"""
A place for internal code

Some things are more easily handled Python.

"""
from __future__ import division, absolute_import, print_function

import re
import sys
import platform

from numpy.compat import unicode
from numpy.core.overrides import set_module
from .multiarray import dtype, array, ndarray
try:
    import ctypes
except ImportError:
    ctypes = None

IS_PYPY = platform.python_implementation() == 'PyPy'

if (sys.byteorder == 'little'):
    _nbo = b'<'
else:
    _nbo = b'>'

def _makenames_list(adict, align):
    allfields = []
    fnames = list(adict.keys())
    for fname in fnames:
        obj = adict[fname]
        n = len(obj)
        if not isinstance(obj, tuple) or n not in [2, 3]:
            raise ValueError("entry not a 2- or 3- tuple")
        if (n > 2) and (obj[2] == fname):
            continue
        num = int(obj[1])
        if (num < 0):
            raise ValueError("invalid offset.")
        format = dtype(obj[0], align=align)
        if (n > 2):
            title = obj[2]
        else:
            title = None
        allfields.append((fname, format, num, title))
    # sort by offsets
    allfields.sort(key=lambda x: x[2])
    names = [x[0] for x in allfields]
    formats = [x[1] for x in allfields]
    offsets = [x[2] for x in allfields]
    titles = [x[3] for x in allfields]

    return names, formats, offsets, titles

# Called in PyArray_DescrConverter function when
#  a dictionary without "names" and "formats"
#  fields is used as a data-type descriptor.
def _usefields(adict, align):
    try:
        names = adict[-1]
    except KeyError:
        names = None
    if names is None:
        names, formats, offsets, titles = _makenames_list(adict, align)
    else:
        formats = []
        offsets = []
        titles = []
        for name in names:
            res = adict[name]
            formats.append(res[0])
            offsets.append(res[1])
            if (len(res) > 2):
                titles.append(res[2])
            else:
                titles.append(None)

    return dtype({"names": names,
                  "formats": formats,
                  "offsets": offsets,
                  "titles": titles}, align)


# construct an array_protocol descriptor list
#  from the fields attribute of a descriptor
# This calls itself recursively but should eventually hit
#  a descriptor that has no fields and then return
#  a simple typestring

def _array_descr(descriptor):
    fields = descriptor.fields
    if fields is None:
        subdtype = descriptor.subdtype
        if subdtype is None:
            if descriptor.metadata is None:
                return descriptor.str
            else:
                new = descriptor.metadata.copy()
                if new:
                    return (descriptor.str, new)
                else:
                    return descriptor.str
        else:
            return (_array_descr(subdtype[0]), subdtype[1])

    names = descriptor.names
    ordered_fields = [fields[x] + (x,) for x in names]
    result = []
    offset = 0
    for field in ordered_fields:
        if field[1] > offset:
            num = field[1] - offset
            result.append(('', '|V%d' % num))
            offset += num
        elif field[1] < offset:
            raise ValueError(
                "dtype.descr is not defined for types with overlapping or "
                "out-of-order fields")
        if len(field) > 3:
            name = (field[2], field[3])
        else:
            name = field[2]
        if field[0].subdtype:
            tup = (name, _array_descr(field[0].subdtype[0]),
                   field[0].subdtype[1])
        else:
            tup = (name, _array_descr(field[0]))
        offset += field[0].itemsize
        result.append(tup)

    if descriptor.itemsize > offset:
        num = descriptor.itemsize - offset
        result.append(('', '|V%d' % num))

    return result

# Build a new array from the information in a pickle.
# Note that the name numpy.core._internal._reconstruct is embedded in
# pickles of ndarrays made with NumPy before release 1.0
# so don't remove the name here, or you'll
# break backward compatibility.
def _reconstruct(subtype, shape, dtype):
    return ndarray.__new__(subtype, shape, dtype)


# format_re was originally from numarray by J. Todd Miller

format_re = re.compile(br'(?P<order1>[<>|=]?)'
                       br'(?P<repeats> *[(]?[ ,0-9L]*[)]? *)'
                       br'(?P<order2>[<>|=]?)'
                       br'(?P<dtype>[A-Za-z0-9.?]*(?:\[[a-zA-Z0-9,.]+\])?)')
sep_re = re.compile(br'\s*,\s*')
space_re = re.compile(br'\s+$')

