base_function

The class base_function becomes a new base class for all function types. It is based on the existing builtin_function_or_method class, but with the following differences and new features:

1. It acts as a descriptor implementing __get__ to turn a function into a method if m_self is NULL. If m_self is not NULL, then this is a no-op: the existing function is returned instead.
2. A new read-only attribute __parent__, represented in the C structure as m_parent. If this attribute exists, it represents the defining object. For methods of extension types, this is the defining class (__class__ in plain Python) and for functions of a module, this is the defining module. In general, it can be any Python object. If __parent__ is a class, it carries special semantics: in that case, the function must be called with self being an instance of that class. Finally, __qualname__ and __reduce__ will use __parent__ as namespace (instead of __self__ before).
3. A new attribute __objclass__ which equals __parent__ if __parent__ is a class. Otherwise, accessing __objclass__ raises AttributeError. This is meant to be backwards compatible with method_descriptor.
4. The field ml_doc and the attributes __doc__ and __text_signature__ (see Argument Clinic 6) are not supported.
5. A new flag METH_PASS_FUNCTION for ml_flags. If this flag is set, the C function stored in ml_meth is called with an additional first argument equal to the function object.
6. A new flag METH_BINDING for ml_flags which only applies to functions of a module (not methods of a class). If this flag is set, then m_self is set to NULL instead of the module. This allows the function to behave more like a Python function as it enables __get__.
7. A new flag METH_CALL_UNBOUND to disable self slicing.
8. A new flag METH_PYTHON for ml_flags. This flag indicates that this function should be treated as Python function. Ideally, use of this flag should be avoided because it goes against the duck typing philosophy. It is still needed in a few places though, for example profiling.

The goal of base_function is that it supports all different ways of calling functions and methods in just one structure. For example, the new flag METH_PASS_FUNCTION will be used by the implementation of methods.

It is not possible to directly create instances of base_function (tp_new is NULL). However, it is legal for C code to manually create instances.

These are the relevant C structures:

PyTypeObject PyBaseFunction_Type;

typedef struct {
    PyObject_HEAD
    PyCFunctionDef *m_ml;     /* Description of the C function to call */
    PyObject *m_self;         /* __self__: anything, can be NULL; readonly */
    PyObject *m_module;       /* __module__: anything (typically str) */
    PyObject *m_parent;       /* __parent__: anything, can be NULL; readonly */
    PyObject *m_weakreflist;  /* List of weak references */
} PyBaseFunctionObject;

typedef struct {
    const char *ml_name;   /* The name of the built-in function/method */
    PyCFunction ml_meth;   /* The C function that implements it */
    int ml_flags;          /* Combination of METH_xxx flags, which mostly
                              describe the args expected by the C func */
} PyCFunctionDef;

Subclasses may extend PyCFunctionDef with extra fields.

The Python attribute __self__ returns m_self, except if METH_STATIC is set. In that case or if m_self is NULL, then there is no __self__ attribute at all. For that reason, we write either m_self or __self__ in this PEP with slightly different meanings.

cfunction

This is the new version of the old builtin_function_or_method class. The name cfunction was chosen to avoid confusion with “built-in” in the sense of “something in the builtins module”. It also fits better with the C API which use the PyCFunction prefix.

The class cfunction is a copy of base_function, with the following differences:

1. m_ml points to a PyMethodDef structure, extending PyCFunctionDef with an additional ml_doc field to implement __doc__ and __text_signature__ as read-only attributes:

   typedef struct {
       const char *ml_name;
       PyCFunction ml_meth;
       int ml_flags;
       const char *ml_doc;
   } PyMethodDef;
   

   Note that PyMethodDef is part of the Python Stable ABI 5 and it is used by practically all extension modules, so we absolutely cannot change this structure.

2. Argument Clinic 6 is supported.
3. __self__ always exists. In the cases where base_function.__self__ would raise AttributeError, instead None is returned.

