worktoy 0.99.31

Collection of Utilities

WorkToy v0.99.xx

WorkToy collects common utilities. It is available for installation via pip:

pip install worktoy

Version 0.99.xx is in final stages of development. It will see no new features, only bug fixes and documentation updates. Upon completion of tasks given below, version 1.0.0 will be released. Navigate with the table of contents below.

Table of Contents

• WorkToy v0.99.xx
  • Table of Contents
  • Installation
  • Usage
    • desc
    • ezdata
    • keenum
    • meta
    • parse
    • text
    • yolo
  • Development

Installation

pip install worktoy

Usage

worktoy.desc

Background

The descriptor protocol in Python allows significant customisation of the attribute access mechanism. To understand this protocol, consider a class body assigning an object to a name. During the class creation process, when this line is reached, the object is assigned to the name. For the purposes of this discussion, the object is created when this line is reached, for example:

class PlanePoint:
  """This class represent an integer valued point in the plane. """
  x = Integer(0)
  y = Integer(0)  # Integer is defined below. In practice, classes should 
  #  be defined in dedicated files.

The above class ´PlanePoint´ owns a pair of attributes. These are instances of the ´Integer´ class defined below. The ´Integer´ class is a descriptor and is thus the focus of this discussion.

class Integer:
  """This descriptor class wraps an integer value. More details will be 
  added throughout this discussion."""
  __fallback_value__ = 0
  __default_value__ = None
  __field_name__ = None
  __field_owner__ = None

  def __init__(self, *args) -> None:
    for arg in args:
      if isinstance(arg, int):
        self.__default_value__ = arg
        break
    else:  # See explanation below for the unusual for-else statement.
      self.__default_value__ = self.__fallback_value__

  def __set_name__(self, owner: type, name: str) -> None:
    """Powerful method called automatically when the class owning the 
    descriptor instance is finally created. It informs the descriptor 
    instance of its owner and importantly, it informs the descriptor of 
    the name by which it appears in the class body. """
    self.__field_name__ = name
    self.__field_owner__ = owner

  def __get__(self, instance: object, owner: type) -> int:
    """Getter-function."""

Unusual for-else statement

The code above features the unusual and under-appreciated for-else statement in the __init__ method. If the for loop terminates by the ´break´ keyword, the ´else´ block is skipped. If the for loop completes without hitting the ´break´ keyword, the ´else´ block is executed. As used here, the for loop tries to find an integer from the received positional arguments. If it finds one, it assigns it and hits the ´break´ keyword and the ´else´ block is skipped. If unable to find an integer, the for loop will terminate normally, and the ´else´ block will execute, where the fallback value is conveniently waiting to be assigned.

The __set_name__ method

This method is a powerful addition to the descriptor protocol. To understand its significance, consider that the descriptor class was instantiated in the class body, during creation of the owning class, but before the owning class was actually created. When the owning class is created, every instance of a class that implements this method, that was assigned to a name in the class body of the newly created class, will have this method called with the owning class and the name at which the instance appears in the class body.

The __get__ method

This method is called in two different situations that differ substantially. When the descriptor is accessed through the owning class and when the descriptor is accessed through an instance of the owning class. This distinction may be likened to that of accessing a method. Accessing a method through its owning class returns an unbound method. In contrast, accessing a method through an instance of the class returns a method bound to this instance. This is why the first argument of a method is ´self´ (except for ´classmethods´ and ´staticmethods´).

If the instance is None, it signifies that the descriptor is being accessed through the owning class. In this case, it is the opinion of this author that the descriptor should always return itself. This allows other objects to access the descriptor object itself, instead of the value it wraps. Choosing this return value also follows the pattern used by methods. Nevertheless, descriptor classes are allowed to return any object when accessed through the owning class.

This brings the discussion to the central situation allowing significant customization of what it even means for a Python class to have an attribute. This part of the discussion will explain some typical uses before describing the novel use case provided by the ´AttriBox´ class, which is the central feature of the ´worktoy.desc´ module.

Property-like behaviour

A common implementation of the descriptor protocol makes use of a 'private' attribute owned by the instance. Python does not enforce 'private' attributes, but the convention is to denote attributes intended to remain 'private' with a leading underscore. While convention only, IDEs and linters will commonly mark as warning or even an error when this convention is not observed. It is the opinion of this author that issues caused by failure to observe this convention does not merit fixing, with the sole exception being security related issues.

Below is an example using a descriptor class to expose a 'private' attribute through dedicated accessor functions.

class SpacePoint:
  """This class represent an integer valued point in the plane. """
  _x = None
  _y = None
  x = Float(0.)
  y = Float(0.)

Like before, it is the descriptor class more so that the owner class that is the subject of this discussion:

class Float:
  """Descriptor class wrapping a floating point value"""
  __field_name__ = None
  __field_owner__ = None
  __fallback_value__ = 0.0
  __default_value__ = None

  def __init__(self, *args, ) -> None:
    for arg in args:
      if isinstance(arg, float):
        self.__default_value__ = arg
        break
    else:  # See explanation below for the unusual for-else statement.
      self.__default_value__ = self.__fallback_value__

  def __set_name__(self, owner: type, name: str) -> None:
    self.__field_name__ = name
    self.__field_owner__ = owner

  def _getPrivateName(self) -> str:
    """This 'private' method formats the name at which instances of this 
    descriptor class will expect 'private' attributes. """
    if self.__field_name__ is None:
      e = """Unable to format private name, before owning class is 
      created!"""
      raise RuntimeError(e)
    if isinstance(self.__field_name__, str):
      return """_%s""" % self.__field_name__
    e = """Expected field name to be instance of str, but received '%s' 
    of class '%s'!"""
    fieldName = self.__field_name__
    typeName = type(fieldName).__name__
    raise TypeError(e % (fieldName, typeName))

  def __get__(self, instance: object, owner: type, **kwargs) -> object:
    """Getter-function. If instance is None, the descriptor instance 
    returns itself. Otherwise, the descriptor attempts to find a value at 
    the expected private name. If no value is present, the default value 
    of the descriptor is assigned to the expected private name and the 
    getter function is called recursively again. This pattern ensures 
    that if the descriptor lacks permission or is otherwise unable to 
    assign values to owning instances, an error is raised immediately. """
    if instance is None:
      return self
    pvtName = self._getPrivateName()
    if getattr(instance, pvtName, None) is not None:
      return getattr(instance, pvtName)
    if kwargs.get('_recursion', False):
      raise RecursionError
    setattr(instance, pvtName, self.__default_value__)
    return self.__get__(instance, owner, _recursion=True)