# astr is a string (perhaps comma separated)

_convorder = {b'=': _nbo}

def _commastring(astr):
    startindex = 0
    result = []
    while startindex < len(astr):
        mo = format_re.match(astr, pos=startindex)
        try:
            (order1, repeats, order2, dtype) = mo.groups()
        except (TypeError, AttributeError):
            raise ValueError('format number %d of "%s" is not recognized' %
                                            (len(result)+1, astr))
        startindex = mo.end()
        # Separator or ending padding
        if startindex < len(astr):
            if space_re.match(astr, pos=startindex):
                startindex = len(astr)
            else:
                mo = sep_re.match(astr, pos=startindex)
                if not mo:
                    raise ValueError(
                        'format number %d of "%s" is not recognized' %
                        (len(result)+1, astr))
                startindex = mo.end()

        if order2 == b'':
            order = order1
        elif order1 == b'':
            order = order2
        else:
            order1 = _convorder.get(order1, order1)
            order2 = _convorder.get(order2, order2)
            if (order1 != order2):
                raise ValueError(
                    'inconsistent byte-order specification %s and %s' %
                    (order1, order2))
            order = order1

        if order in [b'|', b'=', _nbo]:
            order = b''
        dtype = order + dtype
        if (repeats == b''):
            newitem = dtype
        else:
            newitem = (dtype, eval(repeats))
        result.append(newitem)

    return result

class dummy_ctype(object):
    def __init__(self, cls):
        self._cls = cls
    def __mul__(self, other):
        return self
    def __call__(self, *other):
        return self._cls(other)
    def __eq__(self, other):
        return self._cls == other._cls
    def __ne__(self, other):
        return self._cls != other._cls

def _getintp_ctype():
    val = _getintp_ctype.cache
    if val is not None:
        return val
    if ctypes is None:
        import numpy as np
        val = dummy_ctype(np.intp)
    else:
        char = dtype('p').char
        if (char == 'i'):
            val = ctypes.c_int
        elif char == 'l':
            val = ctypes.c_long
        elif char == 'q':
            val = ctypes.c_longlong
        else:
            val = ctypes.c_long
    _getintp_ctype.cache = val
    return val
_getintp_ctype.cache = None

# Used for .ctypes attribute of ndarray

class _missing_ctypes(object):
    def cast(self, num, obj):
        return num.value

    class c_void_p(object):
        def __init__(self, ptr):
            self.value = ptr


class _unsafe_first_element_pointer(object):
    """
    Helper to allow viewing an array as a ctypes pointer to the first element

    This avoids:
      * dealing with strides
      * `.view` rejecting object-containing arrays
      * `memoryview` not supporting overlapping fields
    """
    def __init__(self, arr):
        self.base = arr

    @property
    def __array_interface__(self):
        i = dict(
            shape=(),
            typestr='|V0',
            data=(self.base.__array_interface__['data'][0], False),
            strides=(),
            version=3,
        )
        return i


def _get_void_ptr(arr):
    """
    Get a `ctypes.c_void_p` to arr.data, that keeps a reference to the array
    """
    import numpy as np
    # convert to a 0d array that has a data pointer referrign to the start
    # of arr. This holds a reference to arr.
    simple_arr = np.asarray(_unsafe_first_element_pointer(arr))

    # create a `char[0]` using the same memory.
    c_arr = (ctypes.c_char * 0).from_buffer(simple_arr)

    # finally cast to void*
    return ctypes.cast(ctypes.pointer(c_arr), ctypes.c_void_p)


class _ctypes(object):
    def __init__(self, array, ptr=None):
        self._arr = array

        if ctypes:
            self._ctypes = ctypes
            # get a void pointer to the buffer, which keeps the array alive
            self._data = _get_void_ptr(array)
            assert self._data.value == ptr
        else:
            # fake a pointer-like object that holds onto the reference
            self._ctypes = _missing_ctypes()
            self._data = self._ctypes.c_void_p(ptr)
            self._data._objects = array

        if self._arr.ndim == 0:
            self._zerod = True
        else:
            self._zerod = False

    def data_as(self, obj):
        """
        Return the data pointer cast to a particular c-types object.
        For example, calling ``self._as_parameter_`` is equivalent to
        ``self.data_as(ctypes.c_void_p)``. Perhaps you want to use the data as a
        pointer to a ctypes array of floating-point data:
        ``self.data_as(ctypes.POINTER(ctypes.c_double))``.