The type object is PyTypeObject PyCFunction_Type and we define PyCFunctionObject as alias of PyBaseFunctionObject (except for the type of m_ml).

defined_function

The class defined_function is an abstract base class meant to indicate that the function has introspection support. Instances of defined_function are required to support all attributes that Python functions have, namely __code__, __globals__, __doc__, __defaults__, __kwdefaults__, __closure__ and __annotations__. There is also a __dict__ to support attributes added by the user.

None of these is required to be meaningful. In particular, __code__ may not be a working code object, possibly only a few fields may be filled in. This PEP does not dictate how the various attributes are implemented. They may be simple struct members or more complicated descriptors. Only read-only support is required, none of the attributes is required to be writable.

The class defined_function is mainly meant for auto-generated C code, for example produced by Cython 1. There is no API to create instances of it.

The C structure is the following:

PyTypeObject PyDefinedFunction_Type;

typedef struct {
    PyBaseFunctionObject base;
    PyObject *func_dict;        /* __dict__: dict or NULL */
} PyDefinedFunctionObject;

TODO: maybe find a better name for defined_function. Other proposals: inspect_function (anything that satisfies inspect.isfunction), builtout_function (a function that is better built out; pun on builtin), generic_function (original proposal but conflicts with functools.singledispatch generic functions), user_function (defined by the user as opposed to CPython).

function

This is the class meant for functions implemented in Python. Unlike the other function types, instances of function can be created from Python code. This is not changed, so we do not describe the details in this PEP.

The layout of the C structure is the following:

PyTypeObject PyFunction_Type;

typedef struct {
    PyBaseFunctionObject base;
    PyObject *func_dict;        /* __dict__: dict or NULL */
    PyObject *func_code;        /* __code__: code */
    PyObject *func_globals;     /* __globals__: dict; readonly */
    PyObject *func_name;        /* __name__: string */
    PyObject *func_qualname;    /* __qualname__: string */
    PyObject *func_doc;         /* __doc__: can be anything or NULL */
    PyObject *func_defaults;    /* __defaults__: tuple or NULL */
    PyObject *func_kwdefaults;  /* __kwdefaults__: dict or NULL */
    PyObject *func_closure;     /* __closure__: tuple of cell objects or NULL; readonly */
    PyObject *func_annotations; /* __annotations__: dict or NULL */
    PyCFunctionDef _ml;         /* Storage for base.m_ml */
} PyFunctionObject;

The descriptor __name__ returns func_name. When setting __name__, also base.m_ml->ml_name is updated with the UTF-8 encoded name.

The _ml field reserves space to be used by base.m_ml.

A base_function instance must have the flag METH_PYTHON set if and only if it is an instance of function.

When constructing an instance of function from code and globals, an instance is created with base.m_ml = &_ml, base.m_self = NULL.

To make subclassing easier, we also add a copy constructor: if f is an instance of function, then types.FunctionType(f) copies f. This conveniently allows using a custom function type as decorator:

>>> from types import FunctionType
>>> class CustomFunction(FunctionType):
...     pass
>>> @CustomFunction
... def f(x):
...     return x
>>> type(f)
<class '__main__.CustomFunction'>

This also removes many use cases of functools.wraps: wrappers can be replaced by subclasses of function.

bound_method

The class bound_method is used for all bound methods, regardless of the class of the underlying function. It adds one new attribute on top of base_function: __func__ points to that function.

bound_method replaces the old method class which was used only for Python functions bound as method.

There is a complication because we want to allow constructing a method from an arbitrary callable. This may be an already-bound method or simply not an instance of base_function. Therefore, in practice there are two kinds of methods:

• For arbitrary callables, we use a single fixed PyCFunctionDef structure with the METH_PASS_FUNCTION flag set.
• For methods which bind instances of base_function (more precisely, which have the Py_TPFLAGS_BASEFUNCTION flag set) that have self slicing, we instead use the PyCFunctionDef from the original function. This way, we don’t lose any performance when calling bound methods. In this case, the __func__ attribute is only used to implement various attributes but not for calling the method.

When constructing a new method from a base_function, we check that the self object is an instance of __objclass__ (if a class was specified as parent) and raise a TypeError otherwise.

