Chapter 18: lojbau mekso: Mathematical Expressions in Lojban

18. Using Lojban resources within mekso

The following cmavo are discussed in this section:

   na'u    NAhU    selbri to operator
ni'e    NIhE    selbri to operand
mo'e    MOhE    sumti to operand
te'u    TEhU    terminator for all three

One of the mekso design goals requires the ability to make use of Lojban's vocabulary resources within mekso to extend the built-in cmavo for operands and operators. There are three relevant constructs: all three share the elidable terminator “te'u” (which is also used to terminate vectors marked with “jo'i”).

The cmavo “na'u” makes a selbri into an operator. In general, the first place of the selbri specifies the result of the operator, and the other unfilled places specify the operands:

✥18.1    li na'u tanjo te'u
    vei pai fe'i re [ve'o] du li ci'i
the-number the-operator tangent
    ( pi / 2 ) ⇔ the-number infinity
tan(pi/2) ⇔ ¥

“tanjo” is the gismu for “x1 is the tangent of x2”, and the “na'u” here makes it into an operator which is then used in forethought.

The cmavo “ni'e” makes a selbri into an operand. The x1 place of the selbri generally represents a number, and therefore is often a “ni” abstraction, since “ni” abstractions represent numbers. The “ni'e” makes that number available as a mekso operand. A common application is to make equations relating pure dimensions:

✥18.2    li ni'e ni clani [te'u] pi'i
    ni'e ni ganra [te'u] pi'i
    ni'e ni condi te'u
    du li ni'e ni canlu
the-number quantity-of length times
    quantity-of width times
    quantity-of depth
    equals the-number quantity-of volume.
Length × Width × Depth ⇔ Volume

The cmavo “mo'e” operates similarly to “ni'e”, but makes a sumti (rather than a selbri) into an operand. This construction is useful in stating equations involving dimensioned numbers:

✥18.3    li mo'e re ratcu su'i mo'e re ractu
    du li mo'e vo danlu
the-number two rats plus two rabbits
    equals the-number four animals
2 rats + 2 rabbits ⇔ 4 animals.

Another use is in constructing Lojbanic versions of so-called “folk quantifiers”, such as “a pride of lions”:

✥18.4    mi viska vei mo'e lo'e lanzu ve'o cinfo
I see ( the-typical family )-number-of lions.
I see a pride of lions.