There is a VM model for APL languages[1] which can make optimizations comparable to those made by CLP(FD). If you read about CLP(FD) implementations[2], you'll see operations similar to what the "An APL Machine" paper calls beating. I'm not sure if any APL-like languages actually implement such optimizations.
There are different models of arrays (and their types) used by APL-like languages[3]. Also array frame agreement can be statically typed[4], though it usually isn't.
Some other OSS implementations of similar languages include Nial[5], ngn/k[6], and GNU APL[7]. My favorite is ngn/k. If you use a K-like language, a great source of inspiration is nsl[8].
There is an unusual and fun calculus book that uses J, by Iverson, but it moves somewhat quickly and loosely[9]. It perhaps gives a good example of what APL was intended to be(?). On that note, his original paper, "Notation as a Tool of Thought" is interesting[10]. There is also podcast interview with Robert Kowalski, one of the creators of Prolog, who says - if I remember correctly - that he was looking for a better way of thinking when he came up with SLD resolution[11]. It's interesting how these languages came out of different paths towards a similar goal.
Also beware the reverence of Arthur Whitney. His work is definitely inspired, but the community around K can seem schizoid-like[12], in a way comparable to Wolfram's projects[13].
That said, J is an exceptionally fun language to use. My favorite insight from an APL-like language that generalizes is how K encourages writing functions that converge by the easiest-to-use loop operator being one that applies a function to an argument repeatedly until the output stops changing.
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[1]: https://www.softwarepreservation.org/projects/apl/Papers/197...
[2]: http://cri-dist.univ-paris1.fr/diaz/publications/GNU-PROLOG/... (there are probably more to the point papers, this is just the one I read when I noticed the similarities).
[3]: https://aplwiki.com/wiki/Array_model
[4]: https://www.khoury.northeastern.edu/home/jrslepak/typed-j.pd... (implemented in racket iirc)
[5]: https://www.nial-array-language.org/
[6]: https://codeberg.org/ngn/k (honestly it is a miracle this exists)
[7]: https://www.gnu.org/software/apl/
[8]: https://nsl.com
[10]: https://www.eecg.utoronto.ca/~jzhu/csc326/readings/iverson.p...
[11]: https://thesearch.space/episodes/1-the-poet-of-logic-program...
[12]: https://www.ijpsy.com/volumen3/num2/63/the-schizoid-personal...
[13]: http://genius.cat-v.org/richard-feynman/writtings/letters/wo...