Monads¶

Basics¶

In functional programming, a monad is a structure that combines program fragments (functions) and wraps their return values in a type with additional computation.
In addition to defining a wrapping monadic type, monads define two operators:
- one to wrap a value in the monad type
- another to compose together functions that output values of the monad type (these are known as monadic functions).
General-purpose languages use monads to reduce boilerplate code needed for common operations (such as dealing with undefined values or fallible functions, or encapsulating bookkeeping code).
Functional languages use monads to turn complicated sequences of functions into succinct pipelines that abstract away control flow, and side-effects.

Formal Definition: Monads is a monoid in a category of endofunctors.

Explanation:

Functor: It is an object or value combined with a mechanism to do something with that value.
Endofunctors: A subclass of functor which returns the object of same shape as the functor on which it is applied to.
- Example:
```
class Functor:
    def __init__(self, value):
        self.value = value

    def map(self, func):
        return Functor(func(self.value))
```
- Here, the map function is an endofunctor because it returns the same type Functor on which it was ran.
- It preserves the structure after the operations.
Monad: It is a specific type of endofunctor which is meant to preserve structure and composition.