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

Monoid appears to be something that ensures that all operations defined on a Monoid and a supported type will always return a supported type inside the Monoid. Eg, Any number + Any number = A number, no errors.

Whereas division accepts two fractionals, and returns a fractional, which defined division by zero as Infinity in haskell somewhy(which happens to be a fractional somewhy)...

In any case, it appears Monads are just a way to ensure that your chain of operations behaves in a predictable way, and a function that claims to be Num -> Num, composed with another function of Num->Num called with x does not say, fire the missiles.

On the other hand, if we have a function which does fire the missiles, we can compose it with other functions which also fire the missiles, because our intent is clear -- we want to fire the missiles -- but it won't try printing "Hello World" for some odd reason.

In Haskell, main is of type IO (), or IO [()], the distiction is strange and I will not discuss it but here's what I think happens:

If I have main, I want it to do a chain of actions, the reason I run the program is to produce an effect -- usually though IO. Thus I can chain IO operations together in main in order to -- do IO, nothing else.

If I try to do something which does not "return IO", the program will complain that the chain does not flow, or basically "How does this relate to what we are trying to do -- an IO action", it appears to force the programmer to keep their train of thought, without straying off and thinking about firing the missiles, while creating algorithms for sorting -- which does not flow.

Basically, Monads appear to be a tip to the compiler that "hey, you know this function that returns a number here, it doesn't actually always work, it can sometimes produce a Number, and sometimes Nothing at all, just keep this in mind". Knowing this, if you try to assert a monadic action, the monadic action may act as a compile time exception saying "hey, this isn't actually a number, this CAN be a number, but you can't assume this, do something to ensure that the flow is acceptable." which prevents unpredictable program behavior -- to a fair extent.

It appears monads are not about purity, nor control, but about maintaining an identity of a category on which all behavior is predictable and defined, or does not compile. You cannot do nothing when you are expected to do something, and you cannot do something if you are expected to do nothing (visible).

The biggest reason I could think of for Monads is -- go look at Procedural/OOP code, and you will notice that you do not know where the program starts, nor ends, all you see is a lot of jumping and a lot of math,magic,and missiles. You will not be able to maintain it, and if you can, you will spend quite a lot of time wrapping your mind around the whole program before you can understand any part of it, because modularity in this context is based on interdependant "sections" of code, where code is optimized to be as related as possible for promise of efficiency/inter-relation. Monads are very concrete, and well defined by definition, and ensure that the flow of program is possible to analyze, and isolate parts which are hard to analyze -- as they themselves are monads. A monad appears to be a "comprehensible unit which is predictable upon its full understanding" -- If you understand "Maybe" monad, there's no possible way it will do anything except be "Maybe", which appears trivial, but in most non monadic code, a simple function "helloworld" can fire the missiles, do nothing, or destroy the universe or even distort time -- we have no idea nor have any guarantees that IT IS WHAT IT IS. A monad GUARANTEES that IT IS WHAT IT IS. which is very powerful.

All things in "real world" appear to be monads, in the sense that it is bound by definite observable laws preventing confusion. This does not mean we have to mimic all the operations of this object to create classes, instead we can simply say "a square is a square", nothing but a square, not even a rectangle nor a circle, and "a square has area of the length of one of it's existing dimensions multiplied by itself. No matter what square you have, if it's a square in 2D space, it's area absolutely cannot be anything but its length squared, it's almost trivial to prove. This is very powerful because we do not need to make assertions to make sure that our world is the way it is, we just use implications of reality to prevent our programs from falling off track.

Im pretty much guaranteed to be wrong but I think this could help somebody out there, so hopefully it helps somebody.