List monad


Martin McBride, 2020-07-02
Tags monad list monad design pattern
Categories functional programming

In the article on the Failure monad we looked at a simple definition of what a monad is:

A monad is a design pattern that allows us to add a context to data values, and also allows us to easily compose existing functions so that they execute in a context aware manner.

In this article we will look at the List monad. This is a monad that allows us to process lists of values, without cluttering our code with looping constructs.

How a List monad is used

As with the Failure monad, our List monad should do three main things:

  • Allow us to wrap a value (in this case, a list value) in a List monad.
  • Allow us to apply ant existing function to the entire list, using bind().
  • Allow us to retrieve the List from a monad.

So a simple use might be like this:

k = List([1, 2, 3])
n = k.bind(neg)
print(n)              # List([-1, -2, -3])

We will call our monad List because that is the name that is commonly used for similar monads in other languages. Notice that a List monad is quite different to a normal Python list.

List monad implementation

Based on the previous implementation of the Failure monad, here is our List monad:

class List():

    def __init__(self, value):
        self.value = value

    def get(self):
        return self.value

    def bind(self, f):
        result = list(map(f, self.value))
        return List(result)

    def __str__(self):
        return 'List(' + ', '.join(map(str, self.value)) + ')'

    def __or__(self, f):
        return self.bind(f)

The List monad just wraps a single value, which should be a list or other sequence. This is stored as self.value.

The bind function uses map to apply the supplied function f to each element in self.value. The resulting list is wrapped in a new List monad.

We override str to return 'List([contents of list])'. Finally we override the or operator | so we can use it as a bind operator.

If you found this article useful, you might be interested in the book Functional Programming in Python or other books by the same author.

Prev
Next

Popular tags

2d arrays abstract data type alignment and angle animation arc array arrays bar chart bar style behavioural pattern bezier curve built-in function callable object chain circle classes clipping close closure cmyk colour combinations comparison operator comprehension context context manager conversion count creational pattern data science data types decorator design pattern device space dictionary drawing duck typing efficiency ellipse else encryption enumerate fill filter font font style for loop function function composition function plot functools game development generativepy tutorial generator geometry gif global variable gradient greyscale higher order function hsl html image image processing imagesurface immutable object in operator index inner function input installing iter iterable iterator itertools join l system lambda function len lerp line line plot line style linear gradient linspace list list comprehension logical operator lru_cache magic method mandelbrot mandelbrot set map marker style matplotlib monad mutability named parameter numeric python numpy object open operator optimisation optional parameter or pandas partial application path pattern permutations pie chart polygon positional parameter print pure function python standard library radial gradient range recipes rectangle recursion reduce regular polygon repeat rgb rotation roundrect scaling scatter plot scipy sector segment sequence setup shape singleton slice slicing sound spirograph sprite square str stream string stroke structural pattern subpath symmetric encryption template text text metrics tinkerbell fractal transform translation transparency triangle truthy value tuple turtle unpacking user space vectorisation webserver website while loop zip