Add an `under` macro for bidirectional transformation about alma

[vendethiel]

APL can actually do "under"... ish. Its Star Diaeresis (⍣) operator repeats an operation N times, but the number of times can actually be ¯1.

It's gonna be really hard to show a legible example, because of how APL reads in general, but I'll still try:

(×∘2)⍣¯1⊢3 ⍝ The whole operation
(×∘2)           ⍝ A partially applied multiplication operator, in Raku this'd be *×2
        ⍣¯1      ⍝ Repeated -1 times, inverse of this function
             ⊢3  ⍝ Applied to 3

This results in 1.5.

The way you could have "dual" would be to first, apply the "forward" operation, then apply the whole block, then apply the inverse of the "forward" operation.
I'm gonna post a "dual" here. I can detail it, but it's gonna be hard to read no matter what.
⍺⍺ is "function to the left", ⍵⍵ is "function to the right", and ⍵ is "argument to the right".

      f←{⍺⍺⍣¯1⊢⍵⍵⍺⍺⍵}
      (×∘2)f(+∘2)⊢5
6

(×∘2) is the function to the left (⍺⍺), (+∘2) is the function to the right (⍵⍵), 5 is the argument to the right (⍵).
So what happens is this:

(×∘2)⍣¯1⊢2+2×5

Which calculates (2*5+2)/2, 6.

A bit long-winded for a narrow use case, but the sentiment is the same. Dyalog APL Extended, which is an extension to Dyalog APL, has this "under" function as the operator ⍢.

[masak]

@vendethiel Thank you for the explanation. It's good to know about prior art. I agree APL is somewhat opaque, but (thanks to your explanations), I think I actually got it.

It feels to me the under macro is doing something more, semantically. The APL version passes around values fairly to transform forwards-and-backwards fairly explicitly. The under macro implicitly injects/wraps forward and backward calls around values which cross in and out (respectively) of the lexical environment of the under block.

I don't recall seeing that technique before; the closest thing it reminds me of is our treatment of free variables in quasi blocks (which turn into "direct lookups" per #410). Maybe variable interpolations in Raku regexes could be considered a variant of this pattern, too. under is lexically changing the "meaning" of free variables — I'm a bit surprised myself at how OK I am with that. It feels slightly related to exists (#292) and delete (#290) in that it "changes how we evaluate something" (but via a syntax transformation).