prompt: We are currently solving the following issue within our repository. Here is the issue text:
  --- BEGIN ISSUE ---
  behaviors with decorated mixin methods cannot be pickled
  ### Version of Awkward Array
  
  main
  
  ### Description and code to reproduce
  
  The mixin machinery introduces a closure, which `pickle` can't serialise.
  
  --- END ISSUE ---
  
  Below are some code segments, each from a relevant file. One or more of these files may contain bugs.
  --- BEGIN FILES ---
  Path: `src/awkward/behaviors/mixins.py`
  Content:
  ```
  1 # BSD 3-Clause License; see https://github.com/scikit-hep/awkward-1.0/blob/main/LICENSE
  2 
  3 
  4 import sys
  5 
  6 import awkward as ak
  7 
  8 
  9 def mixin_class(registry, name=None):
  10     """
  11     Args:
  12         registry (dict): The destination behavior mapping registry. Typically,
  13             this would be the global registry #ak.behavior, but one may wish
  14             to register methods in an alternative way.
  15         name (str): The name to assign to the behaviour class.
  16 
  17     This decorator can be used to register a behavior mixin class.
  18 
  19     Any inherited behaviors will automatically be made available to the decorated
  20     class.
  21 
  22     See the "Mixin decorators" section of #ak.behavior for further details.
  23     """
  24 
  25     def register(cls):
  26         cls_name = cls.__name__
  27         if name is None:
  28             behavior_name = cls_name
  29         else:
  30             behavior_name = name
  31 
  32         record = type(
  33             cls_name + "Record",
  34             (cls, ak.highlevel.Record),
  35             {"__module__": cls.__module__},
  36         )
  37         setattr(sys.modules[cls.__module__], cls_name + "Record", record)
  38         registry[behavior_name] = record
  39         array = type(
  40             cls_name + "Array",
  41             (cls, ak.highlevel.Array),
  42             {"__module__": cls.__module__},
  43         )
  44         setattr(sys.modules[cls.__module__], cls_name + "Array", array)
  45         registry["*", behavior_name] = array
  46         for basecls in cls.mro():
  47             for method in basecls.__dict__.values():
  48                 if hasattr(method, "_awkward_mixin"):
  49                     ufunc, rhs, transpose = method._awkward_mixin
  50                     if rhs is None:
  51                         registry.setdefault((ufunc, behavior_name), method)
  52                         continue
  53                     for rhs_name in list(rhs) + [behavior_name]:
  54                         registry.setdefault((ufunc, behavior_name, rhs_name), method)
  55                         if transpose is not None and rhs_name != behavior_name:
  56                             registry.setdefault(
  57                                 (ufunc, rhs_name, behavior_name), transpose
  58                             )
  59                     if basecls.__name__ in rhs:
  60                         rhs.add(behavior_name)
  61         return cls
  62 
  63     return register
  64 
  65 
  66 def mixin_class_method(ufunc, rhs=None, *, transpose=True):
  67     """
  68     Args:
  69         ufunc (numpy.ufunc): A universal function (or NEP18 callable) that is
  70             hooked in Awkward Array, i.e. it can be the first argument of a behavior.
  71         rhs (Set[type] or None): Set of right-hand side argument types, optional
  72             if wrapping a unary function. The left-hand side is expected to
  73             always be `self` of the parent class.
  74         transpose (bool): If true, automatically create a transpose signature
  75             (only makes sense for binary ufuncs).
  76 
  77     This decorator can be used to register a mixin class method.
  78 
  79     Using this decorator ensures that derived classes that are declared with the
  80     #ak.mixin_class decorator will also have the behaviors that this class has.
  81     """
  82 
  83     def register(method):
  84         if not isinstance(rhs, (set, type(None))):
  85             raise ak._errors.wrap_error(
  86                 ValueError("expected a set of right-hand-side argument types")
  87             )
  88         if transpose and rhs is not None:
  89 
  90             def transposed(left, right):
  91                 return method(right, left)
  92 
  93             # make a copy of rhs, we will edit it later
  94             method._awkward_mixin = (ufunc, set(rhs), transposed)
  95         else:
  96             method._awkward_mixin = (ufunc, rhs, None)
  97         return method
  98 
  99     return register
  100
  ```
  --- END FILES ---
  
  Please first localize the bug based on the issue statement, and then generate a patch according to the `git diff` format fenced by three backticks.
  
