Since testing is crucial for ensuring that one's code is working correctly, a unit test was created for the linked answer. It is included down below and can be run along the side of the asynchronous module it is testing.
test_asynchronous.py
#! /usr/bin/env python3
import _thread
import atexit
import contextlib
import functools
import inspect
import itertools
import io
import math
import operator
import os
import queue
import sys
import time
import unittest
import asynchronous
# noinspection PyUnresolvedReferences
class TestConstructor:
    def instantiate(self, *args):
        parameters = len(inspect.signature(self.CLASS).parameters)
        return self.CLASS(*args[:parameters])
    def test_valid_timeout(self):
        instance = self.instantiate(None, print, (), {})
        self.assertEqual(instance.get_timeout(), math.inf)
        instance = self.instantiate(1, print, (), {})
        self.assertEqual(instance.get_timeout(), 1)
        float_timeout = (math.e ** (1j * math.pi) + 1).imag
        self.assertIsInstance(float_timeout, float)
        instance = self.instantiate(float_timeout, print, (), {})
        self.assertEqual(instance.get_timeout(), float_timeout)
    def test_error_timeout(self):
        self.assertRaises(TypeError, self.instantiate, '60', print, (), {})
        self.assertRaises(ValueError, self.instantiate, 0, print, (), {})
        self.assertRaises(ValueError, self.instantiate, -1, print, (), {})
# noinspection PyUnresolvedReferences
class TestTimeout(TestConstructor):
    def test_valid_property(self):
        instance = self.instantiate(None, None, None, None)
        instance.timeout = 1
        self.assertIsInstance(instance.timeout, int)
        instance.timeout = 1 / 2
        self.assertIsInstance(instance.timeout, float)
        kilo_bit = int.from_bytes(os.urandom(1 << 7), 'big')
        instance.timeout = kilo_bit
        self.assertEqual(instance.timeout, kilo_bit)
    def test_error_property(self):
        instance = self.instantiate(None, None, None, None)
        for exception, value in (
                (TypeError, 'inf'),
                (TypeError, complex(123456789, 0)),
                (ValueError, 0),
                (ValueError, 0.0),
                (ValueError, -1),
                (ValueError, -math.pi)
        ):
            with self.assertRaises(exception):
                instance.timeout = value
            self.assertEqual(instance.timeout, math.inf)
class Timer:
    __timers = {}
    @classmethod
    def start_timer(cls):
        ident, now = _thread.get_ident(), time.perf_counter()
        if now is not cls.__timers.setdefault(ident, now):
            raise KeyError(ident)
    @classmethod
    def stop_timer(cls, expected_time, error=None):
        if error is None:
            error = 1 / 4  # the default is a quarter second
        used = time.perf_counter() - cls.__timers.pop(_thread.get_ident())
        diff = used - expected_time
        return -error <= diff <= +error
# noinspection PyUnresolvedReferences
class TestTimer(Timer):
    def stop_timer(self, expected_time, error=None):
        self.assertTrue(super().stop_timer(expected_time, error))
def delay_run(delay, fn, *args, sync=True, **kwargs):
    def wrapper():
        time.sleep(delay)
        return fn(*args, **kwargs)
    if sync:
        return wrapper()
    _thread.start_new_thread(wrapper, ())
# noinspection PyUnresolvedReferences
class TestModuleOrInstance(TestTimer):
    @property
    def moi(self):
        return self.MODULE_OR_INSTANCE
    def test_valid_timeout(self):
        self.moi.set_timeout(math.inf)
        self.assertEqual(self.moi.get_timeout(), math.inf)
        self.moi.set_timeout(60)
        self.assertEqual(self.moi.get_timeout(), 60)
        self.moi.set_timeout(0.05)
        self.assertEqual(self.moi.get_timeout(), 0.05)
    def test_error_timeout(self):
        self.moi.set_timeout(math.inf)
        self.assertRaises(TypeError, self.moi.set_timeout, None)
        self.assertEqual(self.moi.get_timeout(), math.inf)
        self.assertRaises(ValueError, self.moi.set_timeout, 0)
        self.assertEqual(self.moi.get_timeout(), math.inf)
