MEX paper, draft 1.0, part #5 of 5

[cowan (John Cowan)]

8.  Using Lojban Resources Within mekso

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 main constructs that allow this:
"na'u", which converts a selbri (possibly with accompanying tail terms)
to an operator; "ni'e", which converts a selbri to an operand, and "mo'e",
which converts a sumti to an operand.  All three constructs share the
elidable terminator "te'u".

Example of "na'u":

	li na'u tanjo pai fe'i re du li ci'i
	tan(pi/2) = infinity

"tanjo" is the gismu for "tangent", and the "na'u" here converts it to
an operator, which is then used in forethought.

Example of "ni'e":

	li ni'e sovda be va'u lo'e tanxe te'u du li pa re
	The-number of eggs contained-by the-typical box = 12.
	There are 12 eggs in an egg carton. 

Here the selbri "sovda be va'u lo'e tanxe" (eggs contained-in a-typical box)
is converted into an operand whose value is (in the U.S., anyhow) 12.
The "te'u" is required here to avoid creating the unwanted tanru
"tanxe du"; since "du" has the grammar of a brivla, it is possible for
it to form tanru, but these tanru probably have no meaning.

Example of "mo'e":

	li mo'e lo ni le ratcu cu zvati le panka te'u du li du'e
	The quantity of rats in the park = an excessive number.
	There are too many rats in the park. 

Note the use of "du'e", a member of selma'o PA (and therefore a number)
which means "too many, an excessive number"; its meaning is subjective.


9.  Unusual Uses of mekso

So far we have seen mekso used as sumti (with "li") and as quantifiers
(usually parenthesized).  There are a few other minor uses of
mekso within Lojban.

The cmavo "me'o" has the same grammar as "li" but slightly different
semantics.  "li" means "the number which is the value of the mekso ...",
whereas "me'o" just means "the mekso..."  So it is true that

	li re su'i re du li vo
	the-number two plus two equals the-number four
	2 + 2 = 4

but false that:

	me'o re su'i re du me'o vo
	the-mekso two plus two equals the-mekso four
	"2 + 2" = "4"

since the expressions "2 + 2" and "4" are not the same.  The relationship
between "li" and "me'o" is related to that between "la'e" and "lu'e";
"li" specifies the referent, whereas "me'o" specifies the symbol string.

The cmavo "nu'a" is the inverse of "na'u", and allows a mekso operator
to be used as a normal selbri, with the place structure:

	x1 is the result of applying <the operator> to x2, x3, ...

for as many places as may be required.  For example:

	li ni'umu cu nu'a va'a li ma'umu
	the-number minus-five is-the-additive-inverse-of the-number plus-five

uses "nu'a" to convert the operator "va'a" into a two-place bridi.


10.  Explicit Operator Precedence

As mentioned earlier, Lojban does provide a way for the precedences of
operators to be explicitly declared.  Current parsers do not understand
these declarations, but the facility does exist and can be formalized
at a later date.

The declaration is made in the form of a metalinguistic comment using
"ti'o", a member of selma'o SEI.  "sei", the other member of SEI, is
used to insert metalinguistic comments on a bridi which give information
about the discourse which the bridi comprises.  The format of a "ti'o"
declaration is not formally established, but presumably would take the
form of mentioning a mekso operator and then giving it either an absolute
numerical precedence on some pre-established scale, or else specifying
relative precedences between new operators and existing operators.


11.  Miscellany

A few other points:

"se" can be used to convert an operator, so that its arguments are
exchanged.  For example:

	li ci se vu'u vo du li pa
	the-number three (inverse) minus four equals the-number one

The other converters of selma'o SE can also be used on operators with
more than two operands, and they can be compounded to create unintelligible
operators as needed.

Members of selma'o NAhE are also legal on an operator to negate it.
The semantics of negated operators are not clear.

"la'e" and "lu'e" can be used on operands with the usual semantics to
get the referent of or a symbol for an operand.

"jo'i" is the array indicator, and is used to specify a vector:  it has
a syntax reminiscent of a forethought operator, but has very high precedence;
the components must be operands (not full expressions, unless parenthesized).
The vector can have any number of components; "te'u" is the elidable terminator.
Example:

	li jo'i paboi reboi te'u su'i jo'i ciboi voboi du li jo'i voboi xaboi
	the-number array( one two ) plus array( three four) equals
		the-number array( four six)
	(1,2) + (3,4) = (4,6)


12.  mekso selma'o summary

BOI	elidable terminator for numbers and lerfu strings
BY	lerfu for variables and functions (also BU, LAU, TEI, FOI)
FUhA	reverse-Polish flag
GOhA	includes "du" (mathematical equality)
JOhI	array flag
KUhE	elidable terminator for forethought mekso
LI	mekso articles (li and me'o)
MAhO	lerfu function flag
MOhE	convert sumti to operand
NAhU	convert bridi-tail to operator
NIhE	convert selbri to operand
NUhA	convert operator to selbri
PA	numbers
PEhO	optional forethought mekso marker
VEI	left parenthesis
VEhO	right parenthesis
VUhU	operators