For computer applications of Lojban, there needs to be a formal grammar of numbers. I started from xorxes' grammar below, and revised it in places and made it into a PEG grammar.

I intend to meet all the rules in chapter 18 of CLL, except the one where it contradicts Lojban for Beginners, and LfB has the more useful reading. Namely, you can have a decimal point inside a "digit" (segment) of a mixed-base number like a time.

This involves defining 14 new selma'o. SA is not handled yet (what should it do inside a number?) Also, letters mixed with numbers are not handled, but I consider this a feature and not a bug.

The "number" rule in the existing grammar is replaced, and these rules are inserted:

digits <- digit+

thousand <- digits? KIhO

whole <- thousand+ digits? / digits

approx <- whole / MAhU

after-decimal <- whole? ( RAhE whole? / JIhI approx? )?

approx-decimal <- (whole? PI)? approx

decimal2 <- whole (PI after-decimal / JIhI approx-decimal)? / PAI

decimal1 <- MAhU? decimal2 / MAhU

decimal <- decimal1 CEhI?

digitplace <- decimal PIhE?

tuple <- digitplace+

real <- decimal / tuple / indef

indef <- PI? RO / TUhO

fraction <- real? FIhU fraction? / real

complex <- fraction? KAhO fraction? / fraction

quantity <- real / fraction / DAhA quantity

range <- DAhA? SUhO quantity?

number <- indef number / range+ / complex / quantity

NO <- pre-cmavo NO-words post-cmavo

NO-words <- "no" / "pa" / "re" / "ci" / "vo" / "mu" / "xa" / "ze" / "bi" / "so" / "dau" / "fei" / "gai" / "jau" / "rei" / "vai" / "0" / "1" / "2" / "3" / "4" / "5" / "6" / "7" / "8" / "9"

MAhU <- pre-cmavo MAhU-words post-cmavo

MAhU-words <- "ma'u" / "ni'u"

SUhO <- pre-cmavo SUhO-words post-cmavo

SUhO-words <- "su'e" / "su'o" / "me'i" / "za'u"

TUhO <- pre-cmavo TUhO-words post-cmavo

TUhO-words <- "tu'o" / "xo"

PAI <- pre-cmavo PAI-words post-cmavo

PAI-words <- "pai" / "te'o" / "ci'i"

CEhI <- pre-cmavo CEhI-words post-cmavo

CEhI-words <- "ce'i"

KIhO <- pre-cmavo KIhO-words post-cmavo

KIhO-words <- "ki'o"

PI <- pre-cmavo PI-words post-cmavo

PI-words <- "pi"

PIhE <- pre-cmavo PIhE-words post-cmavo

PIhE-words <- "pi'e"

RAhE <- pre-cmavo RAhE-words post-cmavo

RAhE-words <- "ra'e"

RO <- pre-cmavo RO-words post-cmavo

RO-words <- "ro" / "so'a" / "so'e" / "so'i" / "so'o" / "so'u" / "rau" / "du'e" / "mo'a" / "no'o"

JIhI <- pre-cmavo JIhI-words post-cmavo

JIhI-words <- "ji'i"

KAhO <- pre-cmavo KAhO-words post-cmavo

KAhO-words <- "ka'o"

DAhA <- pre-cmavo DAhA-words post-cmavo

DAhA-words <- "da'a"

FIhU <- pre-cmavo FIhU-words post-cmavo

FIhU-words <- "fi'u"

*mi'e rab.spir*

### Grammar proposed by xorxes (work in progress):

quantifier <- quantity* FIhU quantity* / quantity+ / PI quantity / real CEhI

quantity <- SUhO* RO / SUhO+ digits? / digits

complex <- real? KAhO real? / real

real <- SUhO* MAhU? (decimal / fraction / aleph / digits / PAI)

decimal <- digits? PI digits? (RAhE digits)?

fraction <- digits? FIhU digits?

aleph <- CIhI digits*

digits <- NO+ / TUhO

### New selma'o

NO | no, pa, re, ci, vo, mu, xa, ze, bi, so, dau, fei, gai, jau, rei, vai, ki'o, pi'e |

RO | ro, so'a, so'e, so'i, so'o, so'u, rau, du'e, mo'a, no'o |

SUhO | su'o, su'e, me'i, za'u, ji'i, da'a |

MAhU | ma'u, ni'u |

TUhO | tu'o, xo |

CIhI | ci'i |

PAI | pai, te'o |

FIhU | fi'u |

KAhO | ka'o |

PI | pi |

RAhE | ra'e |

CEhI | ce'i |

### Notes:

- I made {da'a} a SUhO. For da'a in front of a number I propose the following interpretation: {ta mitre li da'a cipimu}, "that is all but 3.5 meters long", i.e. "that is 3.5 meters short of what it ought to be" or something like that.
- I made {ji'i} a SUhO because it is also used to indicate a range. This means that I don't use the position of ji'i as an indicator of the magnitude of fuzziness.
- Any SUhO in front of a quantity returns another quantity, so they can be added indefinitely, even though in usage they probably won't be. For example, {za'u za'u za'u pa}, "more than more than more than one" is equivalent to {su'o vo}, "at least four" (when dealing with integers/quantifiers).
- {pi'e} and {ki'o} can mingle freely with digits, collapsing digits between {pi'e} or {ki'o}s, or between these and {pi} into a single macro-digit. {ki'o} is the special case of {pi'e} for base 1000. Digits after {pi} are decimal unless there is at least one {ki'o} or {pi'e} after {pi}.
- Two quantities in a row give the intersection if it exists, else the union. They group from left to right.

*mi'e xorxes*