  def __set__(self, instance: object, value: object) -> None:
    """Setter-function. Although not provided in this example, setter 
    functions provide a convenient place to enforce constraints, in 
    particular type guarding as well as casting and validation. """
    pvtName = self._getPrivateName()
    setattr(instance, pvtName, value)

  def __delete__(self, instance: object) -> None:
    """IMPORTANT! This method is what is called when the 'del' keyword is 
    used on an attribute through an instance. This method is NOT the same 
    as __del__. This latter method is called when the object itself is 
    deleted. Regarding that particular method, this author finds occasion 
    to mention never having observed it implemented in the wild. """
    pvtName = self._getPrivateName()
    if hasattr(instance, pvtName):
      return delattr(instance, pvtName)
    e = """Instance of class '%s' does not have attribute '%s'!"""
    raise AttributeError(e % (instance.__class__.__name__, pvtName))

The above describes a common pattern of using the descriptor protocol to expose 'private' attributes through dedicated accessor functions. The above is a very straightforward example, but the descriptor protocol is capable of much more!

The property class

It is likely that some readers are familiar with the property class. Where we are going we do not need the property class! Nevertheless, let us now see a descriptor class that implements the behaviour of the property class. The property class may seem like advanced or sophisticated, but as this discussion progresses, the mundane and simple nature of it will reveal itself.

To avoid confusion, this implementation will be named Field as the name property is already taken.

class Field:
  """Descriptor class wrapping a value"""
  __field_name__ = None
  __field_owner__ = None
  __default_value__ = None
  __getter_function__ = None
  __setter_function__ = None
  __deleter_function__ = None

  def __init__(self, *args) -> None:
    if args:
      self.__default_value__ = args[0]

  def __set_name__(self, owner: type, name: str) -> None:
    self.__field_name__ = name
    self.__field_owner__ = owner

  def _getGetterFunction(self, ) -> Callable:
    """This 'private' method returns the getter-function. This must be
      explicitly defined by the GET decorator for the descriptor to 
      implement getting. This allows significant customization of the 
      attribute access mechanism. """
    if self.__getter_function__ is None:
      e = """The getter-function must be explicitly set by the SET 
      decorator!"""
      raise AttributeError(e)
    if callable(self.__getter_function__):
      return self.__getter_function__
    e = """Expected getter-function to be callable, but received '%s'
        of class '%s'!"""
    func = self.__getter_function__
    typeName = type(func).__name__
    raise TypeError(e % (func, typeName))

  def _getSetterFunction(self, ) -> Callable:
    """This 'private' method returns the setter-function. This must be 
    explicitly defined by the SET decorator for the descriptor to 
    implement setting. Please note, that the setter-function is by no 
    means required and in particular when the descriptor is used to 
    provide a readonly attribute, the setter-function should remain 
    undefined or even defined as a Callable raising an exception. If so, 
    this author suggests raising a TypeError to indicate that this is a 
    readonly object. Alternatively, raising an AttributeError is also 
    observed, although such an error indicates that the instance is not 
    presently capable of supporting this attribute. Not that the object 
    is entirely incapable of supporting setting the attribute. """
    if self.__setter_function__ is None:
      e = """The setter-function must be explicitly set by the SET 
      decorator!"""
      raise AttributeError(e)
    if callable(self.__setter_function__):
      return self.__setter_function__
    e = """Expected setter-function to be callable, but received '%s'
        of class '%s'!"""
    func = self.__setter_function__
    typeName = type(func).__name__
    raise TypeError(e % (func, typeName))

  def _getDeleterFunction(self, ) -> Callable:
    """This 'private' method returns the deleter-function. This is the 
    method called when the 'del' keyword is used on an attribute through
    an instance. This method is NOT the same as __del__ as discussed 
    above. This author notes having never had problem solved by 
    implementation of the deleter-function. """
    if self.__deleter_function__ is None:
      e = """The deleter-function must be explicitly set by the SET 
      decorator!"""
      raise AttributeError(e)
    if callable(self.__deleter_function__):
      return self.__deleter_function__
    e = """Expected deleter-function to be callable, but received '%s'
        of class '%s'!"""
    func = self.__deleter_function__
    typeName = type(func).__name__
    raise TypeError(e % (func, typeName))

  def GET(self, callMeMaybe: Callable) -> Callable:
    """As alluded to above, this method sets the method that should be 
    used as the getter-function. Classes owning instances of this 
    descriptor class should use this method as a decorator to define the 
    method that should be invoked by the __get__ method. Please note, 
    that this method as well as the other method setters return the 
    decorated method as it is without augmenting it. """
    if self.__getter_function__ is not None:
      e = """The getter-function has already been set!"""
      raise AttributeError(e)
    if not callable(callMeMaybe):
      e = """Expected getter-function to be callable, but received '%s'
        of class '%s'!"""
      typeName = type(callMeMaybe).__name__
      raise TypeError(e % (callMeMaybe, typeName))
    self.__getter_function__ = callMeMaybe
    return callMeMaybe

  def SET(self, callMeMaybe: Callable) -> Callable:
    """Similar to the GET method defined above, this method should be 
    used to decorate the desired setter-function on the owning class. """
    if self.__setter_function__ is not None:
      e = """The setter-function has already been set!"""
      raise AttributeError(e)
    if not callable(callMeMaybe):
      e = """Expected setter-function to be callable, but received '%s'
            of class '%s'!"""
      typeName = type(callMeMaybe).__name__
      raise TypeError(e % (callMeMaybe, typeName))
    self.__setter_function__ = callMeMaybe
    return callMeMaybe

  def DELETE(self, callMeMaybe: Callable) -> Callable:
    """Similar to the GET and SET methods defined above, this method 
    defines the method on the owning class that is responsible for 
    deleting the attribute from the owning instance. """
    if self.__deleter_function__ is not None:
      e = """The deleter-function has already been set!"""
      raise AttributeError(e)
    if not callable(callMeMaybe):
      e = """Expected deleter-function to be callable, but received '%s'
            of class '%s'!"""
      typeName = type(callMeMaybe).__name__
      raise TypeError(e % (callMeMaybe, typeName))
    self.__deleter_function__ = callMeMaybe
    return callMeMaybe

  def __get__(self, instance: object, owner: type, **kwargs) -> object:
    """Getter-function. As before, when instance is None, the descriptor 
    returns itself. Otherwise, the dedicated getter-function is used to 
    get the descriptor value. As mentioned, this function should be 
    defined by the owning class using the GET decorator. The function 
    should be a bound method, as this method assumes that the first 
    argument should be the instance itself, or 'self'. 
    
