Type function arguments

pytensor/compile/function/__init__.py

 import logging
 import re
 import traceback as tb
+from collections.abc import Iterable
 from pathlib import Path
 
+import pytensor.misc.pkl_utils
 from pytensor.compile.function.pfunc import pfunc
 from pytensor.compile.function.types import orig_function
+from pytensor.compile.mode import Mode
+from pytensor.compile.profiling import ProfileStats
+from pytensor.graph import Variable
 
 
 __all__ = ["types", "pfunc"]
@@ -15,18 +20,22 @@ _logger = logging.getLogger("pytensor.compile.function")
 
 def function_dump(
     filename: str | Path,
-    inputs,
-    outputs=None,
-    mode=None,
-    updates=None,
-    givens=None,
-    no_default_updates=False,
-    accept_inplace=False,
-    name=None,
-    rebuild_strict=True,
-    allow_input_downcast=None,
-    profile=None,
-    on_unused_input=None,
+    inputs: Iterable[Variable],
+    outputs: Variable | Iterable[Variable] | dict[str, Variable] | None = None,
+    mode: str | Mode | None = None,
+    updates: Iterable[tuple[Variable, Variable]]
+    | dict[Variable, Variable]
+    | None = None,
+    givens: Iterable[tuple[Variable, Variable]]
+    | dict[Variable, Variable]
+    | None = None,
+    no_default_updates: bool = False,
+    accept_inplace: bool = False,
+    name: str | None = None,
+    rebuild_strict: bool = True,
+    allow_input_downcast: bool | None = None,
+    profile: bool | ProfileStats | None = None,
+    on_unused_input: str | None = None,
     extra_tag_to_remove: str | None = None,
 ):
     """
@@ -60,24 +69,21 @@ def function_dump(
     `['annotations', 'replacement_of', 'aggregation_scheme', 'roles']`
 
     """
-    filename = Path(filename)
-    d = dict(
-        inputs=inputs,
-        outputs=outputs,
-        mode=mode,
-        updates=updates,
-        givens=givens,
-        no_default_updates=no_default_updates,
-        accept_inplace=accept_inplace,
-        name=name,
-        rebuild_strict=rebuild_strict,
-        allow_input_downcast=allow_input_downcast,
-        profile=profile,
-        on_unused_input=on_unused_input,
-    )
-    with filename.open("wb") as f:
-        import pytensor.misc.pkl_utils
-
+    d = {
+        "inputs": inputs,
+        "outputs": outputs,
+        "mode": mode,
+        "updates": updates,
+        "givens": givens,
+        "no_default_updates": no_default_updates,
+        "accept_inplace": accept_inplace,
+        "name": name,
+        "rebuild_strict": rebuild_strict,
+        "allow_input_downcast": allow_input_downcast,
+        "profile": profile,
+        "on_unused_input": on_unused_input,
+    }
+    with Path(filename).open("wb") as f:
         pickler = pytensor.misc.pkl_utils.StripPickler(
             f, protocol=-1, extra_tag_to_remove=extra_tag_to_remove
         )
@@ -85,18 +91,22 @@ def function_dump(
 
 
 def function(
-    inputs,
-    outputs=None,
-    mode=None,
-    updates=None,
-    givens=None,
-    no_default_updates=False,
-    accept_inplace=False,
-    name=None,
-    rebuild_strict=True,
-    allow_input_downcast=None,
-    profile=None,
-    on_unused_input=None,
+    inputs: Iterable[Variable],
+    outputs: Variable | Iterable[Variable] | dict[str, Variable] | None = None,
+    mode: str | Mode | None = None,
+    updates: Iterable[tuple[Variable, Variable]]
+    | dict[Variable, Variable]
+    | None = None,
+    givens: Iterable[tuple[Variable, Variable]]
+    | dict[Variable, Variable]
+    | None = None,
+    no_default_updates: bool = False,
+    accept_inplace: bool = False,
+    name: str | None = None,
+    rebuild_strict: bool = True,
+    allow_input_downcast: bool | None = None,
+    profile: bool | ProfileStats | None = None,
+    on_unused_input: str | None = None,
 ):
     """
     Return a :class:`callable object <pytensor.compile.function.types.Function>`