TEXT.ADV la me ge'o ly. velkanji

[I.Alexander.bra0122@OASIS.ICL.CO.UK]

Inspired by a combination of Nick's mex piece and a book
I've started reading called "Truth and Modality for
Knowledge Representation" by Raymond Turner, I decided
to try my hand at some Lambda Calculus in Lojban.

        cy. goi (me'o ma'o ge'o ly. boi xy. ma'o fy. ma'o xy. boi xy. lo'o)
        ga'e .ybu goi (li ma'o ge'o ly. boi fy. ma'o cy. boi cy. lo'o)
        ro fy. zo'u
        li ma'o ga'e .ybu boi fy. du li ma'o cy. boi cy. lo'o
        li ma'o fy. ma'o cy. boi cy. lo'o
        (to fi'o jarco tadji lepu'u favgau lenu le funca po'u le pamoi
        meksypau cu se sumti le remoi meksypau toi)
        li ma'o fy. ma'o ga'e .ybu boi fy.

This seems remarkably opaque (even if you know what's going on! -
but then Lambda Calculus isn't easy going even in it's more
usual symbolic forms).

The first problem is that _everything_ is a function, at least
in the pure Lambda Calculus.  Mex isn't designed to work this
way.  There's no easy way to turn the result of a mex expression
(an operand) into an operator.  I've in a sense fudged the issue
by assigning the letteral {cy.} to a part of the expression,
which is just about practical in this comparatively short example,
but even here it would have helped the demonstration if I could
have substituted the expansion of {cy.} as an intermediate step.

I tried {na'u me li ... lo'o} as a way of turning a mex expression
into an operator, but I didn't like it.  I don't >want< {na'u me <sumti>}
to mean "the operator which is associated with <sumti>" - it ought to
mean "the operator 'is associated with <sumti>'", which is a mex
predicate returning a truth value.

I'm not sure whether to propose a cmavo {xa'u} which turns a
mex operand into an operator, which would require a grammar
change, or a cmavo {xe'i} (in ma'okle ME) which means
"the selbri _identified by_ <sumti>", so that {xe'i di'u}
would be (approximately) equivalent to {go'i}, and
{xe'i li ma'o ge'o ly. boi xy. ne'o xy.} would be the same as
{nu'a ne'o} - "x1 is the factorial of x2".

(Note that since the latest gismu list changed the place structure
of {cmavo}, {se cmavo} no longer means "grammatical category",
but "word exemplifying a grammatical category".  We still have
the option, of course, of _defining_ {selma'o} to mean what it
used to, or we could use something like {ma'okle} instead.)

This turns up problem number two, which is the rather odd mixture
of {li} and {me'o} in the prenex.  The definition of {cy.} has to
be a {me'o} - it can't be evaluated, since it contains the free
variable {fy.}.  The definition of {ga'e .ybu}, zu'unai, feels
like it ought to be evaluted.

ta'o I've used {ge'o ly.}, without definition, as the lambda operator,
which is syntactically a prefix (forethought) operator taking two
arguments, the first a letteral string, and the second a mex
expression, producing the function of the first argument whose
result is the value of the second argument.  All other operators
(also forethought) are functions of the Lambda Calculus taking a
single argument and producing a result which is a function.
This is the common "curried" form of the calculus.
(Note that the second argument of {ma'o ge'o ly.} is essentially
an _unevaluated_ expression, but there's no way to indicate that.)

Finally the problem of talking about "applying a function
to its arguments" and "expanding the application".  My suggestion
is given above - alternative recommendations are welcome.

Iain.