WhyWeNeedMonad.txt

Why do we need monads?We want to program only using functions. ("functional programming" after all -FP).

Then, we have a first big problem. This is a program:

f(x) = 2 * x

g(x,y) = x / y

How can we say what is to be executed first? How can we form an ordered sequence of functions (i.e. a program) using no more than functions?

Solution: compose functions. If you want first g and then f, just write f(g(x,y)). OK, but ...

More problems: some functions might fail(i.e. g(2,0), divide by 0). We have no "exceptions" in FP. How do we solve it?

Solution: Let's allow functions to return two kind of things: instead of having g : Real,Real -> Real (function from two reals into a real), let's allow g : Real,Real -> Real | Nothing (function from two reals into (real or nothing)).

But functions should (to be simpler) return only one thing.

Solution: let's create a new type of data to be returned, a "boxing type" that encloses maybe a real or be simply nothing. Hence, we can have g : Real,Real -> Maybe Real. OK, but ...

What happens now to f(g(x,y))? f is not ready to consume a Maybe Real. And, we don't want to change every function we could connect with g to consume a Maybe Real.

Solution: let's have a special function to "connect"/"compose"/"link" functions. That way, we can, behind the scenes, adapt the output of one function to feed the following one.

In our case: g >>= f (connect/compose g to f). We want >>= to get g's output, inspect it and, in case it is Nothing just don't call f and return Nothing; or on the contrary, extract the boxed Real and feed f with it. (This algorithm is just the implementation of >>= for the Maybe type).

Many other problems arise which can be solved using this same pattern: 1. Use a "box" to codify/store different meanings/values, and have functions like gthat return those "boxed values". 2. Have composers/linkers g >>= f to help connecting g's output to f's input, so we don't have to change f at all.

Remarkable problems that can be solved using this technique are:

having a global state that every function in the sequence of functions ("the program") can share: solution StateMonad.

We don't like "impure functions": functions that yield different output for same input. Therefore, let's mark those functions, making them to return a tagged/boxed value: IO monad.

Total happiness !!!!