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.
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