Re: SUO: tuples

[Chris Menzel <cmenzel@tamu.edu>]

On Sat, Jul 06, 2002 at 10:28:23AM -0700, Robert E. Kent wrote:
> ...This notion of abstract IFF tuple is also related to the way that
> the Common Logic (CL) specification
> <http://cl.tamu.edu/discuss/cl-syntax-semantics.pdf> handles sequence
> variables. What do we need here?  Are we thinking of modeling sequences
> as mere strings with concatenation, or are CL sequences more like
> lists. 

We don't say.  We just introduce a primitive notion of sequence and
leave it at that, though of course we assumed that they have the usual
abstract properties (e.g., linear and well-ordered).  Of course, the
standard understanding of a sequence is as a function on some initial
segment of N, and the usual set theoretic representation of a function
is as a certain kind of set of ordered pairs, which in turn are
represented as unordered sets of a certain kind.  And that's what
sequences would be if one were hung up on representing everything in
pure set theory.  But there's no reason why one couldn't think of
"sequence" as a metatheoretic primitive.  I reckon that way of looking
at things would be more amenable to the abstract, category theoretic
approach of IFF.

-chris

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