I'd like to see perhaps a specific brief example, where using Racket booleans within Arc actually is a problem, because I haven't encountered any myself.

If I try to use the hash from your example in actual Arc code, it works fine:

    arc> (if ((w/instring in "{\"foo\": true}" ($.read-json in)) 'foo) 'yes 'no)
    yes
    arc> (if ((w/instring in "{\"foo\": false}" ($.read-json in)) 'foo) 'yes 'no)
    no

Ah, here's perhaps the only special-case we need to handle:

    arc> (= x (w/instring in "{\"foo\": null}" ($.read-json in)))
    #hash((foo . null))  # expected: #hash((foo . nil)) or #hash()
    arc> (if x!foo (prn "error"))
    error

Actually the Racket docs[0] clarifies the situation with null in JSON:

    (json-null) → any/c

    (json-null jsnull) → void?
      jsnull : any/c

If you set the JSON null to nil before running your example, it works as you'd expect:

    arc> ($.json-null nil)
    #<void>
    arc> (= x (w/instring in "{\"foo\": null}" ($.read-json in)))
    #hash((foo . nil))
    arc> (if x!foo (prn "error"))
    nil

I recommend (obj), (obj foo (list 'null)), (obj foo (list 'false)), and (obj foo (list (list))). Arc is good at representing optional values as subsingleton lists:

  ; Access a key that's known to be there.
  t!foo.0
  
  ; Access a key that isn't known to be there.
  (iflet (x) t!foo
    (do-something-then x)
    (do-something-else))

Meanwhile, I don't think there's any big deal when we don't have Arc-style booleans....

  ; Branch on the symbols 'false and 'true.
  (if (isnt 'false x)
    (do-something-then)
    (do-something-else))
  
  ; Alternative
  (case x true
    (do-something-then)
    (do-something-else))

We do already have booleans that work in Arc without any conversion. Please see http://arclanguage.org/item?id=20492

But now that I look closer at the ac.scm history (now ac.rkt in Anarki), I realize I was mistaken to believe Arc treated #f as a different value than nil. Turns out Arc has always equated #f and 'nil with `is`, counted them both as falsy, etc. So this library was already returning nil, from Arc's perspective.

There are some things that slip through the cracks. It looks like (type #f) has always given an "unknown type" error, as opposed to returning 'sym as it does for 'nil and '().

Really, #t and #f are not proper Arc booleans[0], so it makes sense that Arc can't tell what type they are.

You can configure the value Arc chooses for a JSON null with the $.json-null function, which I think is fine as JSON APIs might have differing semantics.

There are a lot of ways to conceive of what Arc "is" outside of the Racket implementations, but I think Arc implementations like Rainbow, Jarc, Arcueid, and so on tend to be inspired first by the rather small set of operations showcased in the tutorial and in arc.arc. (As the tutorial says, "The definitions in arc.arc are also an experiment in another way. They are the language spec.") Since #f isn't part of those, it's not something that an Arc implementation would necessarily focus on supporting, so there's a practical sense in which it's not a part of Arc our Arc code can rely on.

Really, #t and #f are not proper Arc anything, but the language apparently handles them so IMHO Arc should also be able to know what type they are. Otherwise, I fear, this will become a Hodge Podge language that will lose appeal.