The C structure is:

PyTypeObject PyMethod_Type;

typedef struct {
    PyBaseFunctionObject base;
    PyObject *im_func;  /* __func__: function implementing the method; readonly */
} PyMethodObject;

Checking __objclass__

First of all, a type check is done if the __parent__ of the function is a class (recall that __objclass__ then becomes an alias of __parent__): if m_self is NULL (this is the case for unbound methods of extension types), then the function must be called with at least one positional argument and the first (typically called self) must be an instance of __objclass__. If not, a TypeError is raised.

Note that bound methods have m_self != NULL, so the __objclass__ is not checked. Instead, the __objclass__ check is done when constructing the method.

Flags

For convenience, we define a new constant: METH_CALLFLAGS combines all flags from PyCFunctionDef.ml_flags which specify the signature of the C function to be called. It is equal to

METH_VARARGS | METH_FASTCALL | METH_NOARGS | METH_O | METH_KEYWORDS | METH_PASS_FUNCTION

Exactly one of the first four flags above must be set and only METH_VARARGS and METH_FASTCALL may be combined with METH_KEYWORDS. Violating these rules is undefined behaviour.

There are one new flags which affects calling functions, namely METH_PASS_FUNCTION and METH_CALL_UNBOUND. Some flags are already documented in 7. We explain the others below.

Self slicing

If the function has m_self == NULL and the flag METH_CALL_UNBOUND is not set, then the first positional argument (if any) is removed from *args and instead passed as first argument to the C function. Effectively, the first positional argument is treated as __self__. This is meant to support unbound methods such that the C function does not see the difference between bound and unbound method calls. This does not affect keyword arguments in any way.

This process is called self slicing and a function is said to have self slicing if m_self == NULL and METH_CALL_UNBOUND is not set.

Note that a METH_NOARGS function which has self slicing effectively has one argument, namely self. Analogously, a METH_O function with self slicing has two arguments.

METH_PASS_FUNCTION

If this flag is set, then the C function is called with an additional first argument, namely the function itself (the base_function instance). As special case, if the function is a bound_method, then the underlying function of the method is passed (but not recursively: if a bound_method wraps a bound_method, then __func__ is only applied once).

For example, an ordinary METH_VARARGS function has signature (PyObject *self, PyObject *args). With METH_VARARGS | METH_PASS_FUNCTION, this becomes (PyObject *func, PyObject *self, PyObject *args).

METH_FASTCALL

This is an existing but undocumented flag. We suggest to officially support and document it.

If the flag METH_FASTCALL is set without METH_KEYWORDS, then the ml_meth field is of type PyCFunctionFast which takes the arguments (PyObject *self, PyObject *const *args, Py_ssize_t nargs). Such a function takes only positional arguments and they are passed as plain C array args of length nargs.

If the flags METH_FASTCALL | METH_KEYWORDS are set, then the ml_meth field is of type PyCFunctionFastKeywords which takes the arguments (PyObject *self, PyObject *const *args, Py_ssize_t nargs, PyObject *kwnames). The positional arguments are passed as C array args of length nargs. The values of the keyword arguments follow in that array, starting at position nargs. The keys (names) of the keyword arguments are passed as a tuple in kwnames. As an example, assume that 3 positional and 2 keyword arguments are given. Then args is an array of length 3 + 2 = 5, nargs equals 3 and kwnames is a 2-tuple.

Unbound methods of extension types

The type of unbound methods changes from method_descriptor to cfunction. The object which appears as unbound method is the same object which appears in the class __dict__. Python automatically sets the __parent__ attribute to the defining class.

Built-in functions of a module

For the case of functions of a module, __parent__ will be set to the module. Unless the flag METH_BINDING is given, also __self__ will be set to the module (for backwards compatibility).

An important consequence is that such functions by default do not become methods when used as attribute (base_function.__get__ only does that if m_self was NULL). One could consider this a bug, but this was done for backwards compatibility reasons: in an initial post on python-ideas 8 the consensus was to keep this misfeature of built-in functions.