        self.assertRaises(ValueError, self.moi.set_timeout, -1)
        self.assertEqual(self.moi.get_timeout(), math.inf)
    def run_submit_check(self):
        self.start_timer()
        future = self.moi.submit(delay_run, 0.5, operator.add, 1, 2)
        self.assertRegex(repr(future), r'^<_Future at \d+ state=RUNNING>$')
        self.assertEqual(future.result(), 3)
        self.stop_timer(0.5)
        self.assertRegex(
            repr(future),
            r'^<_Future at \d+ state=FINISHED returned int>$'
        )
    def test_submit_one_second_timeout(self):
        self.moi.set_timeout(1)
        self.run_submit_check()
    def test_submit_no_timeout(self):
        self.moi.set_timeout(math.inf)
        self.run_submit_check()
    def test_submit_short_timeout(self):
        self.moi.set_timeout(0.5)
        self.start_timer()
        future = self.moi.submit(delay_run, 1, operator.add, 1, 2)
        self.assertRegex(repr(future), r'^<_Future at \d+ state=RUNNING>$')
        self.assertIsInstance(future.exception(), TimeoutError)
        self.stop_timer(0.5)
        self.assertRegex(
            repr(future),
            r'^<_Future at \d+ state=CANCELLED raised TimeoutError>$'
        )
    def run_map(self, *args):
        return getattr(self.moi, self.NAME_OF_MAP)(delay_run, *args)
    def test_valid_map(self):
        self.moi.set_timeout(1.5)
        for result in self.run_map(
                [1, 1, 1, 1],
                [operator.add] * 4,
                [0, 1, 2, 3],
                [3, 2, 1, 0]
        ):
            self.assertEqual(result, 3)
    def test_error_map(self):
        self.moi.set_timeout(1.5)
        success = 0
        with self.assertRaises(TimeoutError):
            for result in self.run_map(
                    [1, 1, 2, 1],
                    [operator.add] * 4,
                    [0, 1, 2, 3],
                    [3, 2, 1, 0]
            ):
                self.assertEqual(result, 3)
                success += 1
        self.assertEqual(success, 2)
    def run_shutdown_check(self, running, future):
        self.assertRaises(TimeoutError, future.result)
        running.remove(future)
    def run_submit_loop(self, executor):
        running = set()
        done_callback = functools.partial(self.run_shutdown_check, running)
        for _ in range(10):
            future = executor.submit(delay_run, 2, operator.add, 10, 20)
            running.add(future)
            future.add_done_callback(done_callback)
        time.sleep(0.5)
        return running
    def test_valid_shutdown(self):
        self.moi.set_timeout(1.5)
        running = self.run_submit_loop(self.moi)
        self.moi.shutdown()
        self.assertFalse(running)
    def test_error_shutdown(self):
        self.moi.set_timeout(1.5)
        running = self.run_submit_loop(self.moi)
        running.pop()
        self.assertRaises(KeyError, self.moi.shutdown)
        self.assertFalse(running)
class TestExecutorAPI(TestTimeout, TestModuleOrInstance, unittest.TestCase):
    CLASS = asynchronous.Executor
    MODULE_OR_INSTANCE = CLASS()
    NAME_OF_MAP = 'map'
    def test_valid_context_manager(self):
        with self.instantiate(1.5) as executor:
            running = self.run_submit_loop(executor)
        self.assertFalse(running)
    def test_error_context_manager(self):
        error = Exception()
        with self.assertRaises(Exception) as cm:
            with self.instantiate(1.5) as executor:
                running = self.run_submit_loop(executor)
                raise error
        self.assertIs(cm.exception, error)
        self.assertFalse(running)
        with self.assertRaises(KeyError):
            with self.instantiate(1.5) as executor:
                running = self.run_submit_loop(executor)
                running.pop()
        self.assertFalse(running)
class TestModuleAPI(TestModuleOrInstance, unittest.TestCase):
    MODULE_OR_INSTANCE = asynchronous
    NAME_OF_MAP = 'map_'
def verify_error():
    sys.stderr.seek(0, io.SEEK_SET)
    for line in sys.stderr:
        if line == 'queue.Full\n':
            break
    else:
        sys.stderr.seek(0, io.SEEK_SET)
        sys.__stderr__.write(sys.stderr.read())
