[Haskell-beginners] [Haskell-cafe] select :: [(Float, a)] -> a -- Weighted stochastic selection - help?

[apfelmus]

Tony Hannan wrote:
> The IO monad is defined as:
> 
> newtype IO a = IO (RealWorld -> (RealWorld, a))
> 
> Notice that it encapsulates a pure function from RealWorld to RealWord plus
> result. Semantically, the whole state of the world is passed into your main
> function and a new world state is returned containing any changes you made.
> However, the implementation just performs side effects on the world (I/O),
> but the monad type ensures that these side effects are sequential and that
> you can never gain access to the underlying RealWorld so it won't be
> duplicated. These restrictions allow us to view this implementation as a
> pure function.

Note that while

  IO a  ~  RealWorld -> (RealWorld, a)

is an intuitive way to think about IO, it's not the definition of IO and it
doesn't always work. For instance, it's inadequate for modeling concurrency. But
also in a sequential world, there are problems: consider the two programs

  loop, loop' :: IO ()
  loop  = loop
  loop' = putStr "X" >> loop'

Both would have the denotation _|_ while being very different: one does nothing
at all while the other prints an infinite stream of Xs.


For more on the semantics of IO, see also

  Simon Peyton Jones. Tackling the Awkward Squad.
  http://research.microsoft.com/~simonpj/papers/marktoberdorf/


> Non-primitive monads like Control.Monad.State are actually implemented as
> pure functions passing the state around.

Yes, so the difference between IO and the other monads is of course that IO is a
primitive and cannot be implemented with other Haskell constructs.


Regards,
apfelmus