        The returned pointer will keep a reference to the array.
        """
        return self._ctypes.cast(self._data, obj)

    def shape_as(self, obj):
        """
        Return the shape tuple as an array of some other c-types
        type. For example: ``self.shape_as(ctypes.c_short)``.
        """
        if self._zerod:
            return None
        return (obj*self._arr.ndim)(*self._arr.shape)

    def strides_as(self, obj):
        """
        Return the strides tuple as an array of some other
        c-types type. For example: ``self.strides_as(ctypes.c_longlong)``.
        """
        if self._zerod:
            return None
        return (obj*self._arr.ndim)(*self._arr.strides)

    @property
    def data(self):
        """
        A pointer to the memory area of the array as a Python integer.
        This memory area may contain data that is not aligned, or not in correct
        byte-order. The memory area may not even be writeable. The array
        flags and data-type of this array should be respected when passing this
        attribute to arbitrary C-code to avoid trouble that can include Python
        crashing. User Beware! The value of this attribute is exactly the same
        as ``self._array_interface_['data'][0]``.

        Note that unlike `data_as`, a reference will not be kept to the array:
        code like ``ctypes.c_void_p((a + b).ctypes.data)`` will result in a
        pointer to a deallocated array, and should be spelt
        ``(a + b).ctypes.data_as(ctypes.c_void_p)``
        """
        return self._data.value

    @property
    def shape(self):
        """
        (c_intp*self.ndim): A ctypes array of length self.ndim where
        the basetype is the C-integer corresponding to ``dtype('p')`` on this
        platform. This base-type could be `ctypes.c_int`, `ctypes.c_long`, or
        `ctypes.c_longlong` depending on the platform.
        The c_intp type is defined accordingly in `numpy.ctypeslib`.
        The ctypes array contains the shape of the underlying array.
        """
        return self.shape_as(_getintp_ctype())

    @property
    def strides(self):
        """
        (c_intp*self.ndim): A ctypes array of length self.ndim where
        the basetype is the same as for the shape attribute. This ctypes array
        contains the strides information from the underlying array. This strides
        information is important for showing how many bytes must be jumped to
        get to the next element in the array.
        """
        return self.strides_as(_getintp_ctype())

    @property
    def _as_parameter_(self):
        """
        Overrides the ctypes semi-magic method

        Enables `c_func(some_array.ctypes)`
        """
        return self._data

    # kept for compatibility
    get_data = data.fget
    get_shape = shape.fget
    get_strides = strides.fget
    get_as_parameter = _as_parameter_.fget


def _newnames(datatype, order):
    """
    Given a datatype and an order object, return a new names tuple, with the
    order indicated
    """
    oldnames = datatype.names
    nameslist = list(oldnames)
    if isinstance(order, (str, unicode)):
        order = [order]
    seen = set()
    if isinstance(order, (list, tuple)):
        for name in order:
            try:
                nameslist.remove(name)
            except ValueError:
                if name in seen:
                    raise ValueError("duplicate field name: %s" % (name,))
                else:
                    raise ValueError("unknown field name: %s" % (name,))
            seen.add(name)
        return tuple(list(order) + nameslist)
    raise ValueError("unsupported order value: %s" % (order,))

def _copy_fields(ary):
    """Return copy of structured array with padding between fields removed.

    Parameters
    ----------
    ary : ndarray
       Structured array from which to remove padding bytes

    Returns
    -------
    ary_copy : ndarray
       Copy of ary with padding bytes removed
    """
    dt = ary.dtype
    copy_dtype = {'names': dt.names,
                  'formats': [dt.fields[name][0] for name in dt.names]}
    return array(ary, dtype=copy_dtype, copy=True)

def _getfield_is_safe(oldtype, newtype, offset):
    """ Checks safety of getfield for object arrays.

    As in _view_is_safe, we need to check that memory containing objects is not
    reinterpreted as a non-object datatype and vice versa.

