[Haskell-cafe] The values of infinite lists

[Brian Hulley]

Paul Hudak wrote:
> Hi Claus --
>
> I think that you're asking for a semantics of the entire OS, i.e. the
> entire outside world, and for that I agree that something other than
> equational reasoning is needed to reason about it.  However, I would
> argue that that is outside the mandate of a book on Haskell.  But
> maybe that's the point -- i.e. others feel otherwise.
>
> My main point it that if we're reasoning about a single Haskell
> program (with no impure features), then the entire world, with all its
> non-determinism internal to it, can be modelled as a black box --
> i.e. a function -- that interacts with the single Haskell program in a
> completely sequential, deterministic manner.  And for that, equational
> reasoning is perfectly adequate.

I think the problem is that to understand something you need a lot more than 
just the capability to reason about it.
For example, given laws such as:

           x * (y + z) == (x * y) + (x * z)
           x + (y + z) = (x + y) + z

I can reason that

           x * (y + (z + w)) = (x * y + x * z) + x * w

But this does *not* mean that therefore I *understand* it. I think 
understanding is a much deeper process. I have to grapple with the 
underlying shape, the gesture, the motion of the symbolic transformation and 
really *feel* the lawfulness of it as a profound inner life experience.

So to get back to the question of understanding monads, yes I can reason 
about them equationally using pure functions but to understand Haskell I 
need to understand how it is situated in my own human experience and my 
human experience seems to me to be more than just a deterministic sequential 
function of Unique -> Time -> SenseInput.

Regards, Brian.