        sys.__stderr__.flush()
def cause_error(obj):
    sys.stderr = io.StringIO()
    atexit.register(verify_error)
    inspect.currentframe().f_back.f_back.f_locals['queue'].put_nowait(obj)
def return_(obj):
    return obj
# noinspection PyUnusedLocal
def throw(exception, *args):
    raise exception
class Silencer:
    def __init__(self, silenced):
        self.__silenced = silenced
        self.__ident = _thread.get_ident()
    @property
    def silenced(self):
        return self.__silenced
    def __getattr__(self, name):
        return (getattr(self.__silenced, name)
                if _thread.get_ident() == self.__ident else
                self)
    def __call__(self, *args, **kwargs):
        return self
@contextlib.contextmanager
def silence_other_threads():
    sys.stdout, sys.stderr = Silencer(sys.stdout), Silencer(sys.stderr)
    try:
        yield
    finally:
        sys.stdout, sys.stderr = sys.stdout.silenced, sys.stderr.silenced
class TestFutureAPI(TestTimer, TestTimeout, unittest.TestCase):
    CLASS = asynchronous._Future
    def test_valid_representation(self):
        future = self.instantiate(None, time.sleep, (0.1,), {})
        self.assertRegex(repr(future), r'^<_Future at \d+ state=PENDING>$')
        future._set_running_or_notify_cancel()
        self.assertRegex(repr(future), r'^<_Future at \d+ state=RUNNING>$')
        future._set_running_or_notify_cancel()
        self.assertRegex(
            repr(future),
            r'^<_Future at \d+ state=CANCELLED raised TimeoutError>$'
        )
        future = self.instantiate(None, time.sleep, (0.1,), {})
        future._set_running_or_notify_cancel()
        time.sleep(0.5)
        self.assertRegex(
            repr(future),
            r'^<_Future at \d+ state=FINISHED raised TimeoutError>$'
        )
        self.assertIsNone(future.exception())
        self.assertRegex(
            repr(future),
            r'^<_Future at \d+ state=FINISHED returned NoneType>$'
        )
    def test_error_representation(self):
        future = self.instantiate(0.5, cause_error, (None,), {})
        future._set_running_or_notify_cancel()
        self.assertRaises(TypeError, future.result)
        self.assertIsInstance(future.exception(), TimeoutError)
        self.assertRegex(
            repr(future),
            r'^<_Future at \d+ state=ERROR raised TimeoutError>$'
        )
        future = self.instantiate(0.5, cause_error, ((False, 'okay'),), {})
        future._set_running_or_notify_cancel()
        self.assertEqual(future.result(), 'okay')
        self.assertRegex(
            repr(future),
            r'^<_Future at \d+ state=ERROR returned str>$'
        )
    def test_cancel(self):
        future = self.instantiate(None, time.sleep, (0.1,), {})
        self.assertRaises(AttributeError, future.cancel)
        future._set_running_or_notify_cancel()
        future.cancel()
        self.assertTrue(future.cancelled())
        future = self.instantiate(None, time.sleep, (0.1,), {})
        checker = set()
        future.add_done_callback(checker.add)
        future._set_running_or_notify_cancel()
        future.cancel()
        future.cancel()
        self.assertIs(checker.pop(), future)
        self.assertFalse(checker)
    def test_cancelled(self):
        future = self.instantiate(None, time.sleep, (0.1,), {})
        self.assertFalse(future.cancelled())
        future._set_running_or_notify_cancel()
        self.assertFalse(future.cancelled())
        self.assertIsNone(future.result())
        self.assertFalse(future.cancelled())
        future = self.instantiate(None, time.sleep, (0.1,), {})
        future._set_running_or_notify_cancel()
        future.cancel()
        self.assertTrue(future.cancelled())
        future = self.instantiate(0.1, time.sleep, (1,), {})
        future._set_running_or_notify_cancel()
        time.sleep(0.5)
        self.assertTrue(future.cancelled())
    def test_running(self):
        future = self.instantiate(None, time.sleep, (0.1,), {})
        self.assertFalse(future.running())
        future._set_running_or_notify_cancel()
        self.assertTrue(future.running())
        self.assertIsNone(future.result())