    Please note, that the GET decorator is called before the owning 
    instance is ever created. This means that this descriptor instance 
    does own the getter-function, but as an unbound method, meaning that 
    the getter-function thus defined is common between all instances of 
    the owning class, despite being an instance method.  The same is true 
    for the setter-function and the deleter-function. """
    if instance is None:
      return self
    getter = self._getGetterFunction()
    return getter(instance, )

  def __set__(self, instance: object, value: object) -> None:
    """Setter-function. As before, the setter-function should be defined
    by the owning class using the SET decorator. If the descriptor is 
    not intended to support setting, the setter-function should be 
    explicitly defined to raise an appropriate exception rather than 
    just left undefined, although this is not a strict requirement. """
    setter = self._getSetterFunction()
    setter(instance, value)

  def __delete__(self, instance: object) -> None:
    """Deleter-function. As before, the deleter-function should be 
    defined by the owning class using the DELETE decorator. Although not 
    commonly used, this author suggests either providing an 
    implementation or a method that raises a TypeError. """
    deleter = self._getDeleterFunction()
    deleter(instance, )

Having implemented the Field class, some readers will certainly recognize its use as identical, more or less, to that of the property. One exception to note however is that instances of Field should be defined at the top of the class body, unlike the property class.

class Server:
  """This example class uses instances of the Field class to define the 
  address and port attributes typically used in server classes. """

  __fallback_address__ = 'localhost'
  __fallback_port__ = 12345

  __private_address__ = None
  __private_port__ = None

  address = Field()
  port = Field()

  @address.GET
  def _getAddress(self, ) -> str:
    """Getter-function responsible for returning the address."""
    if self.__private_address__ is None:
      return self.__fallback_address__
    return self.__private_address__

  @address.SET
  def _setAddress(self, value: str) -> None:
    """Setter-function responsible for setting the address."""
    self.__private_address__ = value

  @address.DELETE
  def _deleteAddress(self, ) -> Never:
    """For the sake of example, let us disable the deleter-function to 
    illustrate how the accessor provide a convenient protection against 
    inadvertent deletion of attributes. Please note the use of the 
    'Never' type hint. This is meant to indicate that this method will 
    never return. Once this method is invoked, the program will certainly 
    raise an exception. """
    e = """The address attribute is read-only!"""
    raise TypeError(e)

  @port.GET
  def _getPort(self) -> int:
    """Getter-function responsible for returning the port."""
    if self.__private_port__ is None:
      return self.__fallback_port__
    return self.__private_port__

  @port.SET
  def _setPort(self, port: int) -> None:
    """Setter-function responsible for setting the port."""
    self.__private_port__ = port

  @port.DELETE
  def _delPort(self, ) -> Never:
    """Disabled deleter-function for the port attribute. The same as for 
    the address attribute."""
    e = """The port attribute is read-only!"""
    raise TypeError(e)

The above Server class does have an unfortunate boilerplate to functionality ratio. Hopefully it provides a helpful illustration of the descriptor protocol. While implementing all methods of the descriptor protocol, the Field class could be further enhanced by implementing strong type checking or even casting. This is left as an exercise for those readers who have read the guidelines in the contribution section.

The AttriBox class - Prologue

This class is the central feature of the worktoy.desc module. It is the logical next step of the implementations hitherto discussed. Before diving into the implementation, let us begin with a use case.

PySide6 - Qt for Python

The PySide6 library provides Python bindings for the Qt framework. What is Qt? For the purposes of this discussion, Qt is a framework for developing professional and high-quality graphical user interfaces. Entirely with Python. Below is a very simple script that opens an empty window and nothing more.

import sys
from PySide6.QtWidgets import QApplication, QMainWindow
from PySide6.QtCore import QSize


class MainWindow(QMainWindow):
  def __init__(self, parent=None):
    super().__init__(parent)
    self.setWindowTitle("Hello, World!")
    self.setMinimumSize(QSize(480, 320))


if __name__ == "__main__":
  app = QApplication(sys.argv)
  window = MainWindow()
  window.show()
  sys.exit(app.exec())

From here, the window class can be extended to include buttons, text boxes, and other widgets. Qt provides off-the-shelf widgets for much common use. These widgets may be subclassed further customizing their appearance or behaviour. Actually advanced users may even create entirely new widgets from the ground up. The possibilities are endless.

Before we get carried away, we need to keep one very important quirk in mind. Qt provides a vast array of classes that all inherit from the QObject class. This class has an odd, but very unforgiving requirement. No instances of QObject may be instantiated without a running QCoreApplication. This immediately presents a problem to our otherwise elegant descriptor protocol: We are not permitted to instantiate instances before the main script runs. Such as during class creation. For this reason, the AttriBox class was created to implement lazy instantiation! Let us now see how we might create a more advanced graphical user interface whilst adhering to the QObject requirement.

The AttriBox class - Lazy instantiation

from PySide6.QtWidgets import QApplication, QMainWindow, QWidget
from PySide6.QtWidgets import QVBoxLayout, QHBoxLayout, QLabel
from PySide6.QtCore import QSize

from worktoy.desc import AttriBox, THIS


class MainWindow(QMainWindow):
  """Subclass of QMainWindow. This class provides the main window for the 
  application. """

  baseWidget = AttriBox[QWidget](THIS)
  verticalLayout = AttriBox[QVBoxLayout]()
  welcomeLabel = AttriBox[QLabel]()

  def show(self) -> None:
    """Before invoking the parent method, we will setup the window. """
    self.setMinimumSize(QSize(480, 320))
    self.setWindowTitle("WorkToy!")
    self.welcomeLabel.setText("""Welcome to AttriBox!""")
    self.verticalLayout.addWidget(self.welcomeLabel)
    self.baseWidget.setLayout(self.verticalLayout)
    self.setCentralWidget(self.baseWidget)
    QMainWindow.show(self)


if __name__ == "__main__":
  app = QApplication([])
  window = MainWindow()
  window.show()
  app.exec()

The above script makes use of the lazy instantiation provided by the AttriBox class. While some readers may have recognized the similarities between Field and property, many readers are presently picking jaws up from the floor, pinching themselves or seeking spiritual guidance. The AttriBox not only implements an enhanced version of the descriptor protocol, but it does so on a single line, where it even provides syntactic sugar for defining the class intended for lazy instantiation. Let us examine AttriBox in more detail.

