What is a Monad? - Computerphile

The first paragraph introduces the concept of monads, which originated in mathematics in the 1960s and were later rediscovered in computer science in the 1990s. The speaker emphasizes the importance of monads in programming languages, particularly in the last 25 years. The focus is on programming with effects using a simple example in Haskell. The example involves writing a function to evaluate expressions, specifically those involving integer values and division. The speaker assures that even those unfamiliar with Haskell will be able to follow along as everything will be explained step by step. The initial step is defining a data type for expressions using Haskell's `data` keyword, with two constructors: `Val` for integer values and `Div` for division of sub-expressions.

The second paragraph delves into the problem of division by zero in the context of the expression evaluation example. To address this, the speaker introduces a safe division function called `safediv`, which returns a `Maybe Int` type. This function checks if the divisor is zero and returns `Nothing` if so, or `Just` the result of the division otherwise. The `Maybe` type in Haskell is used to handle potential failures, such as division by zero, by allowing for a value to either be present (`Just`) or absent (`Nothing`). The speaker then modifies the expression evaluator to handle these `Maybe` values, ensuring that the program does not crash and instead returns a well-defined result.

In the third paragraph, the speaker identifies a common pattern in the safe evaluator program: the repeated use of case analysis on `Maybe` values. To simplify the program, the speaker abstracts this pattern into a definition, introducing a sequencing operator that allows for chaining operations that might fail. This operator checks if the first operation succeeds (`Just`) and, if so, applies a function to the result. If the operation fails (`Nothing`), the entire sequence fails. This abstraction leads to a cleaner and more concise program, making it easier to understand and maintain.

The fourth paragraph explains the concept of the Maybe monad, which consists of the `Maybe` type constructor and two functions: `return` and the sequencing operator. The speaker discusses the benefits of using monads, such as providing a uniform framework for programming with effects, supporting pure programming with effects, making the use of effects explicit in the types, and enabling effect polymorphism. The speaker also mentions the importance of monads in programming language development and suggests further reading in their book 'Programming in Haskell' for a deeper understanding.

The final paragraph addresses the challenges faced by learners when encountering monads and other abstract concepts in Haskell. The speaker argues for the importance of using proper terminology like 'monad' and credits mathematicians for their original discovery. They acknowledge the difficulty these terms can pose for learners but encourage embracing the terminology. The speaker also mentions the availability of libraries in Haskell that implement various monads, reducing the need for programmers to define their own. The paragraph concludes by highlighting the built-in support for monads in Haskell and the potential for using multiple monads in a single program.