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.
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
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.
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?
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!