Lojban

From HaskellWiki

(Difference between revisions)

Revision as of 21:27, 7 August 2006

1 Introduction
2 Analogies of combinatory logic combinators
3 Filipping
4 Repeating
5 References

1 Introduction

Lojban is a constructed language. “Lojban was not designed primarily to be an international language, however, but rather as a linguistic tool for studying and understanding language. Its linguistic and computer applications make Lojban unique among international languages...” (NC:LojPer, page 15 par 1) -- the entire book is available also online, see the very bottom of the linked page.

It is an artificial language (and, unlike the more a posteriori Esperanto, it is It is rather of an a priori taste (Moo:LojPer)). It is a human language, capable of expressing everything. Its grammar uses (among others) things taken from mathematical logic, e.g. predicate-like structures. Although its does not make use combinatory logic directly (even, from a combinatory logic / functional programming point of view, it uses also rather imperative ideas), but it may give hints and analogies, how combinatory logic can be useful in linguistics. I like searching Lojban examples illustrating the learned statements when learning about applicative universal grammar.

See its official homepage here.

Wikipedia article on Lojban.

2 Analogies of combinatory logic combinators

The Lojban sentence examples are taken from (NC:WhLoj, Chapter 3. Diagrammed Summary of Lojban Grammar). Sometimes, I modified the sentences slightly, if the combinatory logic analogies made it necessary.

Predicates

Somebody	sells	something	to sombebody	for some price
$x 1$	predicate	$x 2$	$x 3$	$x 4$

A little vocabulary:

mi: I
vecnu: sell
do: you
ta: that

Syntax:

I sell this to you for some price.
`mi`	`cu`	`vecnu`	`ta`	`do`	`zo'e`	`vau`
$x 1$	`cu`	predicate	$x 2$	$x 3$	$x 4$	`vau`

cu and vau are separators (and they are optional). zo'e is only a place-keeper: the argument whose place is fiiled in by it is not specified.

3 Filipping

That is sold by you to me for some price
`ta`	`cu`	`se vecnu`	`do`	`mi`	`zo'e`	`vau`
$x 1$	`cu`	predicate	$x 2$	$x 3$	$x 4$	`vau`

Comparing vecnu and se vecnu, it is of taste $\mathbf C$ combinator of combinatory logic. Comparing structure:

$x 1$	`cu`	predicate	$x 2$	$x 3$	$x 4$	`vau`
`do`		`vecnu`	`ta`	`mi`	`zo'e`
`ta`		`se vecnu`	`mi`	`mi`	`zo'e`

4 Repeating

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

Somebody	talks	to sombebody	about something	in some language
$x 1$	predicate	$x 2$	$x 3$	$x 4$

A little vocabulary:

mi: I
tavla: talk
do: you
la lojban.: Lojban

Syntax:

I talk to you about the Lojban language in Lojban
`mi`	`cu`	`tavla`	`do`	`la lojban.`	`la lojban.`	`vau`
$x 1$	`cu`	predicate	$x 2$	$x 3$	$x 4$	`vau`

mi cu tavla do la lojban. la lojban. vau

The word ri helps us avoiding repeating the argument of predicate in this case:

mi cu tavla do la lojban. ri vau

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

$\mathbf W$ (mi cu tavla do) la lojban. vau

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 $\mathbf W_{\left(2\right)}$ helps us even more here:

mi cu ( $\mathbf W_{\left(2\right)}$ tavla) do la lojban. vau

$\mathbf W$ -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!)

mi cu tavla zo'e zo'e zo'e vau

What could help us in lambda calculus?

λ f x y . f x y y y

mi cu ( $\left(\lambda f x y . f x y y y\right)$ tavla) zo'e vau

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

mi cu ( $\mathbf W^2_{\;\left(1\right)}$ tavla) zo'e vau

Lojban does not use combinators this way, it uses also rather imperative solutions. Despite of that, Lojban makes me think of combinatory logic and applicative universal grammar.

5 References

NC:WhLoj: Nicholas, Nick and Cowan, John (ed.): What is Lojban? Logical Language Group, 2003. Available also online, see the very bottom of the linked page.
Moo:LojPer: Todd Moody: Lojban in Perspective. Available from here, part of Lojban's official homepage

Retrieved from "http://www.haskell.org/haskellwiki/Lojban"

Category: Theoretical foundations

@@ Line 5: / Line 5: @@
 Lojban is a constructed language. “Lojban was not designed primarily to be an international language, however, but rather as a linguistic tool for studying and understanding language. Its linguistic and computer applications make Lojban unique among international languages...” ([http://www.lojban.org/tiki/tiki-index.php?page=What+Is+Lojban%3F%2C+The+Book&bl NC:LojPer], page 15 par 1) -- the entire book is available also online, see the very bottom of the linked page.
-It is an artificial language (and, unlike the more a posteriori Esperanto, it is rather of an a priori taste ([http://www.lojban.org/files/why-lojban/moody.txt Moo:LojPer])). It is a human language, capable of expressing everything. Its grammar uses (among others) things taken from mathematical logic, e.g. predicate-like structures. Although its does not make use [[combinatory logic]] directly (even, from a combinatory logic / functional programming point of view, it uses also rather imperative ideas), but it may give hints and analogies, how combinatory logic can be useful in [[Libraries and tools/Linguistics|linguistics]]. I like searching Lojban examples illustrating the learned statements when learning about [[Libraries and tools/Linguistics/Applicative universal grammar|applicative universal grammar]].
+It is an artificial language (and, unlike the more a posteriori Esperanto, it is It is rather of an a priori taste ([http://www.lojban.org/files/why-lojban/moody.txt Moo:LojPer])). It is a human language, capable of expressing everything. Its grammar uses (among others) things taken from mathematical logic, e.g. predicate-like structures. Although its does not make use [[combinatory logic]] directly (even, from a combinatory logic / functional programming point of view, it uses also rather imperative ideas), but it may give hints and analogies, how combinatory logic can be useful in [[Libraries and tools/Linguistics|linguistics]]. I like searching Lojban examples illustrating the learned statements when learning about [[Libraries and tools/Linguistics/Applicative universal grammar|applicative universal grammar]].
 See [http://www.lojban.org its official homepage here].
@@ Line 151: / Line 151: @@
 | <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:
@@ Line 156: / Line 158: @@
 <code>mi cu tavla do la lojban. ri vau</code>
-I think, it is a rather imperative solution, 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>):
+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.</code>
+<math>\mathbf W</math>(<code>mi cu tavla do</code>) <code>la lojban. vau</code>
-Deferred combinator <math>\mathbf W_{\left(2\right)}</math> helps us even more here:
+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.</code>
+<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):
@@ Line 173: / Line 175: @@
 What could help us in lambda calculus?
-:<math>\lambda f x . f x x x</math>
+:<math>\lambda f x y . f x y y y</math>
-<code>mi cu</code> (<math>\left(\lambda f x . f x x x\right)</math> <code>tavla</code>) <code>zo'e vau</code>
+<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</math> makes that:
+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</math> <code>tavla</code>) <code>zo'e vau</code>
+<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]].

Personal tools

Views