[Haskell-cafe] Re: Re: Why monad tutorials don't work
dominic.steinitz at blueyonder.co.uk
Wed Aug 15 17:55:45 EDT 2007
Dan Piponi <dpiponi <at> gmail.com> writes:
> On 8/15/07, Dan Weston <westondan <at> imageworks.com> wrote:
> > "You too could have invented Universal Algebra and Category Theory".
> > I nominate Dan Piponi to write it and eagerly await its release!
> I've already started on it. Well, that's not the exact title and
> subject. And as an example I'll probably use the definition of tensor
> product that I linked to, not the even more compact and elegant one
> that you just gave.
> I'm a strong believer that lots of (but not all) tricky looking
> mathematics is just fancy language for intuitions that people already
> have. I suspect that most computer scientists already have much of the
> intuition behind the idea of a universal property, and that it is in
> fact easier to grasp for a computer scientist than a mathematician.
Some universal properties (initial algebras and final co-algebras) are covered
in Functional Programming with Bananas, Lenses, Envelopes and Barbed Wire (1991)
(http://citeseer.ist.psu.edu/meijer91functional.html). And of course there's
Wadler's Theorems for Free.
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