I think that the original problem is due to the fact that Haskell does not
know how to handle ordinals properly:
Let S be the set of countable finite ordinals; if w = \omega is the first
countably infinite ordinal and N the set of natural numbers, then S can be
identified with N[w], the set of polynomials with coefficients in the set
of natural numbers. The set S is well ordered. If A is a set, then an at
most countably infinite list l with values in A can be viewed as a map l: I
-> A, where I is an interval of S containing 0 (the smallest element of S).
Now look at
l = [(x, y) | x <- [0..], y <- [0..] ]
which in Hugs produces the output
[(0,0),(0,1),(0,2),(0,3),(0,4) ....
without ever terminating or exhausting the first variable. But if lists are
defined as merely maps N -> A, then this object is not even well defined as
a list: we have failed to set up a proper function defining the list.
However, using the definition using ordinals above, we can define l as the map
a + b w |-> (a, b)
which is clearly well defined. One can similarly concatenate infinite lists.
So now the problem is no longer how to properly create the infinite list,
but how to properly print it out once it has been created. That consists of
finding a suitable projection pi: N -> I subset S = N[w], and then print
l_pi(i), i = 0,1,2, ...
But point is that the different possible choices of projection pi does not
affect the mathematical object l.
Hans Aberg
* Email: Hans Aberg <mailto:[EMAIL PROTECTED]>
* Home Page: <http://www.matematik.su.se/~haberg/>
* AMS member listing: <http://www.ams.org/cml/>
