On Wed, Mar 4, 2009 at 3:38 PM, Achim Schneider <bars...@web.de> wrote:
> There's not much to understand about CT, anyway: It's actually nearly > as trivial as set theory. You mean that theory which predicts the existence of infinitely many infinities; in fact for any cardinal, there are at least that many cardinals? That theory in which aleph_1 and 2^aleph_0 are definitely comparable, but we provably cannot compare them? The theory which has omega_0 < omega_1 < omega_2 < ... omega_omega < ..., where obviously omega_a is much larger than a... except for when it catches its tail and omega_alpha = alpha for some crazy-ass alpha. I don't think set theory is trivial in the least. I think it is complicated, convoluted, often anti-intuitive and nonconstructive. Category theory is much more trivial, and that's what makes it powerful. (Although training yourself to think categorically is quite difficult, I'm finding) > One part of the benefit starts when you begin > to categorise different kind of categories, in the same way that > understanding monads is easiest if you just consider their difference > to applicative functors. It's a system inviting you to tackle a problem > with scrutiny, neither tempting you to generalise way beyond > computability, nor burdening you with formal proof requirements or > shackling you to some other ball and chain. > > Sadly, almost all texts about CT are absolutely useless: They > tend to focus either on pure mathematical abstraction, lacking > applicability, or tell you the story for a particular application of CT > to a specific topic, loosing themselves in detail without providing the > bigger picture. That's why I liked that Rosetta stone paper so much: I > still don't understand anything more about physics, but I see how > working inside a category with specific features and limitations is the > exact right thing to do for those guys, and why you wouldn't want to do > a PL that works in the same category. > > > Throwing lambda calculus at a problem that doesn't happen to be a DSL > or some other language of some sort is a bad idea. I seem to understand > that for some time now, being especially fond of automata[1] to model > autonomous, interacting agents, but CT made me grok it. The future will > show how far it will pull my thinking out of the Turing tarpit. > > > [1] Which aren't, at all, objects. Finite automata don't go bottom in > any case, at least not if you don't happen to shoot them and their > health drops below zero. > > -- > (c) this sig last receiving data processing entity. Inspect headers > for copyright history. All rights reserved. Copying, hiring, renting, > performance and/or quoting of this signature prohibited. > > > _______________________________________________ > Haskell-Cafe mailing list > Haskell-Cafe@haskell.org > http://www.haskell.org/mailman/listinfo/haskell-cafe >
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