stevo

On Sat, Feb 23, 2013 at 3:32 P= M, Jacob Errington <nictytan@gmail.com> wrote:
These are impossible to make, due to the lack of a selbri meaning "x1 = is in all the ce'u-places of function x2". So I decided today, in = IRC, to make that selbri. This is the documentation of my quest.

There are two types of reflexive selbri right now. Lujvo of the = first kind are created compositionally whereas lujvo of the second kind are= created non-compositionally. Non-self-reflexive selbri are produced with {= simxu}, e.g. {.i mi joi do simxu lo ka ce'u cinba ce'u} "You a= nd I kiss each other," which in a lujvo looks like {mi joi do cinbysi&= #39;u}, whereas the self-reflexive counterpart is {mi cinba mi/vo'a} wh= ich in a lujvo looks like this {mi sezycinba}. The full Lojban definition o= f {sezycinba} is {.i lo ka sezycinba cu ka ko'a ce'ai ko'a cinb= a lo sevzi be ko'a} where {lo sevzi be ko'a} is taken to reduce int= o plain {ko'a}. This seems pretty hackish to me and is naljvajvo due to= the=A0invocation=A0of {lo sevzi}.

Making up a selbri to mean "x1 does x2 to itself&q= uot; isn't as easy as it seems. Well, I'm not telling the whole tru= th when I say that. It's easy to make up a selbri meaning "x1 does= x2 to itself" as long as the x2 is a function with fixed arity. This = is probably a high percentage of the cases: {mi mi tavla} -> {.i mi brod= a lo ka ce'u tavla ce'u}, where broda is that selbri. However, talk= ing about yourself to yourself can't be expressed with that same selbri= , due to its restriction on the arity of the function. The arity restrictio= n arises from the naive lojban definition:

let ko'e =3D lo ka ce'u broda ce'u

#1 {.i ka ko'a ko'a me'au ko'e} =3D {.i ka ko'a ko= 9;a me'au lo ka ce'u broda ce'u} =3D {.i ka ko'a broda ko&#= 39;a}

Very straightforward. Make new selbri for every new {ko'a} you thr= ow in. Very poorly extensible system.

This brought= me to the very important side-quest of figuring out currying in Lojban. {b= e} as we all know basically curries: {lo broda be ko'a} =3D {zo'e n= oi ke'a broda ko'a} =3D {zo'e noi ke'a ckaji lo ka ce'u= broda ko'a}. Also as demonstrated right there, we can use {ckaji} (and= therefore {me'au}) to simulate the effect of {be}. This led me to prod= uce the following selbri which produces a function with the x1 is filled by= a definite parameter. I've called it kamni'oi for now, based on -k= am- from {ka} and -ni'oi- from -ni'o- from {cnino}.

#2 {.i lo ka kamni'oi cu ka ko'a ko'e ko= 9;i ce'ai ko'a ka ko'e me'au ko'i} "x1 is the func= tion derived from filling the x1 of x3 with x2."

e.g. {lo ka= mi citka ce'u cu kamni'oi mi lo ka ce'u citka ce'u}

e.g. {lo du'u mi citka lo plise cu kamni'oi lo plise lo ka mi = citka ce'u}

Then I needed a selbri to get the = arity of a function. This is possible by converting bridi3 into a set and t= hey using zilkancu. This selbri could arguably be a lujvo, but I've dec= ided to call it ka'ance'u, from {zilkancu} and {ce'u}:

#3 {.i lo ka ka'ance'u cu ka ko'a ko'e = ce'ai ko'a se zilkancu lu'i lo te bridi be ko'e} "x1 (= li) is the arity of function x2."

e.g. {.i li mu ka'ance= 'u me'ei klama}

e.g. {.i li no ka'ance'u lo du'u mi citka lo plise}

<= div>

e.g. {.i mi sevzike lo ka ce'u ce'u = ce'u tavla da poi ce'u finti ke'a ca lo nu ce'u citno mutce= } =3D {.i mi mi mi tavla da poi mi finti ke'a ca lo nu mi citno mutce}<= /div>

An important identity of this function is that when app= lied to unary functions, it becomes equivalent to plain {ckaji} (or {me'= ;au}).

{mi sevzike lo ka ce'u citka lo plise} =3D {mi ckaji l= o ka ce'u citka lo plise} =3D {.i mi citka lo plise}

The function has an interesting quirk due to its defini= tion, namely that if a du'u is supplied in the x2, the x1 becomes compl= etely irrelevant to the relationship.

{sevzike lo du'u broda}= has the same truth value regardless of the sumti supplied in the x1.

Now for an explanation of the definition. (The definiti= on is recursive, which I think is a first for Lojban definitions. Still, th= is is a proof of concept of the sheer power that can be achieved with Lojba= n definitions.) =A0The function checks the arity of the x2. If it is greate= r than zero, it curries the x1 into the x2 to yield an intermediate functio= n which it then passes back to itself. If the arity is zero, which will occ= ur when all the ce'u-places have had x1s curried into them, the functio= n simply evaluates the x2.

With this selbri, it is now possible to create composit= ional self-reflexive lujvo:

{.i mi cinba zei sevzike} =3D {.i mi = sevzike lo ka ce'u ce'u cinba} =3D {.i mi mi cinba}.

If sevzike were a gismu and had a CVV rafsi, it would be possibl= e to neatly create shorter self-reflexive luvjo.

N= ow that I understand how recursion can be used in lujvo and how to create t= hese arity conditions, it may be possible to define n-ary simxu, which we h= ad decided some time ago was not possible.

.i mi'e la tsani mu'o

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