Python 3 function arithmetic

arithmetic test.py

from arithmetic import *

@arithmetic
def foo(thing):
    print(greeting, thing, "!")

foo()
foo("world")
foo.greeting = "Hello"
foo.greeting
foo()
foo("world")

@arithmetic
def bar(thing):
    print("Goodbye", thing)

bar()
foo += bar
foo("additional function")

foo = 3*foo
foo("multiplication")

@arithmetic
def baz():
    return "composition"

foo *= baz
foo()

arithmetic.py

from types import FunctionType

class arithmetic(object):
    def __init__(self, func):
        self._func = func

    def __call__(self, *args, **kwargs):
        return self._func(*args, **kwargs)

    def __add__(self, other):
        def f(*args, **kwargs):
            self._func(*args, **kwargs)
            return other._func(*args, **kwargs)
        return __class__(f)

    def __mul__(self, other):
        def f(*args, **kwargs):
            return self._func(other._func(*args, **kwargs))
        return __class__(f)

    def __setattr__(self, key, val):
        if key.startswith('_'):
            super().__setattr__(key, val)
        else:
            self._func = FunctionType(self._func.__code__,
                                      {**self._func.__globals__, key: val},
                                      self._func.__name__,
                                      self._func.__defaults__,
                                      self._func.__closure__)
    
    def __getattr__(self, key):
        try:
            return getattr(super(), key)
        except AttributeError:
            if key in self._func.__globals__:
                return self._func.__globals__[key]
            else:
                raise

    def __rmul__(self, seq):
        if not hasattr(seq, "__iter__"): seq = range(seq)
        def f(*args, **kwargs):
            return [self._func(*args, **kwargs) for item in seq]
        return __class__(f)

__all__ = ["arithmetic"]