[Haskell-cafe] Are all monads functions?

[Yves Parès]

Hello Café,

One thought occur to me recently when explaining the concept of Monad to
non-haskellers: internally, all standard Monads are newtypes wrapping
functions:
StateT is, WriterT is, ContT is. Even IO and ST are, both conceptually and
in their implementation by GHC.
ParsecT (not part of mtl, but still) is. And so on...

So I'm saying that most of the time, we define a new monad:
- either by building a monad stack of existing transformers (thus "melting"
their internal functions),
- or by creating a newtype containing a custom function.

Thinking thusly, >>= would then just be a special function composition
operator: in the spirit of '.' but for a specific type of functions.

So my questions are:
- Is it reasonable to think like that, or are there too many monads that
cannot be defined like that, and then contradict me?
- Is it reasonable to present monads to newcomers by saying : monads are
basically always functions. 'return x' will then be a function that always
return 'x' regardless of its input and >>= is a special composition for
this occasion.


-- 
The ⊥ is a lie.
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