In my experience, Monad, Applicable, and Monoid are probably the only ones I'd use in Haskell, and maybe none of them in languages without good inference and general support. Pretty wild ideas, though. Fair chance they'd be more confusing than using more specifically named instances, but solid ideas where the class instance documents that you're using the pattern, instead of describing the preferred interface.
Programming with Categories
41–50 of 113 posts
Re: Programming with Categories
#42Re: Programming with Categories
#43As someone who respects functional programming (because it removes geniuses from competing in my space) here's a nice video https://www.youtube.com/watch?v=ADqLBc1vFwI What is the beautiful monospace font in the pdf here http://brendanfong.com/programmingcats_files/cats4progs-DRAF... ?
> here's a nice video https://www.youtube.com/watch?v=ADqLBc1vFwI OMG. That might just be the funniest god-damned thing I've ever seen in my life. Thanks for sharing that! On a separate note: does anyone know where this footage is originally from? Some WWII movie, I would guess?
Probably one of the best "WWII movies" (it's really only about the final days in the bunker) ever.
Re: Programming with Categories
#44When previously taught, people would remain afterwards to ask questions, discuss math, and chat. So this was an iterative-improvement formalization of that.
People would gather in front of the blackboards in fluid discussion clusters. Catalyzed by the three instructors and wizzy others, not all having to stay for the entire hour, but drifting off as discussion died away. They could show material they had pruned from the lecture, for want of time. Or got dropped as they ran over. Alternate presentation approaches they had considered, before selecting another. They could be much more interactive. One commented roughly "If I was tutoring someone, I'd never present the material this way". It was a delightful mix of catching the speaker after a talk to ask questions, a professor's office hours, a math major's lounge, an after-talk social, tutoring, an active-learning inverted classroom, hanging out with neighbors in front of the hallway blackboard, chalk clattering and cellphones clicking to snag key insights... It was very very nifty.
So, the book is nice. And lecture notes. And videos. But... the best part isn't there. Perhaps the next iterative improvement is to capture the aftermath on video, and share that too.
And as we look ahead, planning distance-learning and XR tools... maybe something like this is a vision to aspire too. The insane ratio of expertise to people learning is not something one can plausibly replicate in meatspace. But as conversations in front a virtual blackboard gradually become technically feasible, something like this might pay for the cost of it, with transformative impact.
Re: Programming with Categories
#45"We will assume no background knowledge on behalf of the student, starting from scratch on both the programming and mathematics." This is a fantastic "side effect" of the fact that category theory isn't built on any other mathematical knowledge. You don't even need even any arithmetics for that.
This is almost every upper division undergrad math class. It was always fun watching people squirm when they pulled out some useful fact from their past 14 years of math education and then got told they had to prove it before they could use it.
Re: Programming with Categories
#46Earlier quoted context omitted.
Oh, another Haskell can't do IO joke.
Yes, but this time it was a funny one. I laughed, and not just at AbstractSingletonProxyFactoryBean. Gotta be able to laugh at yourself sometimes.
Re: Programming with Categories
#47Re: Programming with Categories
#48As someone who respects functional programming (because it removes geniuses from competing in my space) here's a nice video https://www.youtube.com/watch?v=ADqLBc1vFwI What is the beautiful monospace font in the pdf here http://brendanfong.com/programmingcats_files/cats4progs-DRAF... ?
Hitler: What's a monad anyway? No one who understands monads can explain what they are Underling (hurriedly): A monad is just a monoid in the category of endofunctors This caused me to choke on my coffee.
Re: Programming with Categories
#49Earlier quoted context omitted.
> here's a nice video https://www.youtube.com/watch?v=ADqLBc1vFwI OMG. That might just be the funniest god-damned thing I've ever seen in my life. Thanks for sharing that! On a separate note: does anyone know where this footage is originally from? Some WWII movie, I would guess?
https://en.wikipedia.org/wiki/Downfall_(2004_film) Probably one of the best "WWII movies" (it's really only about the final days in the bunker) ever.
Re: Programming with Categories
#50I've read a lot about Category Theory, and I'm amazed at the abstraction level that lets you compose with different mathematical domains (geometry, topology, arithmetic, sets, ...). And yet, the current mathematics relies heavily on the ZFC set theory. Why is that ? (Is that assumption even correct ?) From what I've learned so far, the set theory suffers from Russel's Paradox[0] (does the set of all sets that does no…
Because most math fields work at a higher level, and whether they consider set theory or category theory foundational doesn't matter. For instance, the defining property of ordered pairs is: `(a, b) = (c, d) iff a = c and b = d`. {a, {a,b}} is a (set-theoretic) model for ordered pairs, but it's not the only model. As long as a model exists, the question of "which model you're using" isn't relevant.