    Parameters
    ----------
    oldtype : data-type
        Data type of the original ndarray.
    newtype : data-type
        Data type of the field being accessed by ndarray.getfield
    offset : int
        Offset of the field being accessed by ndarray.getfield

    Raises
    ------
    TypeError
        If the field access is invalid

    """
    if newtype.hasobject or oldtype.hasobject:
        if offset == 0 and newtype == oldtype:
            return
        if oldtype.names:
            for name in oldtype.names:
                if (oldtype.fields[name][1] == offset and
                        oldtype.fields[name][0] == newtype):
                    return
        raise TypeError("Cannot get/set field of an object array")
    return

def _view_is_safe(oldtype, newtype):
    """ Checks safety of a view involving object arrays, for example when
    doing::

        np.zeros(10, dtype=oldtype).view(newtype)

    Parameters
    ----------
    oldtype : data-type
        Data type of original ndarray
    newtype : data-type
        Data type of the view

    Raises
    ------
    TypeError
        If the new type is incompatible with the old type.

    """

    # if the types are equivalent, there is no problem.
    # for example: dtype((np.record, 'i4,i4')) == dtype((np.void, 'i4,i4'))
    if oldtype == newtype:
        return

    if newtype.hasobject or oldtype.hasobject:
        raise TypeError("Cannot change data-type for object array.")
    return

# Given a string containing a PEP 3118 format specifier,
# construct a NumPy dtype

_pep3118_native_map = {
    '?': '?',
    'c': 'S1',
    'b': 'b',
    'B': 'B',
    'h': 'h',
    'H': 'H',
    'i': 'i',
    'I': 'I',
    'l': 'l',
    'L': 'L',
    'q': 'q',
    'Q': 'Q',
    'e': 'e',
    'f': 'f',
    'd': 'd',
    'g': 'g',
    'Zf': 'F',
    'Zd': 'D',
    'Zg': 'G',
    's': 'S',
    'w': 'U',
    'O': 'O',
    'x': 'V',  # padding
}
_pep3118_native_typechars = ''.join(_pep3118_native_map.keys())

_pep3118_standard_map = {
    '?': '?',
    'c': 'S1',
    'b': 'b',
    'B': 'B',
    'h': 'i2',
    'H': 'u2',
    'i': 'i4',
    'I': 'u4',
    'l': 'i4',
    'L': 'u4',
    'q': 'i8',
    'Q': 'u8',
    'e': 'f2',
    'f': 'f',
    'd': 'd',
    'Zf': 'F',
    'Zd': 'D',
    's': 'S',
    'w': 'U',
    'O': 'O',
    'x': 'V',  # padding
}
_pep3118_standard_typechars = ''.join(_pep3118_standard_map.keys())

_pep3118_unsupported_map = {
    'u': 'UCS-2 strings',
    '&': 'pointers',
    't': 'bitfields',
    'X': 'function pointers',
}

class _Stream(object):
    def __init__(self, s):
        self.s = s
        self.byteorder = '@'

    def advance(self, n):
        res = self.s[:n]
        self.s = self.s[n:]
        return res

    def consume(self, c):
        if self.s[:len(c)] == c:
            self.advance(len(c))
            return True
        return False

    def consume_until(self, c):
        if callable(c):
            i = 0
            while i < len(self.s) and not c(self.s[i]):
                i = i + 1
            return self.advance(i)
        else:
            i = self.s.index(c)
            res = self.advance(i)
            self.advance(len(c))
            return res

    @property
    def next(self):
        return self.s[0]

    def __bool__(self):
        return bool(self.s)
    __nonzero__ = __bool__


def _dtype_from_pep3118(spec):
    stream = _Stream(spec)
    dtype, align = __dtype_from_pep3118(stream, is_subdtype=False)
    return dtype

def __dtype_from_pep3118(stream, is_subdtype):
    field_spec = dict(
        names=[],
        formats=[],
        offsets=[],
        itemsize=0
    )
    offset = 0
    common_alignment = 1
    is_padding = False

    # Parse spec
    while stream:
        value = None

        # End of structure, bail out to upper level
        if stream.consume('}'):
            break

        # Sub-arrays (1)
        shape = None
        if stream.consume('('):
            shape = stream.consume_until(')')
            shape = tuple(map(int, shape.split(',')))

        # Byte order
        if stream.next in ('@', '=', '<', '>', '^', '!'):
            byteorder = stream.advance(1)
            if byteorder == '!':
                byteorder = '>'
            stream.byteorder = byteorder

        # Byte order characters also control native vs. standard type sizes
        if stream.byteorder in ('@', '^'):
            type_map = _pep3118_native_map
            type_map_chars = _pep3118_native_typechars
        else:
            type_map = _pep3118_standard_map
            type_map_chars = _pep3118_standard_typechars