  Here is an example:
  
  ```diff
  diff --git a/examples/server_async.py b/examples/server_async.py
  --- a/examples/server_async.py
  +++ b/examples/server_async.py
  @@ -313,4 +313,4 @@
   
   
   if __name__ == "__main__":
  -    asyncio.run(run_async_server("."), debug=True)
  +    asyncio.run(run_async_server(), debug=True)
  diff --git a/examples/server_sync.py b/examples/server_sync.py
  --- a/examples/server_sync.py
  +++ b/examples/server_sync.py
  @@ -313,5 +313,5 @@
   
   
   if __name__ == "__main__":
  -    server = run_sync_server(".")
  +    server = run_sync_server()
       server.shutdown()
  
  ```
  
golden_diff: diff --git a/src/awkward/behaviors/mixins.py b/src/awkward/behaviors/mixins.py
  --- a/src/awkward/behaviors/mixins.py
  +++ b/src/awkward/behaviors/mixins.py
  @@ -1,6 +1,7 @@
   # BSD 3-Clause License; see https://github.com/scikit-hep/awkward-1.0/blob/main/LICENSE
   
   
  +import functools
   import sys
   
   import awkward as ak
  @@ -63,6 +64,10 @@
       return register
   
   
  +def _call_transposed(func, left, right):
  +    return func(right, left)
  +
  +
   def mixin_class_method(ufunc, rhs=None, *, transpose=True):
       """
       Args:
  @@ -70,7 +75,8 @@
               hooked in Awkward Array, i.e. it can be the first argument of a behavior.
           rhs (Set[type] or None): Set of right-hand side argument types, optional
               if wrapping a unary function. The left-hand side is expected to
  -            always be `self` of the parent class.
  +            always be `self` of the parent class. The current class is implicitly
  +            included in this set.
           transpose (bool): If true, automatically create a transpose signature
               (only makes sense for binary ufuncs).
   
  @@ -86,12 +92,13 @@
                   ValueError("expected a set of right-hand-side argument types")
               )
           if transpose and rhs is not None:
  -
  -            def transposed(left, right):
  -                return method(right, left)
  -
               # make a copy of rhs, we will edit it later
  -            method._awkward_mixin = (ufunc, set(rhs), transposed)
  +            # use partial & a module-scoped function so that this is pickleable
  +            method._awkward_mixin = (
  +                ufunc,
  +                set(rhs),
  +                functools.partial(_call_transposed, method),
  +            )
           else:
               method._awkward_mixin = (ufunc, rhs, None)
           return method
  