        self.assertFalse(future.running())
        future = self.instantiate(None, time.sleep, (0.1,), {})
        future._set_running_or_notify_cancel()
        future.cancel()
        self.assertFalse(future.running())
        future = self.instantiate(0.1, time.sleep, (1,), {})
        future._set_running_or_notify_cancel()
        time.sleep(0.5)
        self.assertFalse(future.running())
    def test_done(self):
        future = self.instantiate(None, time.sleep, (0.1,), {})
        self.assertFalse(future.done())
        future._set_running_or_notify_cancel()
        self.assertFalse(future.done())
        self.assertIsNone(future.result())
        self.assertTrue(future.done())
        future = self.instantiate(None, time.sleep, (None,), {})
        future._set_running_or_notify_cancel()
        self.assertIsInstance(future.exception(), TypeError)
        self.assertTrue(future.done())
    def test_result_immediate(self):
        data = os.urandom(1 << 20)
        future = self.instantiate(None, return_, (data,), {})
        future._set_running_or_notify_cancel()
        self.assertEqual(future.result(), data)
        test_exception = Exception('test')
        future = self.instantiate(None, throw, (test_exception,), {})
        future._set_running_or_notify_cancel()
        with self.assertRaises(Exception) as cm:
            future.result()
        self.assertIsInstance(cm.exception, type(test_exception))
        self.assertEqual(cm.exception.args, test_exception.args)
    def test_result_delay(self):
        future = self.instantiate(None, delay_run, (0, operator.add, 1, 2), {})
        self.start_timer()
        future._set_running_or_notify_cancel()
        self.assertEqual(future.result(), 3)
        self.stop_timer(0.1)
        future = self.instantiate(None, delay_run, (1, operator.add, 2, 3), {})
        self.start_timer()
        future._set_running_or_notify_cancel()
        self.assertEqual(future.result(), 5)
        self.stop_timer(1)
        future = self.instantiate(0.5, delay_run, (0, operator.add, 1, 2), {})
        self.start_timer()
        future._set_running_or_notify_cancel()
        self.assertEqual(future.result(), 3)
        self.stop_timer(0.1)
        future = self.instantiate(0.5, delay_run, (1, operator.add, 2, 3), {})
        self.start_timer()
        future._set_running_or_notify_cancel()
        self.assertRaises(TimeoutError, future.result)
        self.stop_timer(0.5)
    def test_result_before_running(self):
        future = self.instantiate(0.1, delay_run, (0, operator.add, 1, 2), {})
        delay_run(0.5, future._set_running_or_notify_cancel, sync=False)
        self.start_timer()
        self.assertEqual(future.result(), 3)
        self.stop_timer(0.5)
    def run_time_check(self, test):
        self.start_timer()
        test()
        self.stop_timer(0.5)
    def run_waiter_check(self, threads, *tests):
        future = self.instantiate(1, delay_run, (0.5, operator.add, 1, 2), {})
        future._set_running_or_notify_cancel()
        # noinspection PyUnresolvedReferences
        result = queue.SimpleQueue()
        with silence_other_threads():
            for test in itertools.islice(itertools.cycle(tests), threads):
                args = self.run_time_check, (lambda: test(future),), {}, result
                _thread.start_new_thread(asynchronous._run, args)
            for _ in range(threads):
                error, value = result.get(True, 1.5)
                self.assertFalse(error)
    def test_result_with_waiters(self):
        self.run_waiter_check(
            10,
            lambda future: self.assertEqual(future.result(), 3)
        )
    def test_exception_immediate(self):
        data = os.urandom(1 << 20)
        future = self.instantiate(None, return_, (data,), {})
        future._set_running_or_notify_cancel()
        self.assertIsNone(future.exception())
        test_exception = Exception('test')
        future = self.instantiate(None, throw, (test_exception,), {})
        future._set_running_or_notify_cancel()
        self.assertIsInstance(future.exception(), type(test_exception))
        self.assertEqual(future.exception().args, test_exception.args)