The AttriBox class

from PySide6.QtWidgets import QApplication, QMainWindow, QWidget
from PySide6.QtWidgets import QVBoxLayout, QHBoxLayout, QLabel
from PySide6.QtCore import QSize

from worktoy.desc import AttriBox, THIS


class MainWindow(QMainWindow):
  """Subclass of QMainWindow. This class provides the main window for the 
    application. """

  baseWidget = AttriBox[QWidget](THIS)
  #  The above line creates a descriptor at name 'baseWidget' that will 
  #  instantiate a QWidget instance. When the __get__ on the descriptor
  #  tries to retrieve the value it owns, only then will the value be 
  #  instantiated. When instantiating the value, the arguments in the 
  #  parentheses are passed to the constructor of the class. That brings 
  #  us to the 'THIS' token. When instantiating the value, the 'THIS' token
  #  is replaced with the instance of the owning class. This is convenient 
  #  for the 'baseWidget' attribute, as it allows the instance created to 
  #  set its parent to the owning instance.

The use case pertaining to the PySide6 library makes great use of the lazy instantiation. In fact, the motivation that led to the creation of the AttriBox class was this need for lazy instantiation.

worktoy.desc.AttriBox - Advanced Instantiation

PENDING... WorkToy v1 will not release until this documentation is complete.

worktoy.meta - Understanding the Python metaclass

Readers may associate the word meta with crime on account of the hype created around the term metaverse. This author hopes readers will come to associate the word instead with the Python metaclass. The 'worktoy.meta' module provides functions and classes allowing a more streamlined approach to metaclass programming. This documentation explains the functionality of metaclasses in general and how this module provides helpful tools.

Everything is an object!

Python operates on one fundamental idea: Everything is an object. Everything. All numbers, all strings, all functions, all modules and everything that you can reference. Even object itself is an object. This means that everything supports a core set of attributes and methods defined on the core object type.

Extensions of object

With everything being an object, it is necessary to extend the functionalities in the core object type to create new types, hereinafter classes. This allows objects to share the base object, while having additional functionalities depending on their class. Python provides a number of special classes listed below:

• object - The base class for all classes. This class provides the most basic functionalities.
• int - Extension for integers. The python interpreter uses heavily optimized C code to handle integers. This is the case for several classes on this list.
• float - Extension for floating point numbers. This class provides a number of methods for manipulating floating point numbers.
• list - Extension for lists of objects of dynamic size allowing members to be of any type. As the amount of data increases, the greater the performance penalty for the significant convenience.
• tuple - Extension for tuples of objects of fixed size. This class is similar to the list class, but the size is fixed. This means that the tuple is immutable. While this is inflexible, it does allow instances to be used as keys in mappings.
• dict - Extension for mappings. Objects of this class map keys to values. Keys be of a hashable type, meaning that object itself is not sufficient. The hashables on this list are: int, float, str and tuple.
• set - Extension for sets of objects. This class provides a number of methods for manipulating sets. The set class is optimized for membership testing.
• frozenset - Provides an immutable version of set allowing it to be used as a key in mappings.
• str - Extension for strings. This class provides a number of methods for manipulating strings. The worktoy.text module expands upon some of these.

To reiterate, everything is an object. Each object belongs to the object class but may additionally belong to a class that extends the object class. For example: 7 is an object. It is an instance of object by being an instance of int which extends object. Classes are responsible for defining the instantiation of instances belonging to them. Generally speaking, classes may be instantiated by calling the class object treating it like a function. Classes may accept or even require arguments when instantiated.

Before proceeding, we need to talk about functions. Python provides two builtin extensions of object that provide standalone objects that implement functions: function and lambda. Both of these have quite unique instantiation syntax and does not follow the conventions we shall see later in this discussion.

Defining a function

Python allows the following syntax for creating a function. Please note that all functions are still objects, and all functions created with the syntax below belong to the same class function. Unfortunately, this class cannot be referred to directly. Which is super weird. Anyway, to create a function, use the following syntax:

def multiplication(a: int, b: int) -> int:
  """This function returns the product of two integers."""
  return a * b

RANT

The above function implements multiplication. It also provides the optional features: type hints and a docstring. The interpreter completely ignores these, but they are very helpful for humans. It is the opinion of this author that omitting type hints and docstrings is acceptable only when running a quick test. If anyone except you or God will ever read your code, it must have type hints and docstrings!

END OF RANT

Below is the syntax that invokes the function:

result = multiplication(7, 8)  # result is 56

In the function definition, the positional arguments were named a and b. In the above invocation, the positional arguments were given directly. Alternatively, they might have been given as keyword arguments:

result = multiplication(a=7, b=8)  # result is 56
tluser = multiplication(b=8, a=7)  # result is 56

When keyword arguments are used instead of positional arguments, the order is irrelevant, but names are required.

The star * and double star ** operators

Suppose the function were to be invoked with the numbers from a list: numbers = [7, 8], then we might invoke the multiplication function as follows:

result = multiplication(numbers[0], numbers[1])  # result is 56

Imagine the function took more than two arguments. The above syntax would still work, but would be cumbersome. Enter the star * operator:

result = multiplication(*numbers)  # result is 56

Wherever multiple positional arguments are expected, and we have a list or a tuple, the star operator unpacks it. This syntax will seem confusing, but it is very powerful and is used extensively in Python. It is also orders of magnitude more readable than the equivalent in C++ or Java.

RANT

This rant is left as an exercise to the reader

END OF RANT

Besides function calls, the star operator conveniently concatenates lists and tuples. Suppose we have two lists: a = [1, 2] and b = [3, 4] we may concatenate them in several ways:

a = [1, 2]
b = [3, 4]
ab = [a[0], a[1], b[0], b[1]]  # Method 1: ab is [1, 2, 3, 4]
ab = a + b  # Method 2: ab is [1, 2, 3, 4]
ab = [*a, *b]  # Method 3: ab is [1, 2, 3, 4]
a.extend(b)  # Method 4 modifies list 'a' in place. 
a = [1, 2, 3, 4]  # a is extended by b

Obviously, don't use the first method. The one relevant for the present discussion is the third, but the second and fourth have merit as well, but will not be used here. Finally, list comprehension is quite powerful as well but is the subject for a different discussion.

