How do you explain the concepts of monads, functors, and applicatives to a non-functional programmer?

1 What are functors?

A functor is a type of data structure that can be mapped over with a function. For example, a list is a functor, because you can apply a function to each element of the list and get a new list. A functor is a generalization of the idea of applying a function to a single value, but with more flexibility and composability. You can think of a functor as a container that holds some values and lets you transform them with a function.

2 What are applicatives?

An applicative is a type of functor that also allows you to apply a function that is inside the container to the values inside the container. For example, if you have a list of functions and a list of values, you can use an applicative to apply each function to each value and get a list of results. An applicative is a generalization of the idea of applying a function to multiple arguments, but with more flexibility and composability. You can think of an applicative as a container that holds some functions and some values and lets you combine them with a function.

3 What are monads?

A monad is a type of applicative that also allows you to chain multiple operations that produce containers. For example, if you have a function that takes a value and returns a list of possible outcomes, you can use a monad to apply that function to each element of a list and get a new list of all possible outcomes. A monad is a generalization of the idea of sequencing computations that may have side effects, but with more flexibility and composability. You can think of a monad as a container that holds some values and some effects and lets you chain them with a function.

4 Why are they useful?

Monads, functors, and applicatives are useful because they allow you to write code that is more abstract, concise, and reusable. By using these abstractions, you can avoid explicit loops, conditionals, and state management, and focus on the logic and behavior of your program. You can also compose different types of containers and functions to create complex and powerful operations. For example, you can use a monad to model asynchronous operations, error handling, state transitions, or probabilistic computations.

5 How do you use them in code?

To use monads, functors, and applicatives in code, you need to follow some conventions and laws. First, you need to define how your data structure implements the methods of these abstractions, such as map, apply, and bind. These methods should obey some algebraic properties that ensure consistency and coherence. Second, you need to use some syntactic sugar or helper functions that make your code more readable and expressive. For example, in Haskell, you can use the do notation or the >>= operator to write monadic code. In Scala, you can use the for comprehension or the flatMap method to write monadic code.

7 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?