From: Paul Taylor <pt@dcs.qmw.ac.uk>
To: categories@mta.ca
Subject: Re: Category Theory and Hereditarily-Finite Sets
Date: Thu, 19 Apr 2001 19:29:13 +0100 [thread overview]
Message-ID: <200104191829.TAA04249@koi-pc.dcs.qmw.ac.uk> (raw)
> Hereditarily-finite sets are becoming increasingly more popular
> in computer science research.
Why? Because some ill-advised first year maths lecturer told you that
the element relation was the foundation of mathematics, maybe?
> "object" is a hereditarily-finite set plus some structure on the set
> and a "morphism" would be a structure-preserving function.
If you're really interested in heredity, so the "structure" is the
element relation, this is a well-founded coalgebra for the covariant
powerset functor.
Coalgebras for the powerset functor were first studied by Gerhard Osius
in JPAA in 1974, although he considered recursion rather than induction.
Well founded coalgebras for general functors (but with some emphasis
on the powerset) are defined in Section 6.3 of my book "Practical
Foundations of Mathematics" (Cambridge University Press, 1999).
The exercises for that chapter show how various ideas with recursive
programs may be expressed in these terms. In particular, unary
recursion (with at most one recursive call at each level) is reduced
to tail recursion (equivalent to while programs) together with an
accumulator monoid.
Paul
next reply other threads:[~2001-04-19 18:29 UTC|newest]
Thread overview: 3+ messages / expand[flat|nested] mbox.gz Atom feed top
2001-04-19 18:29 Paul Taylor [this message]
2001-04-19 21:19 ` Wilkins E B
-- strict thread matches above, loose matches on Subject: below --
2001-04-18 23:50 Galchin Vasili
Reply instructions:
You may reply publicly to this message via plain-text email
using any one of the following methods:
* Save the following mbox file, import it into your mail client,
and reply-to-all from there: mbox
Avoid top-posting and favor interleaved quoting:
https://en.wikipedia.org/wiki/Posting_style#Interleaved_style
* Reply using the --to, --cc, and --in-reply-to
switches of git-send-email(1):
git send-email \
--in-reply-to=200104191829.TAA04249@koi-pc.dcs.qmw.ac.uk \
--to=pt@dcs.qmw.ac.uk \
--cc=categories@mta.ca \
/path/to/YOUR_REPLY
https://kernel.org/pub/software/scm/git/docs/git-send-email.html
* If your mail client supports setting the In-Reply-To header
via mailto: links, try the mailto: link
Be sure your reply has a Subject: header at the top and a blank line
before the message body.
This is a public inbox, see mirroring instructions
for how to clone and mirror all data and code used for this inbox;
as well as URLs for NNTP newsgroup(s).