The double star ** operator

The single star is to lists and tuples as the double star is to dictionaries. Suppose we have a dictionary: data = {'a': 1, 'b': 2} then we may invoke the multiplication function as follows:

data = {'a': 1, 'b': 2}
result = multiplication(**data)  # result is 2

Like the star operator, the double star operator can be used to concatenate two dictionaries. Suppose we have two dictionaries: A = {'a': 1, 'b': 2} and B = {'c': 3, 'd': 4}. These may be combined in several ways:

A = {'a': 1, 'b': 2}
B = {'c': 3, 'd': 4}
#  Method 1
AB = {**A, **B}  # AB is {'a': 1, 'b': 2, 'c': 3, 'd': 4}
#  Method 2
AB = A | B
#  Method 3 updates A in place
A |= B
A = {'a': 1, 'b': 2}  # Resetting A
#  Method 4 updates A in place
A.update(B)

As before, the first method is the most relevant for the present discussion. Unlike the example with lists, there is not really a method that is bad like the first method with lists.

In conclusion, the single and double star operators provide powerful unpacking of iterables and mappings respectively. Each have reasonable alternatives, but it is the opinion of this author that the star operators are preferred as they are unique to this use. The plus and pipe operators are used for addition and bitwise OR respectively. When the user first sees the plus or the pipe, they cannot immediately infer that the code is unpacking the operands. Not before having identified the types of the operands. In contrast, the star in front of an object without space immediately says unpacking.

RANT

If you have ever had the misfortune of working with C++ or Java, you would know that the syntax were disgusting, but you didn't know the words for it. The functionalities coded by C++ and Java cannot be inferred easily. It is necessary to see multiple parts of the code to infer what functionality is intended. For example, suppose we have a C++ class with a constructor.

class SomeClass {
private:
  int _a;
  int _b;
public:
  int a;
  SomeClass(int a, int b) {
      // Constructor code
  }
  int b {
    return _b;
  }
};

Find the constructor above. It does not have a name that means "Hello there, I am a constructor". Instead, it is named the same as the class itself. So to find the constructor, you need to identify the class name first then go through the class to find name again. The decision for this naming makes sense in that it creates something with the name called. But it significantly reduces readability. The second attack on human dignity is the syntax for the function definition. Where the class defines the public variable 'a', the syntax used is not bad. But because the syntax is identical for the functions, it increases the amount of code required to infer that a function is being created.

The two examples of nauseating syntax above do not serve any performance related purpose. Software engineering and development requires the full cognitive capability of the human brain. Deliberately obscuring code, reduces the cognitive capacity left over for actual problem-solving. This syntax is kept in place for no other purpose than gate-keeping.

END OF RANT

The famous function signature: def someFunc(*args, **kwargs)

Anyone having browsed through Python documentation or code may have marvelled at the function signature: def someFunc(*args, **kwargs). The signature means that the function accepts any number of positional arguments as well as any number of keyword arguments. This allows one function to accept multiple different argument signatures. While this may be convenient, the ubiquitous use of this pattern is likely motivated by the absense of function overloading in native Python. (Foreshadowing...)

The lambda function

Before getting back to class instantiation, we will round off this discussion of functions with the lambda function. The lambda function is basically the anonymous function. The syntax of it is lambda arguments: expression. Whatever the expression on the right hand side of the colon evaluates to is returned by the function. The lambda function allows inline function definition which is much more condensed that the regular function definition as defined above. This allows it to solve certain problems in one line, for example:

fb = lambda n: ('' if n % 3 else 'Fizz') + ('' if n % 5 else 'Buzz') or n

Besides flexing, the lambda function is useful when working with certain fields of mathematics, requiring implementation of many functions that fit on one line. Below is an example of a series of functions implementing Taylor series expansions. This takes advantage of the fact that many such functions may be distinguished only by a factor mapped from the term in the series.

factorial = lambda n: factorial(n - 1) * n if n else 1
recursiveSum = lambda F, n: F(n) + (recursiveSum(F, n - 1) if n else 0)
taylorTerm = lambda x, t: (lambda n: t(n) * x ** n / factorial(n))
expTerm = lambda n: 1
sinTerm = lambda n: (-1 if ((n - 1) % 4) else 1) if n % 2 else 0
cosTerm = lambda n: sinTerm(n + 1)
sinhTerm = lambda n: 1 if n % 2 else 0
coshTerm = lambda n: sinhTerm(n + 1)
exp = lambda x, n: recursiveSum(taylorTerm(x, expTerm), n)
sin = lambda x, n: recursiveSum(taylorTerm(x, sinTerm), n)
cos = lambda x, n: recursiveSum(taylorTerm(x, cosTerm), n)
sinh = lambda x, n: recursiveSum(taylorTerm(x, sinhTerm), n)
cosh = lambda x, n: recursiveSum(taylorTerm(x, coshTerm), n)

The above collection of functions implement recursive lambda functions to calculate function values of common mathematical functions including:

• exp: The exponential function.
• sin: The sine function.
• cos: The cosine function.
• sinh: The hyperbolic sine function.
• cosh: The hyperbolic cosine function.

The lambda functions implement Taylor-Maclaurin series expansions at a given number of terms and then begin by calculating the last term adding the previous term to it recursively, until the 0th term is reached. This implementation demonstrates the power of the recursive lambda function and is not at all flexing.

Instantiation of classes

Since this discussion includes class instantiations, the previous section discussing functions will be quite relevant. We left the discussion of builtin Python classes having listed common ones. Generally speaking, Python classes have a general syntax for instantiation except for those listed. Below is the instantiation of the builtin classes.

• object: obj = object() - This creates an object. Not particularly useful but does show the general syntax.
• int: number = 69 - This creates an integer.
• float: number = 420.0 - This creates a float.
• str: message = 'Hello World!' - This creates a string.
• list: data = [1, 2, 3] - This creates a list.
• tuple: data = (1, 2, 3) - This creates a tuple.
• ?: what = (1337) - What does this create? Well, you might imagine that this creates a tuple, but it does not. The interpreter first removes the redundant parentheses and then the evaluation makes it an integer. To create a single element tuple, you must add the trailing comma: what = (1337,). This applies to one element tuples, as the comma separating the elements of a multi-element tuple sufficiently informs the interpreter that this is a tuple. The empty tuple requires no commas: empty = ().
• set: data = {1, 2, 3} - This creates a set.
• dict: data = {'key': 'value'} - This creates a dictionary. If the keys are strings, the general syntax may be of greater convenience: data = dict(key='value'). Not requiring quotes around the keys. Although this syntax does not support non-string keys.
• ?: data = {} - What does this create? Does it create an empty set or an empty dictionary. This author is not actually aware, and recommends instead set() or dict() respectively when creating empty sets or dictionaries.

