Monads

[Gozala]

I do believe I have an understanding of state monads & would love a session about other flavors.

[Gozala]

/Cc @luciferous

[Raynos]

The rule is your not allowed to talk about category theory when explaining monads!

[Raynos]

Or you have to teach everyone category theory.

[luciferous]

Let's look at something simple like function application. Consider the following definition of functions f and g:

// f: x -> y
var f = function(x) { return x + 1 }

// g: x -> y
var g = function(x) { return x * 3 }

Remember that every monad has two basic operators: then (composition/concatenation) and unit (think of this as instantiation, or creating a new object). There is a monad which captures the pattern of function application called the Identity monad.

 // then: Identity a -> (a -> Identity b) -> Identity b
var then = function(ma) {
    return function(q) { // q: a -> Identity b
        return q(ma);
    }
}

// unit: a -> Identity a
var unit = function(x) { return x }

Then we can compose Identitys together:

// x: Identity x
var x = unit(1);

then(x, f) // => 2
then(x, g) // => 3
then(then(x, f), g) // => 6

If unit were to box its value instead of returning it without modification, you could imagine something like the following:

x.then(f).then(g) // => 6