However, to allow this anyway for specific or newly implemented built-in functions, the METH_BINDING flag prevents setting __self__.

New type flag

A new PyTypeObject flag (for tp_flags) is added: Py_TPFLAGS_BASEFUNCTION to indicate that instances of this type are functions which can be called and bound as method like a base_function.

This is different from flags like Py_TPFLAGS_LIST_SUBCLASS because it indicates more than just a subclass: it also indicates a default implementation of __call__ and __get__. In particular, such subclasses of base_function must follow the implementation from the section Calling base_function instances.

This flag is automatically set for extension types which inherit the tp_call and tp_descr_get implementation from base_function. Extension types can explicitly specify it if they override __call__ or __get__ in a compatible way. The flag Py_TPFLAGS_BASEFUNCTION must never be set for a heap type because that would not be safe (heap types can be changed dynamically).

C API functions

We list some relevant Python/C API macros and functions. Some of these are existing (possibly changed) functions, some are new:

• int PyBaseFunction_CheckFast(PyObject *op): return true if op is an instance of a class with the Py_TPFLAGS_BASEFUNCTION set. This is the function that you need to use to determine whether it is meaningful to access the base_function internals.
• int PyBaseFunction_Check(PyObject *op): return true if op is an instance of base_function.
• PyObject *PyBaseFunction_New(PyTypeObject *cls, PyCFunctionDef *ml, PyObject *self, PyObject *module, PyObject *parent): create a new instance of cls (which must be a subclass of base_function) from the given data.
• int PyCFunction_Check(PyObject *op): return true if op is an instance of cfunction.
• int PyCFunction_NewEx(PyMethodDef* ml, PyObject *self, PyObject* module): create a new instance of cfunction. As special case, if self is NULL, then set self = Py_None instead (for backwards compatibility). If self is a module, then __parent__ is set to self. Otherwise, __parent__ is NULL.
• For many existing PyCFunction_... and PyMethod_ functions, we define a new function PyBaseFunction_... acting on base_function instances. The old functions are kept as aliases of the new functions.
• int PyFunction_Check(PyObject *op): return true if op is an instance of base_function with the METH_PYTHON flag set (this is equivalent to checking whether op is an instance of function).
• int PyFunction_CheckFast(PyObject *op): equivalent to PyFunction_Check(op) && PyBaseFunction_CheckFast(op).
• int PyFunction_CheckExact(PyObject *op): return true if the type of op is function.
• PyObject *PyFunction_NewPython(PyTypeObject *cls, PyObject *code, PyObject *globals, PyObject *name, PyObject *qualname): create a new instance of cls (which must be a subclass of function) from the given data.
• PyObject *PyFunction_New(PyObject *code, PyObject *globals): create a new instance of function.
• PyObject *PyFunction_NewWithQualName(PyObject *code, PyObject *globals, PyObject *qualname): create a new instance of function.
• PyObject *PyFunction_Copy(PyTypeObject *cls, PyObject *func): create a new instance of cls (which must be a subclass of function) by copying a given function.

Changes to the types module

Two types are added: types.BaseFunctionType corresponding to base_function and types.DefinedFunctionType corresponding to defined_function.

Apart from that, no changes to the types module are made. In particular, types.FunctionType refers to function. However, the actual types will change: in particular, types.BuiltinFunctionType will no longer be the same as types.BuiltinMethodType.

Changes to the inspect module

The new function inspect.isbasefunction checks for an instance of base_function.

inspect.isfunction checks for an instance of defined_function.

inspect.isbuiltin checks for an instance of cfunction.

inspect.isroutine checks isbasefunction or ismethoddescriptor.

NOTE: bpo-33261 3 should be fixed first.

Profiling

Currently, sys.setprofile supports c_call, c_return and c_exception events for built-in functions. These events are generated when calling or returning from a built-in function. By contrast, the call and return events are generated by the function itself. So nothing needs to change for the call and return events.

Since we no longer make a difference between C functions and Python functions, we need to prevent the c_* events for Python functions. This is done by not generating those events if the METH_PYTHON flag in ml_flags is set.