Except for list and tuple, the general class instantiation syntax may be applied as seen below:

• int: number = int(69)
• float: number = float(420.0)
• str: message = str('Hello World!')
• dict: data = dict(key='value') - This syntax is quite reasonable, but is limited to keys of string type.

Now let's have a look at what happens if we try to instantiate tuple, list, set or frozenset using the general syntax:

• list: data = list(1, 2, 3) - NOPE! This does not create the list predicted by common sense: data = [1, 2, 3]. Instead, we are met by the following error message: "TypeError: list expected at most 1 argument, got 3". Instead, we must use the following syntax: data = list((1, 2, 3)) or data = list([1, 2, 3]). Now the attentive reader may begin to object, as one of the above require a list to already be defined and the other requires the tuple to be defined. Let's see how one might instantiate a tuple directly:
• tuple: data = tuple(1, 2, 3) - NOPE! This does not work either! We receive the exact same error message as before. Instead, we must use one of the following: data = tuple((1, 2, 3)) or data = tuple([1, 2, 3]). The logically sensitive readers now see a significant inconsistency in the syntax: One cannot in fact instantiate a tuple nor a list directly without having a list or tuple already created. This author suggests that the following syntax should be accepted: data = smartTuple(1, 2, 3) and even: data = smartList(1, 2, 3). Perhaps this author is just being pedantic. The existing syntax is not a problem, and it's not like the suggested instantiation syntax is used anywhere else in Python.
• set: data = set(1, 2, 3,) This is correct syntax. So this works, but the suggested smartList and smartTuple functions does not, OK sure, makes sense...
• frozenset: data = frozenset([69, 420]) - This is correct syntax.

Let us have another look at the instantiations of dict and of set, but not list and tuple.

def newDict(**kwargs) -> dict:
  """This function creates a new dictionary having the key value pairs 
  given by the keyword arguments. """
  return dict(**kwargs)  # Unpacking the keyword arguments creates the dict.


def newSet(*args) -> set:
  """This function creates a new set having the elements given by the 
  positional arguments. """
  return set(args)  # Unpacking the positional arguments creates the set.


def newList(*args) -> list:
  """As long as we don't use the word 'list', we can actually instantiate 
  a list in a reasonable way."""
  return [*args, ]  # Unpacking the positional arguments creates the list.


def newTuple(*args) -> tuple:
  """Same as for list, but remember the hanging comma!"""
  return (*args,)  # Unpacking the positional arguments creates the tuple.

Custom classes

In the previous section, we examined functions and builtin classes. To reiterate, in the context of this discussion a class is an extension of object allowing objects to belong to different classes implementing different extensions of object. This raises a question: What extension of object contains object extensions? If 7 is an instance of the int extension of object, of what extension is int and instance. The answer is the type. This extension of object provides all extensions of object. This implies the surprising that type is an instance of itself.

The introduction of the type class allows us to make the following insightful statement:

7 is to int as int is to type. This means that type is responsible for instantiating new classes. A few readers may now begin to see where this is going, but before we get there, let us examine how type creates a new class. In the example below, we create a simple class and we will examine the exact steps that the type class takes during class creation.

from worktoy.desc import AttriBox


class PlanePoint:
  """Class representing a point in the plane """

  x = AttriBox[float]()
  y = AttriBox[float]()

  def __init__(self, *args) -> None:
    """Constructor for the PlanePoint class. """
    floatArgs = [float(arg) for arg in args if isinstance(arg, (int, float))]
    self.x, self.y = [*floatArgs, 0.0, 0.0][:2]

  def __abs__(self, ) -> float:
    """Returns the distance from the origin. """
    return (self.x ** 2 + self.y ** 2) ** 0.5


if __name__ == '__main__':
  P = PlanePoint(69, 420)

When the Python interpreter encounters the line beginning with the reserved keyword class, it creates a new class object, it begins a new lexical scope and the contents parentheses after the name determine what happens next. If no such parentheses are present, the default behaviour is to create a new instance of type, meaning an extension of object. This starts the following process:

• namespace: type creates a namespace object that the interpreter will use to build the new class. This object is simply an empty instance of dict.
• Class Body Execution: The interpreter goes through the class body line by line from top to bottom. When encountering an assignment, it updates the namespace accordingly.
• Class Object Creation: The interpreter passes the namespace object back to type that creates the new class object. This happens when the __new__ method of type returns.
• Descriptor Class Notification: All __set_name__ methods on objects owned by the class are notified, receiving the class object as the first argument and the name by which the object is assigned to the owning class. In the above example, the AttriBox objects are notified: PlanePoint.x.__set_name__(PlanePoint, 'x') and PlanePoint.y.__set_name__(PlanePoint, 'y').
• type.__init__: This is the final step before the type is complete and the class object is returned. Please note that the interpreter uses highly optimized C code during this whole procedure, and the type.__init__ has no C code implementation making it a noop.
• Class Instantiation: Once the class object is created, instances of the class may now be created. This begins with a call the __call__ method on the class object. This method is defined by type. If the class itself defines __call__, that method is invoked only when an instance of the class is called.
• type.__call__(cls, *args, **kwargs): This call on the type object creates the new instance of the class.
• cls.__new__(cls, *args, **kwargs): This method is responsible for creating the new instance of the class. Please note that it makes use of the __new__ method defined on the class object. This means that new classes are able to customize how new instances are created, however implementing the __init__ method defined below is more common and quite sufficient for most purposes.
• cls.__init__(self, *args, **kwargs): When the new instance is created, it is passed to the __init__ method on the class. When coding custom classes implementing the __init__ method is the most convenient way to define how new instances are initialized.

What is a metaclass?

In the previous section, we examined how type creates a new class. What exactly is type though? type is an object, but is also an extension of object whose instances themselves are extensions of object. But what if we extended type? We can do that because type itself extends object. This is what a metaclass is. An extension of the type extension of object.

