Duck typing and interfaces

Overview

Teaching: 10 min
Exercises: 15 min

Questions

• How does Python decide what you can and can’t do with an object?

• When is inheritance not appropriate?

• What alternatives are there to inheritance?

Objectives

• Understand how duck typing works, and how interfaces assist with understanding this.

• Understand the circumstances where inheritance can be a hindrance rather than a help.

• Be aware of concepts such as composition which can help where inheritance fails.

There is a principle that if something “looks like a duck, and swims like a duck, and quacks like a duck, then it is probably a duck”.

Python’s type system adopts a similar philosophy—if it looks, swims, and quacks like a duck, and that’s the only duck-like aspects that we need at a particular time, then as far as Python is concerned, then it is a duck.

For example, the Newton–Raphson method solves equations of the form \(f(x)=0\) iteratively from a starting point \(x_0\) as \[x_{n+1}=x_n - \frac{f(x_n)}{f’(x_n)}\;.\] We could implement this in Python as:

def newton(function, derivative, initial_estimate, num_iters=10):
    """Solves the equation `function`(x) == 0 using the Newton–Raphson
    method with `num_iters` iterations, starting from `initial_estimate`.
    `derivative` is the derivative of `function` with respect to x."""

    current_estimate = initial_estimate
    for _ in range(num_iters):
        current_estimate = (
            current_estimate
            - function(current_estimate) / derivative(current_estimate)
        )
    return current_estimate

This clearly works with functions that operate on and return real numbers.

from math import sin, cos

print(newton(sin, cos, 1))
print(newton(sin, cos, 2))
print(newton(sin, cos, 1.5))

0.0
3.141592653589793
-12.566370614359172

If you only planned for this to work with real numbers, you might think of adding a check at the start of the function that the initial_estimate given is a real number, or that each successive current_estimate is real. However, if we think about this in a duck typed way, we don’t really need to care about this—provided that the values can be subtracted and divided, and function and derivative can operate on them, then the algorithm will work.

This means that we can apply this function to cases we may not have considered. For example, when \(f(z)\) is a polynomial, then plotting the solution \(z_n\) (which is now a complex number) obtained as a function of the initial estimate \(z_0\) gives us Newton’s fractal.

%matplotlib inline
from numpy import angle, linspace, newaxis, pi
from matplotlib.pyplot import colorbar, show, subplots

def complex_linspace(lower, upper, num_real, num_imag):
    real_space = linspace(lower.real, upper.real, num_real)
    imag_space = linspace(lower.imag, upper.imag, num_imag) * 1J
    return real_space + imag_space[:, newaxis]

def test_polynomial(x):
    return x ** 3 - 1

def test_derivative(x):
    return 3 * x ** 2


z_min = -1 - 1J
z_max = 1 + 1J
initial_z = complex_linspace(z_min, z_max, 1000, 1000)

results = newton(test_polynomial, test_derivative, initial_z, 20)

fig, ax = subplots()
image = ax.imshow(
    angle(results),
    vmin=-3,
    vmax=3,
    extent=(z_min.real, z_max.real, z_min.imag, z_max.imag),
)
cbar = colorbar(image, ax=ax, ticks=(-2*pi/3, 0, 2*pi/3))
cbar.set_label(r"$\arg(z_n)$")
cbar.ax.set_yticklabels((r"$-\frac{2\pi}{3}$", "0", r"$\frac{2\pi}{3}$"))
ax.set_xlabel(r"$\operatorname{Re}(z_0)$")
ax.set_ylabel(r"$\operatorname{Im}(z_0)$")

show()

Because our Newton–Raphson function was duck typed, it automatically worked for this problem, despite this problem requiring Numpy arrays of complex numbers rather than the real numbers we thought we were writing for.

Protocols

It is frequently useful to codify exactly what requirements are placed on an object (or duck) so that we can design classes to match. In Python, when these requirements are documented, the specification is called a protocol; you may also hear the word (informal) interface used to describe this as well.

An example of a well-known protocol in Python is the iterator protocol, which should be obeyed by objects returned by the __iter__() method. For a class to support the iterator protocol, it must have two methods:

• __iter__(), which returns the object itself. (This is so that an iterator can be given to a for loop directly, which is sometimes desirable rather than relying on it being returned by the __iter__() method of a collection-type object.)
• __next__(), which returns the next item in the sequence. If there are no more items, then this should raise the StopIteration exception, and successive calls should keep raising this exception.

