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{{BPFK Section from tiki|BPFK Section: MEX|84}}
== Proposed Definitions And Examples ==


==  Proposed Definitions And Examples ==
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=== cmavo: bi'e (BIhE) ===
 
=== bi'e (BIhE) ===
 
====  Proposed Definition ====


==== Proposed Definition ====
Indicates an operator has precedence over unmarked operators. When an operator is prefixed with this cmavo, it becomes automatically of higher precedence than other operators not so prefixed. If more than one operator has a ''bi'e'' prefix, grouping is to the right; multiple ''bi'e'' prefixes on a single operator are not allowed.   
Indicates an operator has precedence over unmarked operators. When an operator is prefixed with this cmavo, it becomes automatically of higher precedence than other operators not so prefixed. If more than one operator has a ''bi'e'' prefix, grouping is to the right; multiple ''bi'e'' prefixes on a single operator are not allowed.   


==== Proposed Keywords ====
==== See Also ====


* High priority operator
==== Proposed Keywords ====
* Precedence operator
* high priority operator
 
* precedence operator
==== Usage Examples ====


==== Usage Examples ====
;li ci su'i vo bi'e pi'i mu du li reci:3 + (4 × 5) = 23 (CLL, 18.5.9)
;li ci su'i vo bi'e pi'i mu du li reci:3 + (4 × 5) = 23 (CLL, 18.5.9)


==== Notes ====
==== Notes ====
 
This is distinct from the use of mathematical brackets {vei} and {ve'o}.
This is distinct from the use of mathematical brackets {vei} and {ve'o}.


==== Issues ====
==== Issues ====
 
Xorxes has a plan to replace this by expanding the use of {bo}  
Xorxes has a plan to replace this by expanding the use of {bo}  
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=== fu'a (FUhA) ===
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=== cmavo: fu'a (FUhA) ===
====  Proposed Definition ====


==== Proposed Definition ====
Marks the mekso expression as using Reverse Polish (RP) notation. RP notation is always marked by an explicit ''fu'a'' at the beginning of the expression. Operators acting in RP are required to have two operands (though {tu'o} and {ge'a} can assist when using unitary and ternary operators respectively).
Marks the mekso expression as using Reverse Polish (RP) notation. RP notation is always marked by an explicit ''fu'a'' at the beginning of the expression. Operators acting in RP are required to have two operands (though {tu'o} and {ge'a} can assist when using unitary and ternary operators respectively).


==== Proposed Keywords ====
==== See also ====
* {pe'o} — forethought operator flag
* {tu'o} — null operand
* {ge'a} — null operator


* Reverse Polish Flag
==== Proposed Keywords ====
 
* Reverse Polish flag
==== See also ====
 
* {pe'o} Forethought operator flag
* {tu'o} Null operand
 
* {ge'a} Null operator
 
====  Usage Examples ====
 
(natural example: doi jbokaj li fu'a pa boi re su'i ci su'i)<br />


==== Usage Examples ====
(natural example: doi jbokaj li fu'a pa boi re su'i ci su'i)<br>
;li fu'a reboi ci su'i du li mu: (RP) (2 3 +) = 5 (CLL, 18.16.1)
;li fu'a reboi ci su'i du li mu: (RP) (2 3 +) = 5 (CLL, 18.16.1)
;li fu'a reboi ci pi'i voboi mu pi'i su'i du li rexa: (RP) (2 3 x) (4 5 x) + = 26 (CLL, 18.16.2)
;li fu'a reboi ci pi'i voboi mu pi'i su'i du li rexa: (RP) (2 3 x) (4 5 x) + = 26 (CLL, 18.16.2)
;li fu'a ciboi muboi vu'u du li fu'a reboi tu'o va'a: (RP) (3 5 -) = (RP) (2 ''null'') ''negative'' (CLL, 18.16.3)
;li fu'a ciboi muboi vu'u du li fu'a reboi tu'o va'a: (RP) (3 5 -) = (RP) (2 ''null'') ''negative'' (CLL, 18.16.3)
;li cinoki'oki'o du li fu'a biboi ciboi panoboi ge'a gei: 30,000,000 = (RP) 8 (3 10 ''null'') ''exp'' (CLL, 18.16.4)
;li cinoki'oki'o du li fu'a biboi ciboi panoboi ge'a gei: 30,000,000 = (RP) 8 (3 10 ''null'') ''exp'' (CLL, 18.16.4)