Each of the steps in the class creation process described above may be customized by extending the type class. Below is a list of the methods defined on type that a custom class may override:

• __prepare__: In the previous section when the namespace object was created, this is done by the __prepare__ method on the metaclass. The type implementation of __prepare__ returns an empty dictionary. A metaclass can change this by prepopulating the items in this dictionary or even return a custom namespace object.
• __new__: This method is responsible for creating the object that will be created at the name after the class definition. This is where a new class is conventionally created, but this is by no means a requirement for a custom metaclass. It is possible to implement a metaclass that creates some other object than a new class.
• __init__: After the metaclass has created the new class object, or whatever object is created, it is passed to the __init__ method. Please note that this method is called after the __set_name__ has been applied to the objects implementing the descriptor protocol. When this method returns the new class object is created.

After the metaclass has created the new class and has returned the __init__, the metaclass is still called by the class object under certain circumstances. Below is a list of methods that on the metaclass that may be called during class lifetime:

• __call__: When an instance of the class is called, the __call__ method on the metaclass is invoked. By default, the __new__ on the created class object is called, and the object returned is passed to the __init__ method on the class object. The metaclass may override this behaviour.
• __instance_check__: When the isinstance function is called, the metaclass is called with create class and the instance. Thus, the metaclass may specify how classes derived from it determine if an instance is an instance of it. For example, a custom metaclass creating Numerical classes might recognize instances of float or int as their own.
• __subclass_check__: This is the method called when issubclass is called on a class object derived from the metaclass. It allows the metaclass to customize what classes it regards as subclasses. Similar to the __instance_check__.
• **__str__: When printing a class object, the resulting text is frequently more confusing than helpful. I defined a class named TestClass in the main script and printed it. The output was: <class '__main__.TestClass'>. But suppose we used a custom metaclass MetaType and derived from it a class called TestClass, then the default output would be: <class '[MODULE].TestClass'>, but it will not make reference to the metaclass. Instead, let us have the metaclass improve this output: [MODULE].TestClass(MetaType).
• __iter__ and __next__: Conventionally, iterating over an object happens on the instance level, and only by implementing the iteration protocol on the metaclass level can the class object itself become iterable.
• __getitem__: This method allows a metaclass to define handling of cls[key]. Please note that as of Python version 3.9, Python classes may implement a method called __class_getitem__, which is intended for the same use. In case both the metaclass and the class itself implement these classes respectively, the metaclass implementation is used and the class version is ignored.
• __setitem__: This method allows a metaclass to define handling of cls[key] = value.

Above is a non-exhaustive list of type methods that a custom metaclass may override. Before proceeding, we must discuss the role of the namespace object. A significant aspect of the custom metaclass is the ability to provide a custom namespace object.

Custom Namespace

Going back to the class creation procedure, the interpreter requests a namespace object from the metaclass. A custom metaclass may reimplement the __prepare__ method responsible for creating the custom namespace and have it return an instance of a custom namespace class. Doing so places a few subtle requirements on this class.

Preservation of KeyError

When a dictionary is accessed with a key that does not exist, a KeyError is raised. The interpreter relies on this behaviour to handle lines in the class body that are not directly assignments correctly. This is a particularly important requirement because failing to raise the expected KeyError will affect only classes that happen to include a non-assignment line. Below is a list of known situations that causes the issue:

• Decorators: Unless the decorator is a function defined earlier in the class body as an instance method able to receive a callable at the self argument, the decorator will cause the issue described. Please note that a static method would be able to receive a callable at the first position, but the static method decorator itself would cause the issue even sooner.
• Function calls: If a function not defined previously in the class body is called during the class body without being assigned to a name, the error will occur.

The issue raises an error message that will not bring attention to the namespace object. Further, classes will frequently work fine, if they happen to not include any of the above non-assignments. In summary: failing to raise the expected error must be avoided at all costs, as it will cause undefined behaviour without any indication as to the to cause.

Subclass of dict

After the class body is executed the namespace object is passed to the __new__ method on the metaclass. If the metaclass is intended to create a new class object, the metaclass must eventually call the __new__ method on the parent type class. The type.__new__ method must receive a namespace object that is a subclass of dict. It is only at this stage the requirement is enforced. Thus, it is possible to use a custom namespace object that is not a subclass of dict, but then it is necessary to implement functionality in the __new__ method on the metaclass such that a dict is passed to the type.__new__ call.

Required functionalities

Please note that this section pertains only to functionalities whose absense will cause the interpreter to raise an exception. The functionalities described here cannot be said to be sufficient for any degree of functionality. A custom namespace class must additionally implement whatever functionality is required for its intended purpose.

• __getitem__: This method must implement this method such that if a normal dictionary would raise an error on receiving a key, then that error must still be raised. Please note, that the interpreter handles this exception silently. Other than this situation, the __getitem__ method are otherwise free to do anything it wants.
• __setitem__: The namespace object must return a callable object at name __setitem__, that accepts three positional arguments: the namespace instance at the self argument, as well as the key and the value. As long as a callable is at the name, and it does not raise an error upon receiving three arguments, the namespace object can do whatever it wants. It does not even have to remember anything.

Potential functionalities

This section describes functionalities that is certain to preserve all information received in the class body. This is an enhancement compared to the default namespace object. It permits the __new__ in the metaclass access to all information encountered in the class body. As long as this is satisfied, there is little additional functionality the namespace object may provide to the __new__ method. Nevertheless, readers are encouraged to experiment with custom namespace classes beyond this.

Custom Metaclass Requirements

This section illustrates the immense flexibility of the custom metaclass, by just how little is actually required for the interpreter to go through the class creation process without raising an exception. This author has found only two requirements for the custom metaclass:

• Callable: The object used as metaclass must be callable.
• Accept three positional arguments: As well as being callable, three positional arguments are passed to it. As long as doing so does not raise an exception, the metaclass is free to do whatever it wants.

And that is all that is required. The metaclass is typically a subclass of type, but is not required. Conventionally, some kind of class object is created, but is not required. The metaclass is not even required to return anything in which case, the None object will appear at the given class name. Thus, the custom metaclass can be used to create new classes, but in reality it can be used to create anything. It could be used to replace functions defined with the def keyword. Readers are encouraged to dream up new uses for the custom metaclass.

The remainder of this documentation focus on the worktoy.meta module and the classes and functions defined therein. These focus on the more conventional applications of the custom metaclass, that is, creation of classes having functionalities beyond the default Python classes.

