MEX: a trial text, and some ballyhooing.

[cbmvax!uunet!ee.mu.OZ.AU!nsn]

On Mex.

Two examples of mex texts in forethought mode, and a suggestion that the
Mex review process be taken out of Lojbab's reach, and developed into
textbook level indept. of him. To understand what follows, you will need
Cowan's draft mex paper, posted a month back.

One. Some vector algebra.

A change proposal. As you know, {nu'a} coverts operators into selbri. This
is handy; it gives you expressions like {le nu'a su'i}, the sum, {le se nu'a
ri'o}, the integrand ,etc. I want to say 'vector'. So I get the vector
operator, {jo'i}. But I can't say {le nu'a jo'i}, because {jo'i} is its own
lexeme, and {nu'a} is only allowed before lexeme VUhU. With a matrix row
and matrix column operator in VUhU, the word {jo'i} itself seems unnecessary,
much less deserving of its own lexeme. In the following, I treat {jo'i} as
lexeme VUhU.

I do not give literal translations: work it out yourselves, and then join in
the MEX review group.

>From p.91, ALGEBRA AND GEOMETRY, Holton & Lloyd

Theorem 3.
di'e cimoi le'i cmaci se smadi

Let V be a vector space over F.
.i vy. nu'a jo'i klesi .i fy. lu'a lu'a vy. 
{F is the class of the vector elements, the vectors being the elements of V}

Then (i) 0 x = 0 for all x in V
.inaja ge li pi'i noboi xy. du li no va'o lenu roda po'u xy. cmima vy.

     (ii) -x = (-1) x for all x in V
gi li va'a xy. du li pi'i va'a pa tu'o xy. va'o lenu roda po'u xy. cmima vy

Proof
.i di'e cipra

(i) Note carefully that the two zeroes in the equation 0 x = 0 are different.
.i pamai (to ko zgana sai lenu lore lino pe vi me'o na'u du pi'i noboi xy.boi
no cu na'e mintu
{Note: to shove the whole expression 0x=0, including '=', into a mekso, I
make 'du' itself an operator.}

The zero in the LHS is a scalar in F,
.i le pamoi be le'i noboi cu nu'a na'e jo'i co cmima fy.

while the zero on the RHS is the zero vector in V.)
.i le remoi cu nomei nu'a jo'i co cmima vy. toi)

Now 0 = 0 x + (-[0 x]), by v5
su'anai li 0 du li + * 0boi xy. va'a * 0boi xy. ja'i vy.mu
{I substitute + for su'i, * for pi'i, and use the actual number digits}

	= (0+0)x + (-[0 x])
.i go'i li + * + 0boi 0boi xy. va'a * 0boi xy.

	=(0x+0x) + (-[0 x]), by v8
.i go'i li + + * 0boi xy. * 0boi xy. va'a * 0boi xy. ja'i vy.bi

	= 0x + (0x + (-[0 x]), by v3
.i go'i li + * 0boi xy. + * 0boi xy. va'a * 0boi xy. ja'i vy.ci

	= 0x + 0, by v5
.i go'i li + * 0boi xy. 0boi ja'i vy.mu

	= 0x by v4
.i go'i li * 0boi xy. ja'i vy.vo

ii) x + (-1) x = 1 x + (-1) x, by v10
.i remai li + xy. * va'a 1 tu'o du li + * 1boi xy. * va'a 1 tu'o xy. ja'i 
vy.pano

		= [1 + (-1)] x, by v8
.i go'i li * + 1 va'a 1 tu'o xy. ja'i vy.bi

		= 0x
.i go'i li * 0boi xy.

		= 0 by (i)
.i go'i li no ja'i le pamoi be le'i se cipra

Hence -x = (-1) x
.i seni'ibo li va'a xy. du li * va'a 1 tu'o xy.

Here endeth the lesson. I strongly feel that the mode of expression (Fore-
or reverse polish) should not have to be mentioned explicitly for every
mekso in a series (this is most relevant for RP), but be able to be long-
scoped, a la {fu'e}. {fu'efu'a} would make a happy couple. The only grammar
change that would necessitate would be to take FUhA out of where it's at
(and let the parser worry about what's syntactical: the interpretation of
meksos, I suspect, should be a semantic rather than syntactic function of
the lojban machine), and dumped into freemod.

Again: lojbab, get back to your textbook. This review should not be undertaken
by denizens of Fairfax. Sorry if this means I make more work for John Cowan
instead.

2nd example coming up.