> ...and the right-to-left evaluation logic.

The evaluation order doesn't matter as much as you don't really know what kind of function/operator you have at parse time so have to do a bunch of shenanigans to defer that decision until runtime while still keeping it efficient. Kind of fiddly to get right but once it works, it just works.

Claude and me (and a ton of decades old research) pretty much figured out all the complications in the APL parse/eval stack (https://github.com/dan-eicher/AiPL).