verification_info: {"golden_diff": "diff --git a/src/awkward/behaviors/mixins.py b/src/awkward/behaviors/mixins.py\n--- a/src/awkward/behaviors/mixins.py\n+++ b/src/awkward/behaviors/mixins.py\n@@ -1,6 +1,7 @@\n # BSD 3-Clause License; see https://github.com/scikit-hep/awkward-1.0/blob/main/LICENSE\n \n \n+import functools\n import sys\n \n import awkward as ak\n@@ -63,6 +64,10 @@\n     return register\n \n \n+def _call_transposed(func, left, right):\n+    return func(right, left)\n+\n+\n def mixin_class_method(ufunc, rhs=None, *, transpose=True):\n     \"\"\"\n     Args:\n@@ -70,7 +75,8 @@\n             hooked in Awkward Array, i.e. it can be the first argument of a behavior.\n         rhs (Set[type] or None): Set of right-hand side argument types, optional\n             if wrapping a unary function. The left-hand side is expected to\n-            always be `self` of the parent class.\n+            always be `self` of the parent class. The current class is implicitly\n+            included in this set.\n         transpose (bool): If true, automatically create a transpose signature\n             (only makes sense for binary ufuncs).\n \n@@ -86,12 +92,13 @@\n                 ValueError(\"expected a set of right-hand-side argument types\")\n             )\n         if transpose and rhs is not None:\n-\n-            def transposed(left, right):\n-                return method(right, left)\n-\n             # make a copy of rhs, we will edit it later\n-            method._awkward_mixin = (ufunc, set(rhs), transposed)\n+            # use partial & a module-scoped function so that this is pickleable\n+            method._awkward_mixin = (\n+                ufunc,\n+                set(rhs),\n+                functools.partial(_call_transposed, method),\n+            )\n         else:\n             method._awkward_mixin = (ufunc, rhs, None)\n         return method\n", "issue": "behaviors with decorated mixin methods cannot be pickled\n### Version of Awkward Array\n\nmain\n\n### Description and code to reproduce\n\nThe mixin machinery introduces a closure, which `pickle` can't serialise.\n", "before_files": [{"content": "# BSD 3-Clause License; see https://github.com/scikit-hep/awkward-1.0/blob/main/LICENSE\n\n\nimport sys\n\nimport awkward as ak\n\n\ndef mixin_class(registry, name=None):\n    \"\"\"\n    Args:\n        registry (dict): The destination behavior mapping registry. Typically,\n            this would be the global registry #ak.behavior, but one may wish\n            to register methods in an alternative way.\n        name (str): The name to assign to the behaviour class.\n\n    This decorator can be used to register a behavior mixin class.\n\n    Any inherited behaviors will automatically be made available to the decorated\n    class.\n\n    See the \"Mixin decorators\" section of #ak.behavior for further details.\n    \"\"\"\n\n    def register(cls):\n        cls_name = cls.__name__\n        if name is None:\n            behavior_name = cls_name\n        else:\n            behavior_name = name\n\n        record = type(\n            cls_name + \"Record\",\n            (cls, ak.highlevel.Record),\n            {\"__module__\": cls.__module__},\n        )\n        setattr(sys.modules[cls.__module__], cls_name + \"Record\", record)\n        registry[behavior_name] = record\n        array = type(\n            cls_name + \"Array\",\n            (cls, ak.highlevel.Array),\n            {\"__module__\": cls.__module__},\n        )\n        setattr(sys.modules[cls.__module__], cls_name + \"Array\", array)\n        registry[\"*\", behavior_name] = array\n        for basecls in cls.mro():\n            for method in basecls.__dict__.values():\n                if hasattr(method, \"_awkward_mixin\"):\n                    ufunc, rhs, transpose = method._awkward_mixin\n                    if rhs is None:\n                        registry.setdefault((ufunc, behavior_name), method)\n                        continue\n                    for rhs_name in list(rhs) + [behavior_name]:\n                        registry.setdefault((ufunc, behavior_name, rhs_name), method)\n                        if transpose is not None and rhs_name != behavior_name:\n                            registry.setdefault(\n                                (ufunc, rhs_name, behavior_name), transpose\n                            )\n                    if basecls.__name__ in rhs:\n                        rhs.add(behavior_name)\n        return cls\n\n    return register\n\n\ndef mixin_class_method(ufunc, rhs=None, *, transpose=True):\n    \"\"\"\n    Args:\n        ufunc (numpy.ufunc): A universal function (or NEP18 callable) that is\n            hooked in Awkward Array, i.e. it can be the first argument of a behavior.\n        rhs (Set[type] or None): Set of right-hand side argument types, optional\n            if wrapping a unary function. The left-hand side is expected to\n            always be `self` of the parent class.\n        transpose (bool): If true, automatically create a transpose signature\n            (only makes sense for binary ufuncs).