        # Item sizes
        itemsize_str = stream.consume_until(lambda c: not c.isdigit())
        if itemsize_str:
            itemsize = int(itemsize_str)
        else:
            itemsize = 1

        # Data types
        is_padding = False

        if stream.consume('T{'):
            value, align = __dtype_from_pep3118(
                stream, is_subdtype=True)
        elif stream.next in type_map_chars:
            if stream.next == 'Z':
                typechar = stream.advance(2)
            else:
                typechar = stream.advance(1)

            is_padding = (typechar == 'x')
            dtypechar = type_map[typechar]
            if dtypechar in 'USV':
                dtypechar += '%d' % itemsize
                itemsize = 1
            numpy_byteorder = {'@': '=', '^': '='}.get(
                stream.byteorder, stream.byteorder)
            value = dtype(numpy_byteorder + dtypechar)
            align = value.alignment
        elif stream.next in _pep3118_unsupported_map:
            desc = _pep3118_unsupported_map[stream.next]
            raise NotImplementedError(
                "Unrepresentable PEP 3118 data type {!r} ({})"
                .format(stream.next, desc))
        else:
            raise ValueError("Unknown PEP 3118 data type specifier %r" % stream.s)

        #
        # Native alignment may require padding
        #
        # Here we assume that the presence of a '@' character implicitly implies
        # that the start of the array is *already* aligned.
        #
        extra_offset = 0
        if stream.byteorder == '@':
            start_padding = (-offset) % align
            intra_padding = (-value.itemsize) % align

            offset += start_padding

            if intra_padding != 0:
                if itemsize > 1 or (shape is not None and _prod(shape) > 1):
                    # Inject internal padding to the end of the sub-item
                    value = _add_trailing_padding(value, intra_padding)
                else:
                    # We can postpone the injection of internal padding,
                    # as the item appears at most once
                    extra_offset += intra_padding

            # Update common alignment
            common_alignment = _lcm(align, common_alignment)

        # Convert itemsize to sub-array
        if itemsize != 1:
            value = dtype((value, (itemsize,)))

        # Sub-arrays (2)
        if shape is not None:
            value = dtype((value, shape))

        # Field name
        if stream.consume(':'):
            name = stream.consume_until(':')
        else:
            name = None

        if not (is_padding and name is None):
            if name is not None and name in field_spec['names']:
                raise RuntimeError("Duplicate field name '%s' in PEP3118 format"
                                   % name)
            field_spec['names'].append(name)
            field_spec['formats'].append(value)
            field_spec['offsets'].append(offset)

        offset += value.itemsize
        offset += extra_offset

        field_spec['itemsize'] = offset

    # extra final padding for aligned types
    if stream.byteorder == '@':
        field_spec['itemsize'] += (-offset) % common_alignment

    # Check if this was a simple 1-item type, and unwrap it
    if (field_spec['names'] == [None]
            and field_spec['offsets'][0] == 0
            and field_spec['itemsize'] == field_spec['formats'][0].itemsize
            and not is_subdtype):
        ret = field_spec['formats'][0]
    else:
        _fix_names(field_spec)
        ret = dtype(field_spec)

    # Finished
    return ret, common_alignment

def _fix_names(field_spec):
    """ Replace names which are None with the next unused f%d name """
    names = field_spec['names']
    for i, name in enumerate(names):
        if name is not None:
            continue

        j = 0
        while True:
            name = 'f{}'.format(j)
            if name not in names:
                break
            j = j + 1
        names[i] = name

def _add_trailing_padding(value, padding):
    """Inject the specified number of padding bytes at the end of a dtype"""
    if value.fields is None:
        field_spec = dict(
            names=['f0'],
            formats=[value],
            offsets=[0],
            itemsize=value.itemsize
        )
    else:
        fields = value.fields
        names = value.names
        field_spec = dict(
            names=names,
            formats=[fields[name][0] for name in names],
            offsets=[fields[name][1] for name in names],
            itemsize=value.itemsize
        )

    field_spec['itemsize'] += padding
    return dtype(field_spec)

def _prod(a):
    p = 1
    for x in a:
        p *= x
    return p

def _gcd(a, b):
    """Calculate the greatest common divisor of a and b"""
    while b:
        a, b = b, a % b
    return a

def _lcm(a, b):
    return a // _gcd(a, b) * b

# Exception used in shares_memory()
@set_module('numpy')
class TooHardError(RuntimeError):
    pass

@set_module('numpy')
class AxisError(ValueError, IndexError):
    """ Axis supplied was invalid. """
    def __init__(self, axis, ndim=None, msg_prefix=None):
        # single-argument form just delegates to base class
        if ndim is None and msg_prefix is None:
            msg = axis

