arosien/free-monoid.txt

## free-monoid.txt
@gfixler, free monoid is the easiest and helps generalize the whole "free" thing

let's make a monoid that is a monoid for *anything*

but wait, that doesn't sound possible, everything that can be a monoid has its own rule, that's the whole point

but if you wanted to make a monoid for anything, you can just be really lazy, and instead of actually adding things together, you just collect all the things you want to add

"you want to add an A and an A, sure, the answer is: here's your two A's" HA HA HA free monoids rule

and so on: to add As you just collect all the As and call the collection of them the answer

so it's a monoid with this bogus addition, but it can handle anything

what's does it look like? a list!

the free monoid is a list. the zero is the empty list, and you just append lists together!

other free things are just like that... they cheat, but they can be a free X for anything.
	@gfixler, free monoid is the easiest and helps generalize the whole "free" thing

	let's make a monoid that is a monoid for anything

	but wait, that doesn't sound possible, everything that can be a monoid has its own rule, that's the whole point

	but if you wanted to make a monoid for anything, you can just be really lazy, and instead of actually adding things together, you just collect all the things you want to add

	"you want to add an A and an A, sure, the answer is: here's your two A's" HA HA HA free monoids rule

	and so on: to add As you just collect all the As and call the collection of them the answer

	so it's a monoid with this bogus addition, but it can handle anything

	what's does it look like? a list!

	the free monoid is a list. the zero is the empty list, and you just append lists together!

	other free things are just like that... they cheat, but they can be a free X for anything.