It turns out there's a more powerful and arguably more interesting version of the Löb fixpoint in a setting where we have a ComonadApply, i.e. a structure that's not merely a functor, but also a comonad and comonad's version of Applicative. What emerges looks like spreadsheet evaluation in arbitrarily shaped spaces, with relative references provided by the comonadic structure.
I've always found this stuff tremendously fun, and it's a delight that people keep stumbling across it who share my enthusiasm!
To be fair, loeb was already a generalization of fix. If `f` is the identity functor, then `loeb` has type `(a -> a) -> a`, and the `fmap` used in its definition resolves to `id`.
It's a shame there aren't any other example applications of moeb. The author mentions using `traverse` and `foldMap`, but those are also based fundamentally on `fmap` in some sense, and I wouldn't be too surprised if they also ended up being literally `fmap` for some specific choice of functor.
This stuff is really cool; I’ve literally written an article about it myself. However, unless you address the possibility of entering an infinite loop, it’s not really that useful.
very useful when writing toy assemblers in Haskell as loeb let's you easily resolve labels to addresses once you've output the other instructions. Also a good use of the tardis monad which does the same thing as loeb but with a bit more panache
maybe something to do with Haskell being a beautiful and foundational language that has been a major driver of progress in programming language design for the last two decades?
Ten years ago Dan Piponi's 2006 exploration of this same idea (http://blog.sigfpe.com/2006/11/from-l-theorem-to-spreadsheet...) inspired me to write the paper "Getting a Quick Fix on Comonads" (https://github.com/plaidfinch/GQFC), which ended up in Haskell Symposium 2015.
It turns out there's a more powerful and arguably more interesting version of the Löb fixpoint in a setting where we have a ComonadApply, i.e. a structure that's not merely a functor, but also a comonad and comonad's version of Applicative. What emerges looks like spreadsheet evaluation in arbitrarily shaped spaces, with relative references provided by the comonadic structure.
I've always found this stuff tremendously fun, and it's a delight that people keep stumbling across it who share my enthusiasm!
> This shows how moeb is a generalization of fix.
To be fair, loeb was already a generalization of fix. If `f` is the identity functor, then `loeb` has type `(a -> a) -> a`, and the `fmap` used in its definition resolves to `id`.
It's a shame there aren't any other example applications of moeb. The author mentions using `traverse` and `foldMap`, but those are also based fundamentally on `fmap` in some sense, and I wouldn't be too surprised if they also ended up being literally `fmap` for some specific choice of functor.
(2013) Popular in:
2021 (153 points, 60 comments) https://news.ycombinator.com/item?id=34578411
2018 (86 points, 10 comments) https://news.ycombinator.com/item?id=18159087
I did not expect this to surface after all these years, but here we are! o:-)
Reminds me of this classic doing the same: http://blog.sigfpe.com/2006/11/from-l-theorem-to-spreadsheet...
I’ve read the post carefully and I still don’t get how they proved Santa Claus without proving the proposition.
This stuff is really cool; I’ve literally written an article about it myself. However, unless you address the possibility of entering an infinite loop, it’s not really that useful.
https://colourcoding.net/2018/03/29/marvellous-moeb/
FTFY :)
Nice one. It was meant to be part one of two, but I never wrote part two…
A writer without unwritten article can throw the first stone... :)
Uuh i miss the strange loop conference. It was simply the best and most fun programming related conference ever.
gtk-daemons in Gödel's incompleteness theorem, where Löb functor cell value differ from readiness-to-hand and presence-at-hand.
very useful when writing toy assemblers in Haskell as loeb let's you easily resolve labels to addresses once you've output the other instructions. Also a good use of the tardis monad which does the same thing as loeb but with a bit more panache
Whats up with all these haskell articles being posted all of a sudden (many of them by quchen)
maybe something to do with Haskell being a beautiful and foundational language that has been a major driver of progress in programming language design for the last two decades?
I suppose you could argue when it started being a major driver of progress, but it's actually been around for 3.5 decades!
https://en.wikipedia.org/wiki/Haskell#Haskell_1.0_to_1.4