A Sample of MEX in -gua!spi
Jim Carter , 5/18/90
In Loglan, and now in Lojban, a fairly elaborate syntax was proposed to
express mathematical expressions (MEX). I have prepared this sample of
MEX in -gua!spi to show one trivial solution, and I am posting it to
the list following 's encouragement to get discussion going.
On analysing the MEX problem I came to the conclusion that the basic
syntax of the language, or a substitute of substantially equal
function, was both necessary and sufficient to express MEX, and hence
when designing -gua!spi I omitted any special MEX syntax, rather than
inventing a separate but equivalent syntax for MEX.
However, I put some features into the core grammar specifically
anticipating the demands of MEX, such as default articles. Since the
tones mark where arguments start there is no syntactic need to have any
articles, and hence I caused every case of every primitive word to have
a default article, to be added to the occupying argument if it has none
of its own. Normally this is "xe" (pronounced "zhe"), corresponding to
Lojban "le", and the feature makes a -gua!spi sentence have noticeably
fewer words than the corresponding Lojban. Now for MEX, numbers are
defined, as many mathematicians do, as "X1 is a member of the
equivalence class of all sets with N members". For example, a biplane's
wings are a set, which are equivalent in count to the brothers Gemini,
etc. ad infinitum, and this set (class) of sets is "the number two".
Then the appropriate article for a case for a number, provided by
default on math functions, is "xu" ("all", "lea" in Old Loglan, changed
I think in Lojban), so the case occupant might mean "all pairs".
What follows is a translation of a short paragraph from a physics
textbook. It is hard to demonstrate how neat a certain feature is of
-gua!spi to listeners who do not know the language, and so I have
provided three translations: First, a (nearly) word-for-word
translation, then the original English, and finally a mechanical
translation with phrases marked. In the latter, [] encloses a sentence
(as in an abstraction), <> encloses a modal or subordinate clause, \\
encloses the anaphoric copy of the restricted phrase (internally
generated), and () encloses the antecedent of any other pronoun. The
main predicate of each argument has the case number appended ("vo" =
"to" is the predicate of an abstraction). The translator uses word
order and possessive apostrophes which are often correct in describing
life situations, but which get in the way of the mathematics.
The letterals and equations are written out as if spoken (analogous to
"forty two dollars and seventeen cents"); presumably in a real
mathematics text they would be written as letters.
One form lacking in the paragraph is a good, clear dimensioned
quantity, so I have added a difficult one at the end.
Perhaps the most useful thing you could do with this passage is to
translate it into Lojban using each of the competing MEX syntaxes, and
particularly, try using the core grammar with no MEX extension. You may
have to create ad-hoc case specifications, and I don't believe Lojban
has a word for "derivative", which you will have to jury-rig. There is
enough variety here to give you a broad, if brief, look at the
performance of each candidate.
\x{^:i !kun !vn-qci|qky ^vu-zu-jio !se-xo-pse |vu-gr-tfyn
!fi-va-ga-xim !dvla-qfle ^fi-ve-fta !tl-co /fi-plw !dvla-xble
^cmu !psla ^dvla-vzle }
{ Quantity energy hot absorbed-by some process anti-infinite
(named dQ) by-rule nbr.one sum dE
product p dV }
{ The heat absorbed in an infinitesimal process is given by the first
law as dQ = dE + p dV. (Actually d-bar Q; -gua!spi doesn't handle
unusual letters yet.) }
{[argument energy's2 > degree1 plus all d E2 all all p's2 multiply3 all d V3 ]} %%
\x{^:i |vi-tl-co ^ja /zyn !xo -kqer ^dya !kun !qci |qky
^kqa |gl-kri ^fu-cmu !jvyn ^gzol /va-ga-xim !cfla-vzle }
{ First lets find some expression quotient amount energy hot
big not increasing product degrees moles named cV }
{ Let us first obtain an expression for the molar specific heat cV
at constant volume. }
{[imperative1 (all your2 (something's) set me3 (something)) discover
some mathematics2 to3 [(mathematics1) quotient2 all to's2 [the big1 energy2 ] degree2 all all
kelvin's2 multiply3 all mole3 ]
]} %%
\x{^:o -sno !cy !dvla-vzle }
{ Sufficient-condition zero dV }
{ Then dV = 0 ...}
{[conjunction \discover1 11+22\ sufficient to2 [d V1 zero]]} %%
\x{^:o -sno !can !so-vo-dem !jl ^vu-zu-dre-stl !ci^cu^co
!fu-psy |zu-plm !vo-dem !dvla-qfle ^dvla-xble }
{ Sufficient-condition change equation (address vector 5 2 1)
simple example equal dQ dE }
{ ...and (5.2.1) reduces simply to dQ = dE. ("Example" is not very
good; I need a word for "specifically".}
{[conjunction \sufficient1\ sufficient to2 [to [something1 same2