[lojban] The jai-zenba distribution property

[Jacob Errington <nictytan@gmail.com>]

coi

This post probably won't interest that many, but I felt like the broader community be aware of this. This post makes use of the "functional" interpretation of Lojban, where a lot of {nu} places are {ka} places, where {ka} denotes a n-arity function (where n is the number of ce'u in the function) that "becomes" a {du'u} abstraction (or possibly a {nu} abstraction, which makes the whole concept more useful).

Today in IRC, latro'a mentioned having said something that struck us a being rather intriguing:

#1 {.i .ei mi jai zenba lo ni ce'u cafne kei fai lo nu te vecnu zo'e}

(I personally believe that the {nu} there should be a {ka} by virtue of {jai}, but I digress, and that really isn't the point of this post.)

By the definition of {jai}, #1 is equivalent to 

#2 {.i .ei lo nu mi te vecnu zo'e cu zenba lo ni ce'u cafne}. 

So far so good.

Assuming the functional definition of {zenba}, {lo ka ce'u zenba lo ni ce'u broda cu ka ce'u goi ko'a zo'u lo ni ko'a broda cu zenba dubu} (where {dubu} refers to the identity function {lo ka ce'u du makau}), we can rewrite #2 as

#3 {.i .ei lo ni lo nu mi te vecnu zo'e cu cafne cu zenba dubu}

We can now re-apply a jai to the bridi {lo nu mi te vecnu zo'e cu cafne} forming {mi jai cafne lo nu te vecnu}, such that

#4 {.i .ei lo ni mi jai cafne fai lo nu te vecnu cu zenba dubu}

Finally, we can undo the operation performed in 3, moving {lo ni mi jai cafne fai lo nu te vecnu} into zenba2, extracting {mi} by replacing with {ce'u}, and moving {mi} into zenba1, eliminating dubu, yielding

#5 {.i .ei mi zenba lo ni ce'u jai cafne fai lo nu te vecnu}

Formally: {.i ko'a zo'u lo ka ce'u zenba lo ni ce'u jai broda fai ko'a cu ka ce'u jai zenba lo ni ce'u broda kei fai ko'a}

This same rule can apply to comparatives. 

e.g. {.i mi do sejaisejai zmadu fai ko'a fai ko'a lo ni ce'u cafne} === {.i mi do zmadu lo ni ce'u jai cafne fai ko'a} where ko'a can be for example, something like {lo ka tavla fo la. lojban.}

Note on how I use multiple {jai}: when using two {jai} on the same level, the first fai to appear in the bridi fills the jai closest to the selbri.

In conclusion, this means that #1 and #5 are the same in trivial cases like this, where logical connection or bound variables aren't involved.

.i mi'e la tsani mu'o

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