Yet Another Monad Tutorial

Peter G. Hancock
Tue, 12 Aug 2003 18:24:52 +0100

>>>>> Jeff Newbern wrote (on Tue, 12 Aug 2003 at 17:20):
(proposed revisions)

    > In the section "No Way Out":
    > ----------
    > The IO monad is a familiar example of a one-way monad in Haskell.
    > Because you can't escape from the IO monad, it is impossible to write a
    > function that does a computation in the IO monad but returns a
    > non-monadic value. 

I wouldn't say that, as it is inaccurate.  Of course you can return a
value of _some_ monadic type eg. (Maybe ...).

    > Not only are functions of the type IO a -> a
    > impossible to create, 

You can quite easily write a function of type IO (IO a) -> IO a, which
is a special case of that type. 

    > but any function whose result type does not
    > contain the IO type constructor is guaranteed not to use the IO monad.

That's rather vague: what does it mean for a function to use a monad?

    > Other monads, such as List and Maybe, do allow values out of the monad.
    > So it is possible to write non-monadic functions that internally do
    > computations in those monads. The one-way nature of the IO monad also
    > has consequences when combining monads, a topic that is discussed in
    > part III.
    > ----------

In summary, I've only a vague idea of what you are trying to say.  If you
can't reformulate it more precisely, don't add the above stuff.

    > and a little farther down:

    > ----------
    > Some people argue that using monads to introduce non-pure features into
    > Haskell disqualifies it from claiming to be a pure functional language.
    > This subtle question   not particularly relevant to the practical
    > programmer   is revisited in the context of the I/O monad later in the
    > tutorial.
    > ----------

That's fair enough.  I don't think the question is so much subtle as
religious, as we might expect from the terminology of "purity". 

    > Later, in the section on the I/O monad:
    > ----------
    > In Haskell, the top-level main function must have type IO (), so that
    > programs are typically structured at the top level as an
    > imperative-style sequence of I/O actions and calls to functional-style
    > code. Revisiting the debate about the purity of Haskell (in a functional
    > sense), it is important to note that the IO monad only simulates
    > imperative-style I/O. 

That (about simulation) seems weak.  A simulation isn't a vague syntactic 

    > The functions exported from the IO module do not
    > perform I/O themselves. They return I/O actions, which describe an I/O
    > operation to be performed. The I/O actions are combined within the IO
    > monad (in a purely functional manner) to create more complex I/O
    > actions, resulting in the final I/O action that is the main value of the
    > program. The result of the Haskell compiler is an executable function
    > incorporating the main I/O action. Executing the program "applies" this
    > ultimate I/O action to the outside world to produce a new state of the
    > world. 

That seems to me the wrong thing to say.  There is no application.  Whether
or not the word is put in quotes, it is something involving a function
and an argument.  An IO action is not a function.

    > This occurs only once per execution of the program, and since the
    > state of the world changes for each execution, the issue of purity is
    > neatly side-stepped.
    > ----------

By "the program", I think you mean the IO action.  I think it is right to
speak of the action as something that is executed.  Execution may involve
(side-effect free) calculation; but execution is something essentially 
different from calculation, not an impure form of it.

I'm sorry to sound negative -- it's just that you invited criticism.
Your pages seem generally of a very high quality to me.  Sorry not
to be more constructive too. 

Peter Hancock