Here is an informal grammar of numbers. I am not even
suggesting that this should be part of the formal grammar,
it is just an exercise to sort out which combinations
of PA make sense and which don't. I can make some sort of
sense of all combinations generated by this grammar. As
for those not generated by it, maybe some meaning could
eventually be found for them, but there is nothing as
yet defined as far as I can tell.
<pre-sign> = (ji'i|su'e|su'o|me'i|za'u)...
<sign> = ma'u|ni'u
<digit> = no|pa|re|ci|vo|mu|xa|ze|bi|so|dau|fei|gai|jau|rei|vai|ki'o|xo
<indef> = ro|so'a|so'e|so'i|so'o|so'u|su'o|da'a|no'o|rau|du'e|mo'a
<bare> = [<digit>...][pi [[<digit>...][[ra'e <digit>...]]|[pi] <indef>
<real> = [<pre-sign>][<sign>][<bare>|ci'i|pai|te'o][ce'i]
<fraction> = [<real>][fi'u <real>]
<complex> = [<fraction>][ka'o <fraction>] | tu'o
<n-tuple> = [<complex>][pi'e <complex>]...
Notes:
- I didn't put the indefinites at the same level as the digits, because it doesn't really make sense to me for so'a to stand for 8 or 9, so'e for 6 or 7, etc. To me they are always full numbers, not positional digits.
- I allowed ce'i in a couple of weird places, for example you could say muce'ifi'ucice'i, 5%/3%, which does not have a very obvious meaning, but to restrict ce'i more would have complicated the grammar a lot and it didn't seem justified.
- I chose to make fi'u more close binding than ka'o. Either choice was possible. So cika'ovofi'umu is 3+(4/5)i and not (3+4i)/5.
- I didn't allow double fractions, so that 3/4/5 is neither (3/4)/5 nor 3/(4/5), it is simply not meaningful in my scheme.
- I allowed fractions such as 3.5/2.7, why not?
- Probably ji'i needs more work, but I didn't want it as a positional digit.
- I left xo as a positional digit, but I have my doubts about it.
Comments welcome!
co'o mi'e xorxes
- tinkit try xei instead of rei. xo really should be an indef. oh, and what's the initial non-terminal?