Why not simply change existing classes?

One could try to solve the problem by keeping the existing classes without introducing a new base_function class.

That might look like a simpler solution but it is not: it would require introspection support for 3 distinct classes: function, builtin_function_or_method and method_descriptor. For the latter two classes, “introspection support” would mean at a minimum allowing subclassing. But we don’t want to lose performance, so we want fast subclass checks. This would require two new flags in tp_flags. And we want subclasses to allow __get__ for built-in functions, so we should implement the LOAD_METHOD opcode for built-in functions too. More generally, a lot of functionality would need to be duplicated and the end result would be far more complex code.

It is also not clear how the introspection of built-in function subclasses would interact with __text_signature__. Having two independent kinds of inspect.signature support on the same class sounds like asking for problems.

And this would not fix some of the other differences between built-in functions and Python functions that were mentioned in the motivation.

Why __text_signature__ is not a solution

Built-in functions have an attribute __text_signature__, which gives the signature of the function as plain text. The default values are evaluated by ast.literal_eval. Because of this, it supports only a small number of standard Python classes and not arbitrary Python objects.

And even if __text_signature__ would allow arbitrary signatures somehow, that is only one piece of introspection: it does not help with inspect.getsourcefile for example.

defined_function versus function

In many places, a decision needs to be made whether the old function class should be replaced by defined_function or the new function class. This is done by thinking of the most likely use case:

1. types.FunctionType refers to function because that type might be used to construct instances using types.FunctionType(...).
2. inspect.isfunction() refers to defined_function because this is the class where introspection is supported.
3. The C API functions must refer to function because we do not specify how the various attributes of defined_function are implemented. We expect that this is not a problem since there is typically no reason for introspection to be done by C extensions.

Scope of this PEP: which classes are involved?

The main motivation of this PEP is fixing function classes, so we certainly want to unify the existing classes builtin_function_or_method and function.

Since built-in functions and methods have the same class, it seems natural to include bound methods too. And since there are no “unbound methods” for Python functions, it makes sense to get rid of unbound methods for extension types.

For now, no changes are made to the classes staticmethod, classmethod and classmethod_descriptor. It would certainly make sense to put these in the base_function class hierarchy and unify classmethod and classmethod_descriptor. However, this PEP is already big enough and this is left as a possible future improvement.

Slot wrappers for extension types like __init__ or __eq__ are quite different from normal methods. They are also typically not called directly because you would normally write foo[i] instead of foo.__getitem__(i). So these are left outside the scope of this PEP.

Python also has an instancemethod class, which seems to be a relic from Python 2, where it was used for bound and unbound methods. It is not clear whether there is still a use case for it. In any case, there is no reason to deal with it in this PEP.

TODO: should instancemethod be deprecated? It doesn’t seem used at all within CPython 3.7, but maybe external packages use it?

Not treating METH_STATIC and METH_CLASS

Almost nothing in this PEP refers to the flags METH_STATIC and METH_CLASS. These flags are checked only by the automatic creation of built-in functions. When a staticmethod, classmethod or classmethod_descriptor is bound (i.e. __get__ is called), a base_function instance is created with m_self != NULL. For a classmethod, this is obvious since m_self is the class that the method is bound to. For a staticmethod, one can take an arbitrary Python object for m_self. For backwards compatibility, we choose m_self = __parent__ for static methods of extension types.

__self__ in base_function

It may look strange at first sight to add the __self__ slot in base_function as opposed to bound_method. We took this idea from the existing builtin_function_or_method class. It allows us to have a single general implementation of __call__ and __get__ for the various function classes discussed in this PEP.

It also makes it easy to support existing built-in functions which set __self__ to the module (for example, sys.exit.__self__ is sys).

Two implementations of __doc__

base_function does not support function docstrings. Instead, the classes cfunction and function each have their own way of dealing with docstrings (and bound_method just takes the __doc__ from the wrapped function).