For instance, an iterator that returns the Fibonacci numbers up to some upper bound may look something like:

class FibonacciIterator:
    def __init__(self, max_value):
        self.max_value = max_value
        self.last_two_numbers = (1, 0)

    def __iter__(self):
        return self

    def __next__(self):
        next_number = sum(self.last_two_numbers)

        if self.max_value < next_number:
            raise StopIteration
        else:
            self.last_two_numbers = (self.last_two_numbers[1], next_number)
            return next_number

This is an example of where we want to use the iterator directly with the for loop, since we want to initialise it with a max_value. Testing this:

for number in FibonacciIterator(100):
    print(number)

1
1
2
3
5
8
13
21
34
55
89

Triangular numbers

Write a class that implements the iterator protocol and that returns the first \(n\) triangular numbers. These are defined such that the \(n\)th triangular number is the sum of the first \(n\) positive integers, so the first five are 1, 3, 6, 10, and 15.

What would happen if you removed the upper bound (and so never raised StopIteration) and used the iterator in a for loop? When might this behaviour be useful?

Solution

class TriangularIterator:
    def __init__(self, n):
        self.n = n
        self.total = 0
        self.index = 0

    def __iter__(self):
        return self

    def __next__(self):
        if self.index >= self.n:
            raise StopIteration
        self.index += 1
        self.total += self.index
        return self.total

A loop over an iterator that can’t raise StopIteration will run forever. This could be useful if you’re using zip() to iterate over another, bounded, iterable at the same time; then each element will get a corresponding triangular number, no matter how many elements there are.

Spot the problem

Look back at the solutions for the QuadraticPlotter, PolynomialPlotter, and FunctionPlotter. What problems do you see with the plot method of these classes?

Solution

The arguments to FunctionPlotter.plot(), PolynomialPlotter.plot(), and QuadraticPlotter.plot() are all different—one expects a callable, one expects a list of coefficients as one argument, and one expects three coefficients as separate arguments. In general, specialistations of a class should keep the same interface to its functions, and the parent class should be interchangeable with its specialisations.

Over to you

Thinking about your own research software, what kind of places might an interface be useful to better codify how different parts of the software interact?

Abstract base classes

Python also allows us to go a step further than a protocol, and formalise the requirements we place on our interfaces in code. An abstract base class is a class that must be inherited from—you can’t create instances of it directly. Python provides these for many of its protocols in the collections.abc module. For example, the Fibonacci iterator above could inherit from abc.Iterator. This would allow other code to check in advance that it supports the protocol, and also would guard against us forgetting to implement some part of the protocol. For example, if we forgot the __next__() method:

from collections.abc import Iterator
class FibonacciIterator(Iterator):
    def __init__(self, max_value):
        self.max_value = max_value
        self.last_two_numbers = (1, 0)

    def __iter__(self):
        return self

for number in FibonacciIterator(100):
    print(number)

In this case Python gives us an error:

TypeError                                 Traceback (most recent call last)
<ipython-input-3-a96ac2788df3> in <module>
      5         self.last_two_numbers = (1, 0)
      6
----> 7 for number in FibonacciIterator(100):
      8     print(number)

TypeError: Can't instantiate abstract class FibonacciIterator with abstract methods __next__

This can be useful when working with more complex interfaces. (On the other hand, removing the __iter__() method works fine, because abc.Iterator helpfully defines __iter__() for us, so we can inherit it.)

Implementing multiple interfaces

You may find yourself wanting to implement multiple interfaces in a single class. This is possible by making use of multiple inheritance, where a class inherits from more than one base class. This is not supported in all programming languages, and in many programming languages it is considered to be problematic. It is more common in Python, but we don’t have space to go into detail about it in this lesson.

Hashable Polygons

The hashable protocol allows classes to be used as dictionary keys and as members of sets. Look up the hashable protocol and adjust the Polygon class so that it follows this.