    def test_exception_delay(self):
        future = self.instantiate(None, delay_run, (0, operator.add, 1, 2), {})
        self.start_timer()
        future._set_running_or_notify_cancel()
        self.assertIsNone(future.exception())
        self.stop_timer(0.1)
        future = self.instantiate(None, delay_run, (1, operator.add, 2, 3), {})
        self.start_timer()
        future._set_running_or_notify_cancel()
        self.assertIsNone(future.exception())
        self.stop_timer(1)
        future = self.instantiate(0.5, delay_run, (0, operator.add, 1, 2), {})
        self.start_timer()
        future._set_running_or_notify_cancel()
        self.assertIsNone(future.exception())
        self.stop_timer(0.1)
        future = self.instantiate(0.5, delay_run, (1, operator.add, 2, 3), {})
        self.start_timer()
        future._set_running_or_notify_cancel()
        self.assertIsInstance(future.exception(), TimeoutError)
        self.assertFalse(future.exception().args)
        self.stop_timer(0.5)
    def test_exception_before_running(self):
        future = self.instantiate(0.1, delay_run, (0, operator.add, 1, 2), {})
        delay_run(0.5, future._set_running_or_notify_cancel, sync=False)
        self.start_timer()
        self.assertIsNone(future.exception())
        self.stop_timer(0.5)
    def test_exception_with_waiters(self):
        self.run_waiter_check(
            10,
            lambda future: self.assertIsNone(future.exception())
        )
    def test_result_and_exception_waiters(self):
        self.run_waiter_check(
            10,
            lambda future: self.assertEqual(future.result(), 3),
            lambda future: self.assertIsNone(future.exception())
        )
        self.run_waiter_check(
            10,
            lambda future: self.assertIsNone(future.exception()),
            lambda future: self.assertEqual(future.result(), 3)
        )
    def test_valid_add_done_callback(self):
        future = self.instantiate(None, time.sleep, (0,), {})
        requires_callback = {future}
        future.add_done_callback(requires_callback.remove)
        self.assertIn(future, requires_callback)
        future._set_running_or_notify_cancel()
        self.assertIsNone(future.exception())
        self.assertFalse(requires_callback)
        requires_callback.add(future)
        future.add_done_callback(requires_callback.remove)
        self.assertFalse(requires_callback)
    def test_error_add_done_callback(self):
        future = self.instantiate(None, time.sleep, (0,), {})
        requires_callback = [{future} for _ in range(10)]
        callbacks = [s.remove for s in requires_callback]
        error = Exception()
        callbacks.insert(5, functools.partial(throw, error))
        for fn in callbacks:
            future.add_done_callback(fn)
        future._set_running_or_notify_cancel()
        with self.assertRaises(Exception) as cm:
            future.exception()
        self.assertIs(cm.exception, error)
        self.assertFalse(any(requires_callback))
    def test_set_running_or_notify_cancel(self):
        future = self.instantiate(None, time.sleep, (0.1,), {})
        self.assertFalse(future.running() or future.done())
        future._set_running_or_notify_cancel()
        self.assertTrue(future.running())
        future._set_running_or_notify_cancel()
        self.assertTrue(future.cancelled())
    def test_not_empty_queue(self):
        data = os.urandom(1 << 20)
        future = self.instantiate(None, return_, (data,), {})
        future._set_running_or_notify_cancel()
        # noinspection PyUnresolvedReferences
        result = queue.SimpleQueue()
        with silence_other_threads():
            for _ in range(2):
                delay_run(
                    0.1,
                    asynchronous._run,
                    lambda: self.assertEqual(future.result(), data),
                    (),
                    {},
                    result,
                    sync=False
                )
            for _ in range(2):
                error, value = result.get(True, 0.2)
                self.assertFalse(error)
if __name__ == '__main__':
    unittest.main()