For cfunction, the docstring is stored (together with the text signature) as C string in the read-only ml_doc field of a PyMethodDef. For function, the docstring is stored as a writable Python object and it does not actually need to be a string. It looks hard to unify these two very different ways of dealing with __doc__. For backwards compatibility, we keep the existing implementations.

For defined_function, we require __doc__ to be implemented but we do not specify how. A subclass can implement __doc__ the same way as cfunction or using a struct member or some other way.

Subclassing

We disallow subclassing of cfunction and bound_method to enable fast type checks for PyCFunction_Check and PyMethod_Check.

We allow subclassing of the other classes because there is no reason to disallow it. For Python modules, the only relevant class to subclass is function because the others cannot be instantiated anyway.

Replacing tp_call: METH_PASS_FUNCTION and METH_CALL_UNBOUND

The new flags METH_PASS_FUNCTION and METH_CALL_UNBOUND are meant to support cases where formerly a custom tp_call was used. It reduces the number of special fast paths in Python/ceval.c for calling objects: instead of treating Python functions, built-in functions and method descriptors separately, there would only be a single check.

The signature of tp_call is essentially the signature of PyBaseFunctionObject.m_ml.ml_meth with flags METH_VARARGS | METH_KEYWORDS | METH_PASS_FUNCTION | METH_CALL_UNBOUND (the only difference is an added self argument). Therefore, it should be easy to change existing tp_call slots to use the base_function implementation instead.

It also makes sense to use METH_PASS_FUNCTION without METH_CALL_UNBOUND in cases where the C function simply needs access to additional metadata from the function, such as the __parent__. This is for example needed to support PEP 573. Converting existing methods to use METH_PASS_FUNCTION is trivial: it only requires adding an extra argument to the C function.

Changes to types and inspect

The proposed changes to types and inspect are meant to minimize changes in behaviour. However, it is unavoidable that some things change and this can cause code which uses types or inspect to break. In the Python standard library for example, changes are needed in the doctest module because of this.

Also, tools which take various kinds of functions as input will need to deal with the new function hierarchy and the possibility of custom function classes.

Python functions

For Python functions, essentially nothing changes. The attributes that existed before still exist and Python functions can be initialized, called and turned into methods as before.

The name function is kept for backwards compatibility. While it might make sense to change the name to something more specific like python_function, that would require a lot of annoying changes in documentation and testsuites.

Built-in functions of a module

Also for built-in functions, nothing changes. We keep the old behaviour that such functions do not bind as methods. This is a consequence of the fact that __self__ is set to the module.

Built-in bound and unbound methods

The types of built-in bound and unbound methods will change. However, this does not affect calling such methods because the protocol in base_function.__call__ (in particular the handling of __objclass__ and self slicing) was specifically designed to be backwards compatible. All attributes which existed before (like __objclass__ and __self__) still exist.

New attributes

Some objects get new special double-underscore attributes. For example, the new attribute __parent__ appears on all built-in functions and all methods get a __func__ attribute. The fact that __self__ is now a special read-only attribute for Python functions caused trouble in 4. Generally, we expect that not much will break though.

method_descriptor and PyDescr_NewMethod

The class method_descriptor and the constructor PyDescr_NewMethod should be deprecated. They are no longer used by CPython itself but are still supported.

Phase one: keep existing classes but add base classes

Initially, implement the base_function class and use it as common base class but otherwise keep the existing classes (but not their implementation).

In this proposal, the class hierarchy would become:

                      object
                         |
                         |
                  base_function
                 /       |     \
                /        |      \
               /         |       \
      cfunction          |     defined_function
       |     |           |         \
       |     |      bound_method    \
       |     |                       \
       |  method_descriptor       function
       |
builtin_function_or_method

The leaf classes builtin_function_or_method, method_descriptor, bound_method and function correspond to the existing classes (with method renamed to bound_method).

Automatically created functions created in modules become instances of builtin_function_or_method. Unbound methods of extension types become instances of method_descriptor.

The class method_descriptor is a copy of cfunction except that __get__ returns a builtin_function_or_method instead of a bound_method.

