[moonchild]

> Admittedly the J implementation at least of deriving a generalized inverse for an arbitrary function f is a somewhat ill-defined hack

Have you seen the version used by dzaima/apl[1]? The equivalent of '(-&.:{:) i.5' works and results in 0 1 2 3 _4.

> APL has some really dumb but cherished-by-the-community ideas that make the language less expressive and much more awkward to learn, e.g. the idea of replicating the terrible defect of normal mathematical notation where - is overloaded for negation and subtraction to every other function

Klong[2] is a partial attempt to resolve this. I won't repeat the arguments in favour of ambivalent functions, as I guess you've heard them a dozen times before

> u(f,g) = x => f^-1(g(f(x)).

Other way round; it's g^-1(f(g(x)))

1. https://github.com/dzaima/apl

2. https://t3x.org/klong/

[patrec]

Is there an argument for ambivalent function definitions other than "keyword" recycling (possibly in a mnemonic fashion)?

I hadn't seen Dzaima's APL, thanks! I like that he made a processing binding; APL always seemed like it would be such an obvious choice for doing dweet style graphics code golfing that I wondered why no one seemed to be doing it. A web-based APL would be a better choice though.

[moonchild]

> web-based

In that case you'll be wanting ngn/apl[1], which runs in a browser and compiles to js.

> ambivalent

The arguments are mostly linguistic. Natural language is also context-sensitive, so we are well-equipped to parse such formations; and they allow us to reuse information. The monadic and dyadic forms of '-' are related, so it's less cognitive overhead to recognize its meaning.

1. https://gitlab.com/n9n/apl

[dzaima]

Keyboard space is another somewhat important factor. My layout for dzaima/APL already uses all altgr keys, so I could definitely not afford multiplying the number of needed characters by 2. Not having ambivalently callable operators would also mean needing 2 versions of most of them.

dzaima/APL being written in Java means getting it to run in a browser would be a bit hard, and ngn has given up on ngn/apl, but BQN[0] could definitely get a web canvas based graphics interface.

Somewhat interesting to add to the conversation about Under is that, in my impl, calling a function, calling its inverse, or doing something under it (i.e. structural under) are all equally valid ways to "use" a function, it's just a "coincidence" that there's direct syntax for invoking only one. (Dyalog does not yet have under, but it definitely is planned.)

0. https://mlochbaum.github.io/BQN/