\n\n    This decorator can be used to register a mixin class method.\n\n    Using this decorator ensures that derived classes that are declared with the\n    #ak.mixin_class decorator will also have the behaviors that this class has.\n    \"\"\"\n\n    def register(method):\n        if not isinstance(rhs, (set, type(None))):\n            raise ak._errors.wrap_error(\n                ValueError(\"expected a set of right-hand-side argument types\")\n            )\n        if transpose and rhs is not None:\n\n            def transposed(left, right):\n                return method(right, left)\n\n            # make a copy of rhs, we will edit it later\n            method._awkward_mixin = (ufunc, set(rhs), transposed)\n        else:\n            method._awkward_mixin = (ufunc, rhs, None)\n        return method\n\n    return register\n", "path": "src/awkward/behaviors/mixins.py"}], "after_files": [{"content": "# BSD 3-Clause License; see https://github.com/scikit-hep/awkward-1.0/blob/main/LICENSE\n\n\nimport functools\nimport sys\n\nimport awkward as ak\n\n\ndef mixin_class(registry, name=None):\n    \"\"\"\n    Args:\n        registry (dict): The destination behavior mapping registry. Typically,\n            this would be the global registry #ak.behavior, but one may wish\n            to register methods in an alternative way.\n        name (str): The name to assign to the behaviour class.\n\n    This decorator can be used to register a behavior mixin class.\n\n    Any inherited behaviors will automatically be made available to the decorated\n    class.\n\n    See the \"Mixin decorators\" section of #ak.behavior for further details.\n    \"\"\"\n\n    def register(cls):\n        cls_name = cls.__name__\n        if name is None:\n            behavior_name = cls_name\n        else:\n            behavior_name = name\n\n        record = type(\n            cls_name + \"Record\",\n            (cls, ak.highlevel.Record),\n            {\"__module__\": cls.__module__},\n        )\n        setattr(sys.modules[cls.__module__], cls_name + \"Record\", record)\n        registry[behavior_name] = record\n        array = type(\n            cls_name + \"Array\",\n            (cls, ak.highlevel.Array),\n            {\"__module__\": cls.__module__},\n        )\n        setattr(sys.modules[cls.__module__], cls_name + \"Array\", array)\n        registry[\"*\", behavior_name] = array\n        for basecls in cls.mro():\n            for method in basecls.__dict__.values():\n                if hasattr(method, \"_awkward_mixin\"):\n                    ufunc, rhs, transpose = method._awkward_mixin\n                    if rhs is None:\n                        registry.setdefault((ufunc, behavior_name), method)\n                        continue\n                    for rhs_name in list(rhs) + [behavior_name]:\n                        registry.setdefault((ufunc, behavior_name, rhs_name), method)\n                        if transpose is not None and rhs_name != behavior_name:\n                            registry.setdefault(\n                                (ufunc, rhs_name, behavior_name), transpose\n                            )\n                    if basecls.__name__ in rhs:\n                        rhs.add(behavior_name)\n        return cls\n\n    return register\n\n\ndef _call_transposed(func, left, right):\n    return func(right, left)\n\n\ndef mixin_class_method(ufunc, rhs=None, *, transpose=True):\n    \"\"\"\n    Args:\n        ufunc (numpy.ufunc): A universal function (or NEP18 callable) that is\n            hooked in Awkward Array, i.e. it can be the first argument of a behavior.\n        rhs (Set[type] or None): Set of right-hand side argument types, optional\n            if wrapping a unary function. The left-hand side is expected to\n            always be `self` of the parent class. The current class is implicitly\n            included in this set.\n        transpose (bool): If true, automatically create a transpose signature\n            (only makes sense for binary ufuncs).\n\n    This decorator can be used to register a mixin class method.\n\n    Using this decorator ensures that derived classes that are declared with the\n    #ak.mixin_class decorator will also have the behaviors that this class has.\n    \"\"\"\n\n    def register(method):\n        if not isinstance(rhs, (set, type(None))):\n            raise ak._errors.wrap_error(\n                ValueError(\"expected a set of right-hand-side argument types\")\n            )\n        if transpose and rhs is not None:\n            # make a copy of rhs, we will edit it later\n            # use partial & a module-scoped function so that this is pickleable\n            method._awkward_mixin = (\n                ufunc,\n                set(rhs),\n                functools.partial(_call_transposed, method),\n            )\n        else:\n            method._awkward_mixin = (ufunc, rhs, None)\n        return method\n\n    return register\n", "path": "src/awkward/behaviors/mixins.py"}]}