The class builtin_function_or_method has the same C structure as a bound_method, but it inherits from cfunction. The __func__ attribute is not mandatory: it is only defined when binding a method_descriptor.

We keep the implementation of the inspect functions as they are. Because of this and because the existing classes are kept, backwards compatibility is ensured for code doing type checks.

Since showing an actual DeprecationWarning would affect a lot of correctly-functioning code, any deprecations would only appear in the documentation. Another reason is that it is hard to show warnings for calling isinstance(x, t) (but it could be done using __instancecheck__ hacking) and impossible for type(x) is t.

Phase two

Phase two is what is actually described in the rest of this PEP. In terms of implementation, it would be a relatively small change compared to phase one.

builtin_function_or_method: built-in functions and bound methods

These are of type PyCFunction_Type with structure PyCFunctionObject:

typedef struct {
    PyObject_HEAD
    PyMethodDef *m_ml; /* Description of the C function to call */
    PyObject    *m_self; /* Passed as 'self' arg to the C func, can be NULL */
    PyObject    *m_module; /* The __module__ attribute, can be anything */
    PyObject    *m_weakreflist; /* List of weak references */
} PyCFunctionObject;

struct PyMethodDef {
    const char  *ml_name;   /* The name of the built-in function/method */
    PyCFunction ml_meth;    /* The C function that implements it */
    int         ml_flags;   /* Combination of METH_xxx flags, which mostly
                               describe the args expected by the C func */
    const char  *ml_doc;    /* The __doc__ attribute, or NULL */
};

where PyCFunction is a C function pointer (there are various forms of this, the most basic takes two arguments for self and *args).

This class is used both for functions and bound methods: for a method, the m_self slot points to the object:

>>> dict(foo=42).get
<built-in method get of dict object at 0x...>
>>> dict(foo=42).get.__self__
{'foo': 42}

In some cases, a function is considered a “method” of the module defining it:

>>> import os
>>> os.kill
<built-in function kill>
>>> os.kill.__self__
<module 'posix' (built-in)>

method_descriptor: built-in unbound methods

These are of type PyMethodDescr_Type with structure PyMethodDescrObject:

typedef struct {
    PyDescrObject d_common;
    PyMethodDef *d_method;
} PyMethodDescrObject;

typedef struct {
    PyObject_HEAD
    PyTypeObject *d_type;
    PyObject *d_name;
    PyObject *d_qualname;
} PyDescrObject;

function: Python functions

These are of type PyFunction_Type with structure PyFunctionObject:

typedef struct {
    PyObject_HEAD
    PyObject *func_code;        /* A code object, the __code__ attribute */
    PyObject *func_globals;     /* A dictionary (other mappings won't do) */
    PyObject *func_defaults;    /* NULL or a tuple */
    PyObject *func_kwdefaults;  /* NULL or a dict */
    PyObject *func_closure;     /* NULL or a tuple of cell objects */
    PyObject *func_doc;         /* The __doc__ attribute, can be anything */
    PyObject *func_name;        /* The __name__ attribute, a string object */
    PyObject *func_dict;        /* The __dict__ attribute, a dict or NULL */
    PyObject *func_weakreflist; /* List of weak references */
    PyObject *func_module;      /* The __module__ attribute, can be anything */
    PyObject *func_annotations; /* Annotations, a dict or NULL */
    PyObject *func_qualname;    /* The qualified name */

    /* Invariant:
     *     func_closure contains the bindings for func_code->co_freevars, so
     *     PyTuple_Size(func_closure) == PyCode_GetNumFree(func_code)
     *     (func_closure may be NULL if PyCode_GetNumFree(func_code) == 0).
     */
} PyFunctionObject;

In Python 3, there is no “unbound method” class: an unbound method is just a plain function.

method: Python bound methods

These are of type PyMethod_Type with structure PyMethodObject:

typedef struct {
    PyObject_HEAD
    PyObject *im_func;   /* The callable object implementing the method */
    PyObject *im_self;   /* The instance it is bound to */
    PyObject *im_weakreflist; /* List of weak references */
} PyMethodObject;