I was reading "Upwards and downwards accumulations on trees" by Jeremy Gibbons, and it's written in the Bird-Meertens formalism (a.k.a. Squiggol) of yesteryear. Not that I have anything against people who can write and understand this stuff (in fact, I have a lot of respect for them), but for me, the inconsistent and seemingly arbitrary notation leaves something to be desired. In an attempt to understand what was actually being done, I translated most of the equations to Haskell code. If you plan on reading this paper, here's hoping I could jump-start your comprehension with this contribution.
The only real issue that I ran into while performing this translation is in the function
s_fork_sl2. The second component of the catamorphism, ((⊙ ↟ ≪) ∘ ≪²), does not have the expected type
(b, b) -> a -> (b, b) -> (b, b). After attempting to puzzle through how to unify the two, I eventually gave up and just came up with a function that seemed to do what I thought it should do,
pairs g (x, _) _ (y, _) = (g x y, x) where
g :: b -> b -> b is ⊙. But I'm not sure whether there's a bug in the definition in the paper or the one in my code. The code seems to work for a few tests. If you've already read this paper or you're at all interested in debugging Squiggol, I would be happy to learn how this works.