[anon291]

I mean people need to be familiar with mathematics. In mathematics things form things without having to understand them.

For example, The natural numbers form a ring and field over normal addition and multiplication , but you don't need to know ring theory to add numbers..

People need to stop worrying about not understanding things. No one understands everything.

[wat10000]

Now imagine if every single explanation of natural numbers talked about rings and fields. Nobody ever just says "they're the counting numbers starting from one." A few of them might say, "they're the counting numbers starting from one, and they form a ring and field over addition and multiplication." And I might think, I understand the first part, but I'm not sure what the second part is and it sounds important, so maybe I still don't know what natural numbers are.

I'm not worried, but it's amusing to see this person say it's so simple, and then immediately trample on it.

[anon291]

Well most people explain monads for no reason. I'm probably one of the rare Haskell developers who never explains them to anyone. It has nothing to do with IO.

If someone is concerned with how to do IO in a pure language then I show them how it actually happens in GHC, which is via the type system enforcing only one instance of RealWorld# is alive at once. There is ABSOLUTELY nothing you need to know about monads to understand IO in Haskell. It's just function composition and careful use of case to force the evaluation of a token of type RealWorld#. Nothing magic about it.. you're just passing the state of the world around.

[a57721]

I get your point, but the natural numbers do not form a ring or field.

[anon291]

Sorry you're right. I was tired commenting.

S/naturals/rationals/g for rings

and s/naturals/algebraic numbers/g for fields