I find the Monad instance for Maybe and Either very useful. You can do things like the following (which technically only uses the Applicative instance):

Prelude Control.Applicative> (*3) <$> (+2) <$> Just 1

Just 9

Prelude Control.Applicative> (*3) <$> (+2) <$> Nothing

Nothing

Prelude Control.Applicative> (*3) <$> (+2) <$> Left "error" :: Either String Int

Left "error"

Prelude Control.Applicative> (*3) <$> (+2) <$> Right 1 :: Either String Int

Right 9

Also, Maybe and Either are not "implemented as monads". They are defined using `data` like you suggest:

data Maybe a = Nothing | Just a

data Either a b = Left a | Right b

You can even look up their definitions using ghci using `:i Either` or `:i Maybe`. Monad comes in because they're both instances of the Monad type class.

Take a look at the list monad for another one that doesn't modify state or communicate with an outside interface.

- Joel

Everyone in the Haskell cafe probably has a secret dream to give the
best "five minute monad talk." Challenge: get someone to have a
competition at one of the conferences where students all give their
best "five minute monad talk" and try to find the most comprehensible
one!

Haha, maybe that's why I'm writing.

Agree on all points, not just this quotation.

Yeah, IO and Maybe are the first monads most new Haskell programmers encounter. Perhaps a tour of RVars or the accelerate library would give a better impression. I bet a lot of students get the concept of pure functional programming, and if you shock them with: "So how would you implement a PRNG?", they would understand the role monads play.

Given that Maybe and Either don't modify state, nor do they communicate with outside interfaces, nor do they specify computation ordering, I don't understand why they're implemented as monads. Why not a primitive typeclass or even datatype declaration?

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