The worktoy.meta module

Nomenclature

Before proceeding, let us define terms:

• cls - A newly created class object
• self - A newly created object that is an instance of the newly created class.
• mcls - The metaclass creating the new class.
• namespace - This is where the class body is stored during class creation.

AbstractMetaclass and AbstractNamespace

These abstract baseclass illustrates an elegant metaclass pattern. The namespace class records every assignment in the class body, even if a name is assigned a value for the second time. The namespace class also implements a method called compile which returns a regular dictionary with the items the metaclass should pass on to the type.__new__ method. Without further subclassing, instances of this namespace class, will provide behaviour indistinguishable from the default behaviour.

The abstract metaclass implements the __prepare__ class method which returns creates an instance of the abstract namespace class defined above. In the __new__ method the metaclass retrieves the final namespace dictionary by calling the compile method on the namespace object. With this it calls the type.__new__ method with the thus obtained namespace object. The class object returned from the call to type.__new__ is returned by the abstract metaclass.

This pair of abstract classes provides a solid pair of baseclasses. The pattern is convenient, the metaclass instantiates the namespace object. Without loss of information, the namespace object is returned to the metaclass. Here the metaclass obtains the final namespace dictionary from the compile method on the namespace object.

Singleton

The singleton term is well understood as a class having only one instance. Typically, such a class is callable, but instead of creating a new instance, the same singleton instance is returned. However, when the singleton class is called the singleton instance will have its __init__ repeated with whatever arguments are passed. This allows the singleton instance to update itself. If this is undesirable, the singleton class should itself prevent its __init__ method from updating values intended to immutable.

worktoy.meta provides a metaclass called SingletonMeta and a derived class called Singleton. Custom singleton classes may either set SingletonMeta as the metaclass or subclass Singleton. The metaclass subclasses the BaseMetaclass discussed below.

Zeroton

The Zeroton class is a novelty. What specified the singleton class is the fact that it has only one instance. The Zeroton class in contrast has not even one instance. Such a class is essentially a token. The purpose of it is to retain itself across multiple modules. Presently, it finds use in the AttriBox implementation of the worktoy.desc module. For more information, readers are referred to the section on "Advanced Instantiation" in the worktoy.desc documentation.

Function overloading in Python

When creating a new class using the default type, only the most recent assigned value at each name is retained. As such, implementing overloading of methods in the class body requires a custom metaclass providing a custom namespace. The worktoy.meta module provides the BaseObject class derived from the BaseMetaclass, which implements function overloading of the methods in the class body. Before demonstrating the syntactic use of the BaseObject class, an explanation of the implementation is provided. To skip directly to the usage, see section worktoy.meta.overload - Usage.

Background

The main issue with function overloading is that multiple callables are now present on the same name. Thus, a new step is required to determine which available implementation to invoke, given the arguments received. The procedure chosen here is to contain the pairs of type signatures and callables in a dictionary. When the overloaded function is called, the type signature of the arguments is determined and used to look up the appropriate callable in the dictionary, before invoking it with the argument values. This step does add some overhead, but in testing has not exceeded 20 %.

Type Decoration

When a class body is to define multiple callables at the same name, but with different functions, the worktoy.meta.overload decorator factory is used. When calling it with types as positional arguments, it returns a decorator. When this decorator is called it sets the type signature of the decorated function at the attribute named __overloaded_signature__ to the type signature given the factory.

Function Dispatcher

The BaseNamespace uses a dedicated class called Dispatcher to encapsulates the type signature to callable mapping. The Dispatcher class implements both the descriptor protocol and the __call__ method allowing it to emulate the behaviour of bounded and unbounded methods as appropriate. When called it determines the type signature of the arguments received, resolve the matching callable, invokes it with the arguments received and returns the return value.

Namespace Compilation

The BaseMetaclass implements the pattern described previously, where the namespace class provides functionality for creating a dictionary to be used in the type.__new__ method. This compile method retrieves the callables encountered during class body execution that were decorated with by the overload decorator and for each name creates a Dispatcher instance as described above, which is placed in the final dictionary at the appropriate name.

worktoy.meta.overload - Usage

To make use of the 'overload' functionality in a class definition, import the overload decorator factory and the BaseObject class from the worktoy.meta.overload module. The BaseObject class already uses the BaseMetaclass as the metaclass, provides replacements for __init__ and __init_subclass__ which do not raise exceptions every time they see an argument, in contrast to object.__init__ and object.__init_subclass__:

from __future__ import annotations

from worktoy.meta import BaseMetaclass


class BaseObject(metaclass=BaseMetaclass):
  """BaseObject provides argument-tolerant implementations of __init__ and
  __init_subclass__ preventing the errors explained in the documentation."""

  def __init__(self, *args, **kwargs) -> None:
    """Why are we still here?"""

  def __init_subclass__(cls, *args, **kwargs) -> None:
    """Just to suffer?"""

Implement the custom class as a subclass of BaseObject. In the function body, provide implementations of the overloaded functions by reusing the name of the function. Decorate each such function with the overload decorator factory and provide the type signatures of the as positional arguments. For example:

from worktoy.meta import overload, BaseObject
from worktoy.desc import AttriBox
from typing import Self


class ComplexNumber(BaseObject):
  """Class representing complex numbers. """

  __fallback_value__ = 0j

  realPart = AttriBox[float]()
  imagPart = AttriBox[float]()

  @overload(int, int)
  def __init__(self, a: int, b: int) -> None:
    self.__init__(float(a), float(b))

  @overload(float, float)
  def __init__(self, a: float, b: float) -> None:
    self.realPart, self.imagPart = a, b

  @overload(complex)
  def __init__(self, z: complex) -> None:
    self.realPart, self.imagPart = z.real, z.imag

  @overload()
  def __init__(self, ) -> None:
    self.__init__(self.__fallback_value__)

  def __abs__(self) -> float:
    return (self.realPart ** 2 + self.imagPart ** 2) ** 0.5

  def __sub__(self, other: Self) -> Self:
    return ComplexNumber(self.realPart - other.realPart,
                         self.imagPart - other.imagPart)

  def __add__(self, other: Self) -> Self:
    return ComplexNumber(self.realPart + other.realPart,
                         self.imagPart + other.imagPart)

  def __eq__(self, other: Self) -> bool:
    return False if abs(self - other) > 1e-08 else True


if __name__ == '__main__':
  z1 = ComplexNumber(69, 420)
  z2 = ComplexNumber(69.0, 420.0)
  z3 = ComplexNumber(69 + 420j)
  print(z1 == z2 == z3)