        # do the string formatting here, to save work in the C code
        else:
            msg = ("axis {} is out of bounds for array of dimension {}"
                   .format(axis, ndim))
            if msg_prefix is not None:
                msg = "{}: {}".format(msg_prefix, msg)

        super(AxisError, self).__init__(msg)


def array_ufunc_errmsg_formatter(dummy, ufunc, method, *inputs, **kwargs):
    """ Format the error message for when __array_ufunc__ gives up. """
    args_string = ', '.join(['{!r}'.format(arg) for arg in inputs] +
                            ['{}={!r}'.format(k, v)
                             for k, v in kwargs.items()])
    args = inputs + kwargs.get('out', ())
    types_string = ', '.join(repr(type(arg).__name__) for arg in args)
    return ('operand type(s) all returned NotImplemented from '
            '__array_ufunc__({!r}, {!r}, {}): {}'
            .format(ufunc, method, args_string, types_string))


def array_function_errmsg_formatter(public_api, types):
    """ Format the error message for when __array_ufunc__ gives up. """
    func_name = '{}.{}'.format(public_api.__module__, public_api.__name__)
    return ("no implementation found for '{}' on types that implement "
            '__array_function__: {}'.format(func_name, list(types)))


def _ufunc_doc_signature_formatter(ufunc):
    """
    Builds a signature string which resembles PEP 457

    This is used to construct the first line of the docstring
    """

    # input arguments are simple
    if ufunc.nin == 1:
        in_args = 'x'
    else:
        in_args = ', '.join('x{}'.format(i+1) for i in range(ufunc.nin))

    # output arguments are both keyword or positional
    if ufunc.nout == 0:
        out_args = ', /, out=()'
    elif ufunc.nout == 1:
        out_args = ', /, out=None'
    else:
        out_args = '[, {positional}], / [, out={default}]'.format(
            positional=', '.join(
                'out{}'.format(i+1) for i in range(ufunc.nout)),
            default=repr((None,)*ufunc.nout)
        )

    # keyword only args depend on whether this is a gufunc
    kwargs = (
        ", casting='same_kind'"
        ", order='K'"
        ", dtype=None"
        ", subok=True"
        "[, signature"
        ", extobj]"
    )
    if ufunc.signature is None:
        kwargs = ", where=True" + kwargs

    # join all the parts together
    return '{name}({in_args}{out_args}, *{kwargs})'.format(
        name=ufunc.__name__,
        in_args=in_args,
        out_args=out_args,
        kwargs=kwargs
    )


def npy_ctypes_check(cls):
    # determine if a class comes from ctypes, in order to work around
    # a bug in the buffer protocol for those objects, bpo-10746
    try:
        # ctypes class are new-style, so have an __mro__. This probably fails
        # for ctypes classes with multiple inheritance.
        if IS_PYPY:
            # (..., _ctypes.basics._CData, Bufferable, object)
            ctype_base = cls.__mro__[-3]
        else:
            # # (..., _ctypes._CData, object)
            ctype_base = cls.__mro__[-2]
        # right now, they're part of the _ctypes module
        return 'ctypes' in ctype_base.__module__
    except Exception:
        return False


class recursive(object):
    '''
    A decorator class for recursive nested functions.
    Naive recursive nested functions hold a reference to themselves:

    def outer(*args):
        def stringify_leaky(arg0, *arg1):
            if len(arg1) > 0:
                return stringify_leaky(*arg1)  # <- HERE
            return str(arg0)
        stringify_leaky(*args)

    This design pattern creates a reference cycle that is difficult for a
    garbage collector to resolve. The decorator class prevents the
    cycle by passing the nested function in as an argument `self`:

    def outer(*args):
        @recursive
        def stringify(self, arg0, *arg1):
            if len(arg1) > 0:
                return self(*arg1)
            return str(arg0)
        stringify(*args)

    '''
    def __init__(self, func):
        self.func = func
    def __call__(self, *args, **kwargs):
        return self.func(self, *args, **kwargs)

