Editing Lojban (section)

== Analogies of [[combinatory logic]] combinators ==

The Lojban sentence examples are taken from ([http://lojban.org/publications/level0/brochure/diagsumm.html NC:WhLoj, Chapter 3. Diagrammed Summary of Lojban Grammar]). Sometimes, I modified the sentences slightly, if the [[combinatory logic]] analogies made it necessary.

Predicates

{| border=5
| Somebody
| sells
| something
| to somebody
| for some price
|-
| <math>x_1</math>
| predicate
| <math>x_2</math>
| <math>x_3</math>
| <math>x_4</math>
|}

A little vocabulary:
; <code>mi</code>
: I, me
; <code>do</code>
: you
; <code>ta</code>
: that
; <code>vecnu</code>
: sell

Syntax:

{| border=5
|+ you sell that to me for some price.
| <code>do</code>
| rowspan=2 | <code>cu</code>
| <code>vecnu</code>
| <code>ta</code>
| <code>mi</code>
| <code>zo'e</code>
| rowspan=2 | <code>vau</code>
|-
| <math>x_1</math>
| predicate
| <math>x_2</math>
| <math>x_3</math>
| <math>x_4</math>
|}

<code>cu</code> and <code>vau</code> are separators (and they are optional).

<code>zo'e</code> is only a place-keeper: the argument whose place is filled in but it is not specified. For didactical reasons, sometimes its meaning is rendered as “some…”, “unspecified…” etc. But in fact, most natural languages do not use such a place-keeper (because they are not based on predicate logic the way Lojban is), so in most cases, <code>zo'e</code> is not translated into English directly. An analogy with translating a decimal number representation into English: 2001 becomes “two thousand one”, so the notion of zero is not translated directly -- in fact, notion of zero is a rather late innovation (compared to language).

=== Flipping (is it something like “voice”?) ===

{| border=5
|+ That is sold by you to me for some price
| <code>ta</code>
| rowspan=2 | <code>cu</code>
| <code>se vecnu</code>
| <code>do</code>
| <code>mi</code>
| <code>zo'e</code>
| rowspan=2 | <code>vau</code>
|-
| <math>x_1</math>
| predicate
| <math>x_2</math>
| <math>x_3</math>
| <math>x_4</math>
|} 

Comparing <code>vecnu</code> and <code>se vecnu</code>, it is of taste <math>\mathbf C</math> combinator of [[combinatory logic]].
Comparing structure:

{| border=5
! <math>x_1</math>
| rowspan=3 | <code>cu</code>
! predicate
! <math>x_2</math>
! <math>x_3</math>
! <math>x_4</math>
| rowspan=3 | <code>vau</code>
|-
| <code>do</code>
| <code>vecnu</code>
| <code>ta</code>
| rowspan=2 | <code>mi</code>
| rowspan=2 | <code>zo'e</code>
|-
| <code>ta</code>
| <code>se vecnu</code>
| <code>do</code>
|}

To illustrate this analogy, I write a semi-Lojban-semi-CL version:

<code>do cu vecnu ta mi zo'e vau</code>

<code>ta cu</code> (<math>\mathbf C</math> <code>vecnu</code>) <code>do mi zo'e vau</code>

=== Repeating ===

Words <code>mi</code>, <code>do</code> correspond to English personal pronouns I (me), you. Lojban has other similar words, e.g. <code>ri</code>. Word <code>ri</code> fills in an argument (of the predicate) which repeats the previous argument.

{| border=5
| Somebody
| talks
| to somebody
| about something
| in some language
|-
| <math>x_1</math>
| predicate
| <math>x_2</math>
| <math>x_3</math>
| <math>x_4</math>
|}

A little vocabulary:
; <code>mi</code>
: I, me
; <code>do</code>
: you
; <code>la lojban.</code>
: Lojban
; <code>tavla</code>
: talk

Syntax:

{| border=5
|+ I talk to you about the Lojban language in Lojban
| <code>mi</code>
| rowspan=2 | <code>cu</code>
| <code>tavla</code>
| <code>do</code>
| <code>la lojban.</code>
| <code>la lojban.</code>
| rowspan=2 | <code>vau</code>
|-
| <math>x_1</math>
| predicate
| <math>x_2</math>
| <math>x_3</math>
| <math>x_4</math>
|}

<code>mi cu tavla do la lojban. la lojban. vau</code>

The word <code>ri</code> helps us avoiding repeating the argument of predicate in this case:

<code>mi cu tavla do la lojban. ri vau</code>

I think, it is a rather imperative solution (using some notion of state / memory), compared to the <math>\mathbf W</math> combinator of [[combinatory logic]], but in this case, it has the same effect. If Lojban used combinators, I should write (using the elementary duplicator <math>\mathbf W</math>):

<math>\mathbf W</math>(<code>mi cu tavla do</code>) <code>la lojban. vau</code>

It seems to me even better to modify only the predicate directly, not an arbitrary subexpression of the sentence -- if it is possible. Thus the deferred combinator <math>\mathbf W_{\left(2\right)}</math> helps us even more here:

<code>mi cu</code> (<math>\mathbf W_{\left(2\right)}</math> <code>tavla</code>) <code>do la lojban. vau</code>

<math>\mathbf W</math>-sequences could be used also for avoiding the many-many repeating zo'e words (of course, if Lojban used combinators):

I talk.

(Not specified, to whom, about what topic, in what language!)

<code>mi cu tavla zo'e zo'e zo'e vau</code>

What could help us in lambda calculus?
:<math>\lambda f x y . f x y y y</math>

<code>mi cu</code> (<math>\left(\lambda f x y . f x y y y\right)</math> <code>tavla</code>) <code>zo'e vau</code>

In [[combinatory logic]], <math>\mathbf W^2_{\;\left(1\right)}</math> makes that (let us note the little slant of the indices: powered combinator <math>\mathbf W^2</math> is deferred here, not deferred combinator <math>\mathbf W_{\left(1\right)}</math> is powered!):

<code>mi cu</code> (<math>\mathbf W^2_{\;\left(1\right)}</math> <code>tavla</code>) <code>zo'e vau</code>

Lojban does not use combinators this way, it uses also rather imperative solutions. Despite of that, Lojban makes me think of [[combinatory logic]] and [[Libraries and tools/Linguistics/Applicative universal grammar|applicative universal grammar]].