[Haskell-cafe] The values of infinite lists

Brian Hulley brianh at metamilk.com
Wed May 10 14:49:07 EDT 2006

Robert Dockins wrote:
> On Wednesday 10 May 2006 12:30 pm, Brian Hulley wrote:
>> Bjorn Lisper wrote:
>>> Nontermination is not
>>> the precisely the same as _|_. Only certain kinds of nontermination
>>> can be modeled by _|_ in a non-strict language.
>> What kinds of non-termination are *not* modelled by _|_ in Haskell?
> Non-termination that is "doing something".
> For example consider:
> ] ones = 1 : ones
> If I try to take its length, I get _|_.  So:
> ] main = print (length ones)
> Will churn my CPU forever without producing any output.
> However, if I print each item sequentially:
> ] main = mapM print ones
> I'll get a never-ending stream of '1' on my console.  This is not the
> same as bottom because it's "doing something".

I can see what you're getting at, but I don't know if I agree with the idea 
that "doing" should affect whether or not one sees the result of the above 
computation as bottom or not. With a hypothetical implementation of

              runIO :: IO a -> RealWorld -> (RealWorld, a)

I could write:

] (r',_) = runIO (mapM print ones) realWorld

and this computation, even though some printing would be observable, still 
evaluates to bottom, because r' will never be bound.

> Now, obviously this definition is pretty imprecise, but maybe it
> helps you get the idea.  Now for the corner cases.  What about:
> ] main = sequence_ repeat (return ())
> ?  I'd personally say it is _not_ bottom.  Even though "return ()" is
> a completely useless action, I'm inclined to say its "doing
> something" in some theoretical sense (mostly because I think of _|_
> as being a property of the functional part of Haskell).

I thought everything in Haskell is purely functional - surely that is the 
whole point of using monads? :-)
I'd have thought that "doing" is simply a  projection of the purely 
functional "being" into the stream of time and therefore cannot be part of 
the discourse regarding the nature of bottom...

Regards, Brian. 

More information about the Haskell-Cafe mailing list