Implement extensible deepcopy in numba

pytensor/link/numba/dispatch/compile_ops.py

+from copy import deepcopy
 from hashlib import sha256
 
+import numba
 import numpy as np
 
 from pytensor.compile.builders import OpFromGraph
@@ -15,7 +17,34 @@ from pytensor.link.numba.dispatch.basic import (
     register_funcify_default_op_cache_key,
 )
 from pytensor.raise_op import CheckAndRaise
-from pytensor.tensor.type import TensorType
+
+
+def numba_deepcopy(x):
+    return deepcopy(x)
+
+
+@numba.extending.overload(numba_deepcopy)
+def numba_deepcopy_tensor(x):
+    if isinstance(x, numba.types.Number):
+
+        def number_deepcopy(x):
+            return x
+
+        return number_deepcopy
+
+    if isinstance(x, numba.types.Array):
+
+        def array_deepcopy(x):
+            return np.copy(x)
+
+        return array_deepcopy
+
+    if isinstance(x, numba.types.UnicodeType):
+
+        def string_deepcopy(x):
+            return x
+
+        return string_deepcopy
 
 
 @register_funcify_and_cache_key(OpFromGraph)
@@ -64,19 +93,11 @@ def numba_funcify_type_casting(op, **kwargs):
 
 @register_funcify_default_op_cache_key(DeepCopyOp)
 def numba_funcify_DeepCopyOp(op, node, **kwargs):
-    if isinstance(node.inputs[0].type, TensorType):
-
     @numba_basic.numba_njit
     def deepcopy(x):
-            return np.copy(x)
-
-    else:
-
-        @numba_basic.numba_njit
-        def deepcopy(x):
-            return x
+        return numba_deepcopy(x)
 
-    return deepcopy
+    return deepcopy, 1
 
 
 @register_funcify_default_op_cache_key(IfElse)

pytensor/link/numba/dispatch/random.py

 from collections.abc import Callable
-from copy import copy, deepcopy
+from copy import deepcopy
 from functools import singledispatch
 from hashlib import sha256
 from textwrap import dedent
@@ -20,6 +20,7 @@ from pytensor.link.numba.dispatch.basic import (
     numba_funcify,
     register_funcify_and_cache_key,
 )
+from pytensor.link.numba.dispatch.compile_ops import numba_deepcopy
 from pytensor.link.numba.dispatch.vectorize_codegen import (
     _jit_options,
     _vectorized,
@@ -35,16 +36,16 @@ from pytensor.tensor.type_other import NoneTypeT
 from pytensor.tensor.utils import _parse_gufunc_signature
 
 
-@overload(copy)
-def copy_NumPyRandomGenerator(rng):
-    def impl(rng):
-        # TODO: Open issue on Numba?
-        with numba.objmode(new_rng=types.npy_rng):
-            new_rng = deepcopy(rng)
+@numba.extending.overload(numba_deepcopy)
+def numba_deepcopy_random_generator(x):
+    if isinstance(x, numba.types.NumPyRandomGeneratorType):
 
+        def random_generator_deepcopy(x):
+            with numba.objmode(new_rng=types.npy_rng):
+                new_rng = deepcopy(x)
             return new_rng
 
-    return impl
+        return random_generator_deepcopy
 
 
 @singledispatch
@@ -449,7 +450,7 @@ def numba_funcify_RandomVariable(op: RandomVariableWithCoreShape, node, **kwargs
     def ov_random(core_shape, rng, size, *dist_params):
         def impl(core_shape, rng, size, *dist_params):
             if not inplace:
-                rng = copy(rng)
+                rng = numba_deepcopy(rng)
 
             draws = _vectorized(
                 core_op_fn,

pytensor/link/numba/dispatch/subtensor.py

@@ -18,6 +18,7 @@ from pytensor.link.numba.dispatch.basic import (
     register_funcify_and_cache_key,
     register_funcify_default_op_cache_key,
 )
+from pytensor.link.numba.dispatch.compile_ops import numba_deepcopy
 from pytensor.tensor import TensorType
 from pytensor.tensor.rewriting.subtensor import is_full_slice
 from pytensor.tensor.subtensor import (
@@ -104,6 +105,18 @@ def enable_slice_boxing():
 enable_slice_boxing()
 
 
+@numba.extending.overload(numba_deepcopy)
+def numba_deepcopy_slice(x):
+    if isinstance(x, types.SliceType):
+
+        def deepcopy_slice(x):
+            return slice(
+                numba_deepcopy(x.start), numba_deepcopy(x.stop), numba_deepcopy(x.step)
+            )
+
+        return deepcopy_slice
+
+
 @register_funcify_default_op_cache_key(MakeSlice)
 def numba_funcify_MakeSlice(op, **kwargs):
     @numba_basic.numba_njit