This kata corresponds to Five-Fundamental-Monads in Codewars Difficulty: 4 kyu Tags: `FUNDAMENTALS`

`MONADS`

`DATA STRUCTURES`

`FUNCTIONAL PROGRAMMING`

## Questions

In this kata we will implement five of the most fundamental monads.

Newcomers to Haskell find monads to be one of the most intimidating concepts but on a basic level - they are not too difficult to understand.

A datatype forms a monad if it is possible to complete the following definitions such that the monad laws (described below) hold. There's nothing more to it! For a more intuitive understanding then there are a plethora of tutorials which use (sometimes wild) analogies to explain this concept.

1 | class Monad m where |

Monad laws

1 | return x >>= f = f x |

It turns out that many different types of computation can be encapsulated by monads. For example the Maybe monad encapsulates a computation which can fail and State a computation with mutable state.

The five we will implement here are `Identity`

, `Maybe`

, `State`

, `Writer`

and `Reader`

.

Hint: https://www.haskell.org/haskellwiki/Monad_tutorials_timeline

Note: Please feel free to contribute!

## Sources Code

1 | {-# LANGUAGE NoImplicitPrelude #-} |

## How to solve

### Identity Monad

Above all, we need to implement the Identity monad instance at first, according to the law of identity in Category Theory: which means for every object \(x\), there exists a morphism \(id_x : x \mapsto x\) called the identity morphism for \(x\), such that for every morphism \(f : a \mapsto x\) and every morphism \(g : x \mapsto b\), we have \(id_x \circ f = f\) and \(g \circ id_x = g\). Straightforwardly we can call this as a morphism (or function in a programming language) which always return itself, and for every morphism combine with any identity must be equals to morphism itself anyway.

By looking at Monad typeclass defination:

1 | class Applicative m => Monad (m :: * -> *) where |

So, in Haskell we can implement identity instance like this:

1 | instance Monad Identity where |

`return`

function was return a Identity which accepted a parameter `a`

implicitly, and as explicitly can be write like this: `return a = Identity a`

`>>=`

is a monad-binding operator function, means that `(Identity v)`

was bound on function `f`

, by looking at type definition of this function, which accept the parameter `m a`

, `(a -> m b)`

and return the monad `m b`

finally. So now let's turn back to this instance, `(Identity v)`

is the first parameter `m a`

also `f`

represents to `(a -> m b)`

, after the `(Identity v)`

is done the pattern-matching, by take the parameter `v`

out and put it into `f`

and finally return the monad `m b`

, that's it what we need!

### Maybe Monad

After done the identity monad, we are learned about how to construct the simple monad in Haskell, but just the only identity? Not enough! So now I'll start to talk about the next most useful monad in Haskell, the `Maybe Monad`

.

In this monad, defined two data types: `Nothing`

and `Just a`

, which `Nothing`

does not accept any type parameter but `Just a`

will accept a type parameter `a`

here. So when we hold something just like an integer 1, they we can put it into `Just 1`

, but when holding nothing, then we didn't need to put anything into `Just a`

, so we use `Nothing`

to alternative that.

So let's implement `return`

function on `Maybe Monad`

first, it seems like the identity monad, but still have some differences. In this case, we need to specify the `Nothing`

and `Just`

, just take a look at the type definition of `return`

function, it's must provide a parameter `a`

, then we can be wrapping it into `Just a`

to becomes `return = Just`

in instance.

Second, after completed `return`

function, to finish the `>>=`

function, it's also closed to the identity instance, but we know when we put a `Nothing`

into `f`

, there must always return `Nothing`

, otherwise return the result moand from `f`

, so here could be using pattern-matching to partition these two case.

Finally the `Maybe Monad`

likes:

1 | instance Monad Maybe where |

### State Monad

### Reader Monad

### Writer Monad

## Conclusion

Great thanks to Henry for fixing my noob English grammar problem!