engine/processes/functions.py
index b1dbdef865..c91faf838e 100644
--- a/aiida/engine/processes/functions.py
+++ b/aiida/engine/processes/functions.py
@@ -49,6 +49,12 @@
     # This type is not available for Python 3.9 and older
     UnionType = None  # type: ignore[assignment,misc]  # pylint: disable=invalid-name
 
+try:
+    from typing import ParamSpec
+except ImportError:
+    # Fallback for Python 3.9 and older
+    from typing_extensions import ParamSpec  # type: ignore[assignment]
+
 try:
     get_annotations = inspect.get_annotations
 except AttributeError:
@@ -88,18 +94,18 @@ def get_stack_size(size: int = 2) -> int:  # type: ignore[return]
         return size - 1
 
 
-P = t.ParamSpec('P')
-R = t.TypeVar('R', covariant=True)
+P = ParamSpec('P')
+R_co = t.TypeVar('R_co', covariant=True)
 N = t.TypeVar('N', bound=ProcessNode)
 
 
-class ProcessFunctionType(t.Protocol, t.Generic[P, R, N]):
+class ProcessFunctionType(t.Protocol, t.Generic[P, R_co, N]):
     """Protocol for a decorated process function."""
 
-    def __call__(self, *args: P.args, **kwargs: P.kwargs) -> R:
+    def __call__(self, *args: P.args, **kwargs: P.kwargs) -> R_co:
         ...
 
-    def run(self, *args: P.args, **kwargs: P.kwargs) -> R:
+    def run(self, *args: P.args, **kwargs: P.kwargs) -> R_co:
         ...
 
     def run_get_pk(self, *args: P.args, **kwargs: P.kwargs) -> tuple[dict[str, t.Any] | None, int]:
@@ -119,7 +125,7 @@ def run_get_node(self, *args: P.args, **kwargs: P.kwargs) -> tuple[dict[str, t.A
     spec: t.Callable[[], ProcessSpec]
 
 
-def calcfunction(function: t.Callable[P, R]) -> ProcessFunctionType[P, R, CalcFunctionNode]:
+def calcfunction(function: t.Callable[P, R_co]) -> ProcessFunctionType[P, R_co, CalcFunctionNode]:
     """
     A decorator to turn a standard python function into a calcfunction.
     Example usage:
@@ -143,10 +149,10 @@ def calcfunction(function: t.Callable[P, R]) -> ProcessFunctionType[P, R, CalcFu
     :param function: The function to decorate.
     :return: The decorated function.
     """
-    return process_function(node_class=CalcFunctionNode)(function)
+    return process_function(node_class=CalcFunctionNode)(function)  # type: ignore[arg-type]
 
 
-def workfunction(function: t.Callable[P, R]) -> ProcessFunctionType[P, R, WorkFunctionNode]:
+def workfunction(function: t.Callable[P, R_co]) -> ProcessFunctionType[P, R_co, WorkFunctionNode]:
     """
     A decorator to turn a standard python function into a workfunction.
     Example usage:
@@ -170,7 +176,7 @@ def workfunction(function: t.Callable[P, R]) -> ProcessFunctionType[P, R, WorkFu
     :param function: The function to decorate.
     :return: The decorated function.
     """
-    return process_function(node_class=WorkFunctionNode)(function)
+    return process_function(node_class=WorkFunctionNode)(function)  # type: ignore[arg-type]
 
 
 def process_function(node_class: t.Type['ProcessNode']) -> t.Callable[[FunctionType], FunctionType]:
diff --git a/aiida/parsers/parser.py b/aiida/parsers/parser.py
index 92e988a778..943ff1ae5b 100644
--- a/aiida/parsers/parser.py
+++ b/aiida/parsers/parser.py
@@ -167,7 +167,7 @@ def parse_calcfunction(**kwargs):
         inputs = {'metadata': {'store_provenance': store_provenance}}
         inputs.update(parser.get_outputs_for_parsing())
 
-        return parse_calcfunction.run_get_node(**inputs)  # type: ignore[attr-defined]
+        return parse_calcfunction.run_get_node(**inputs)
 
     @abstractmethod
     def parse(self, **kwargs) -> Optional[ExitCode]:
diff --git a/docs/source/nitpick-exceptions b/docs/source/nitpick-exceptions
index d9286bc889..da1eebfa24 100644
--- a/docs/source/nitpick-exceptions
+++ b/docs/source/nitpick-exceptions
@@ -103,6 +103,15 @@ py:class aiida.storage.sqlite_zip.models.DbGroupNode
 py:class aiida.engine.processes.workchains.context.ToContext
 py:func aiida.orm.implementation.BackendQueryBuilder
 
+### Typing aliases
+py:obj aiida.engine.processes.functions.P
+py:obj aiida.engine.processes.functions.N
+py:obj aiida.engine.processes.functions.R_co
+py:class P
+py:class N
+py:class aiida.engine.processes.functions.N
+py:class aiida.engine.processes.functions.R_co
+
 ### third-party packages
 # Note: These exceptions are needed if
 # * the objects are referenced e.g. as param/return types types in method docstrings (without intersphinx mapping)
@@ -117,7 +126,7 @@ py:class click.types.Path
 py:class click.types.File
 py:class click.types.StringParamType
 py:func click.shell_completion._start_of_option
-py:meth  click.Option.get_default
+py:meth click.Option.get_default
 py:meth fail
 
 py:class requests.models.Response