What is a monad?

Question

Having briefly looked at Haskell recently, what would be a brief, succinct, practical explanation as to what a monad essentially is?

I have found most expla

Answer 1

A monad is, effectively, a form of "type operator". It will do three things. First it will "wrap" (or otherwise convert) a value of one type into another type (typically called a "monadic type"). Secondly it will make all the operations (or functions) available on the underlying type available on the monadic type. Finally it will provide support for combining its self with another monad to produce a composite monad.

The "maybe monad" is essentially the equivalent of "nullable types" in Visual Basic / C#. It takes a non nullable type "T" and converts it into a "Nullable", and then defines what all the binary operators mean on a Nullable.

Side effects are represented simillarly. A structure is created that holds descriptions of side effects alongside a function's return value. The "lifted" operations then copy around side effects as values are passed between functions.

They are called "monads" rather than the easier-to-grasp name of "type operators" for several reasons:

1. Monads have restrictions on what they can do (see the definiton for details).
2. Those restrictions, along with the fact that there are three operations involved, conform to the structure of something called a monad in Category Theory, which is an obscure branch of mathematics.
3. They were designed by proponents of "pure" functional languages
4. Proponents of pure functional languages like obscure branches of mathematics
5. Because the math is obscure, and monads are associated with particular styles of programming, people tend to use the word monad as a sort of secret handshake. Because of this no one has bothered to invest in a better name.