Test this by using a Triangle instance as a dict key:

triangle_descriptions = {
    Triangle([3, 4, 5]): "The basic Pythagorean triangle"
}

Solution

The hashable protocol requires implementing one method, __hash__(), which should return a hash of the aspects of the instance that make it unique. Lists can’t be hashed, so we also need to turn the list of side_lengths into a tuple.

    def __hash__(self):
        return hash(tuple(self.side_lengths))

Composition

Composition is a technique where rather than adding more and more functionality to a single class (either explicitly, or via inheritance), functionality is added by adding instances of other classes that group together the related functionality.

An example of a library that makes heavy use of composition is the Matplotlib object-oriented API. While Matplotlib makes its pyplot API available for basic plotting, it is built on top of a very intricate hierarchy of classes and objects. Those who want more control over their plots are encouraged to use this interface instead of the simplified pyplot version.

To get a feel for how Matplotlib uses composition to separate its concerns while having a large amount of functionality, we can write a small test function to recursively walk through a member variables of an object that are themselves instances of a non-builtin class.

from matplotlib.pyplot import subplots

def traverse_objects(base_object, level=0, max_level=5):
    """Recursively walk through the member variables of base_object,
    and print out information about each that is an instance of a
    non-built-in class. max_level controls the depth that the
    recursion may continue to, to avoid infinite loops."""

    if hasattr(base_object, "__dict__") and level < max_level:
        for child_name, child_object in vars(base_object).items():
            if child_object.__class__.__module__ != "builtins":
                print(" " * level, child_name, ":", type(child_object))
                traverse_objects(child_object, level=level+1)


# Create a simple plot
fig, ax = plt.subplots()
ax.scatter([1, 2, 3], [1, 4, 9])
ax.scatter([1, 1.5, 2, 2.5, 3], [1, 1, 2, 3, 5])

# Inspect the object hierarchy of ths figure object
traverse_objects(fig)

This gives a lot of output—72 lines, so in principle 72 different classes are combining here. In practice this number is not accurate; there is some duplication in this list, since for example both canvas and patch have a figure member variable so that they can refer back to the Figure that they work with. Conversely, this simple traversal ignores some additional composition; for example, fig._axstack._elements is a list of tuples, but within some of those tuples are more objects of type matplotlib.gridspec.SubplotSpec and matplotlib.axes._subplots.AxesSubplot.

This is why when you have errors in your code, tracebacks from some libraries can be quite long. Having lots of small methods in classes that are dedicated to one very specific aspect means that it is easier to reason about what each one is doing in isolation by itself, but can make it more complicated to get a view of the big picture.

Composing plotters

How could the FunctionPlotter, PolynomialPlotter, and QuadraticPlotter be refactored to make use of composition instead of inheritance?

Solution

One way of doing this is to define a “plottable function” interface. An object respecting this interface would:

• be callable
• accept one argument
• return \(f(x)\)

Then, with the FunctionPlotter as defined previously, there is no need to subclass to create QuadraticPlotters and PolynomialPlotters; instead, we can define a QuadraticFunction class as:

class Quadratic:
    def __init__(self, a, b, c):
        self.a = a
        self.b = b
        self.c = c

    def __call__(self, x):
        return self.a * x ** 2 + self.b * x + self.c

This can then be passed to a FunctionPlotter:

plotter = FunctionPlotter()
plotter.plot(Quadratic(1, -1, 1))

Alternatively, we can encapsulate the function to be plotted as part of the class.

from matplotlib.colors import is_color_like

class FunctionPlotter:
    def __init__(self, function, color="red", linewidth=1, x_min=-10, x_max=10):
        assert is_color_like(color)
        self.color = color
        self.linewidth = linewidth
        self.x_min = x_min
        self.x_max = x_max
        self.function = function

    def plot(self):
        """Plot a function of a single argument.
        The line is plotted in the colour specified by color, and with width
        linewidth."""
        fig, ax = subplots()
        x = linspace(self.x_min, self.x_max, 1000)
        ax.plot(x, self.function(x), color=self.color, linewidth=self.linewidth)

This could then be used as:

from numpy import sin

sin_plotter = FunctionPlotter(sin)
quadratic_plotter = FunctionPlotter(Quadratic(1, -1, 1), color="blue")
sin_plotter.plot()
quadratic_plotter.plot()

show()

Key Points

• Provided a class exposes all required functionality for an operation to work, Python allows it.

• Only use inheritance to express relationships where the subclass is the same kind of thing as the superclass.

• Implementing interfaces and adding functionality with composition can be better alternatives to inheritance in some cases.