==== Issues ====
==== Issues ====
It seems quite arbitrary that operators acting in reverse polish notation are required to have exactly 2 operands. Especially considering that in polish notation, operators are allowed to have as many operands as they like. It does not make semantic sense for all operators (for example the negation operator, used in the example usage above). Though there is a problem in determining which operands belong to which operator, and the solution currently is quite elegant for usage, it lacks symmetry with forethought equivalent and seems arbitrary.


It seems quite arbitrary that operators acting in reverse polish notation are required to have exactly 2 operands. Especially considering that in polish notation, operators are allowed to have as many operands as they like. It does not make semantic sense for all operators (for example the negation operator, used in the example usage above) Though there is a problem in determining which operands belong to which operator, and the solution currently is quite elegant for usage, it lacks symmetry with forethought equivalent and seems contrived. I'm working on a better way, talk to me if you're interested in this problem. .i pe'i lo du'u va'o lo fu'a zei mekso lo meksu'i be lo cmavo be zo vu'u cu remei cu na'e nutli .i ganai do se cinri gi ko tavla mi
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(mi'e Ross Ogilvie, 15/5/10)
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=== cmavo: jo'i (JOhI) ===
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=== jo'i (JOhI) ===
 
====  Proposed Definition ====


==== Proposed Definition ====
Joins a sequence of simple operands or bracketed full expressions into a vector. A vector may have any number of components. It's corresponding terminator {te'u} is elidable.
Joins a sequence of simple operands or bracketed full expressions into a vector. A vector may have any number of components. It's corresponding terminator {te'u} is elidable.


==== Proposed Keywords ====
==== See also ====
* {te'u} — Mekso terminator for NAhU, NIhE, MOhE, MAhO, and JOhI


* Vector flag
==== Proposed Keywords ====
 
* vector flag
==== See also ====
 
* {te'u} Mekso terminator for NAhU, NIhE, MOhE, MAhO, and JOhI
 
====  Usage Examples ====


==== Usage Examples ====
;li jo'i paboi reboi te'u su'i jo'i ciboi voboi du li jo'i voboi xaboi: ''vector'' (1, 2) + ''vector'' (3, 4) = ''vector'' (4, 6) (CLL, 18.15.1)
;li jo'i paboi reboi te'u su'i jo'i ciboi voboi du li jo'i voboi xaboi: ''vector'' (1, 2) + ''vector'' (3, 4) = ''vector'' (4, 6) (CLL, 18.15.1)


;li ma'o fy. boi pa jo'i re jo'i ci: f(1,[[,[3|,[3]])  (Re: ~91~lojban~93~ loi preti be fi lo nincli zo'u tu'e, Thu, 23 Jan 2003 11:10:25 -0800, Robin Lee Powell, [http://www.lojban.org/eo/lists/lojban-list/msg03809.html ink])
;li ma'o fy. boi pa jo'i re jo'i ci: f(1,[2,[3]])  (Re: ~91~lojban~93~ loi preti be fi lo nincli zo'u tu'e, Thu, 23 Jan 2003 11:10:25 -0800, Robin Lee Powell, [http://www.lojban.org/eo/lists/lojban-list/msg03809.html link])
 
====  Notes ====


==== Notes ====
It is the only member of selma'o JOhI
It is the only member of selma'o JOhI


{BOX}
"Vector" may not be the mathematically best way to describe it. "Ordered list" or "ordered tuple" is better. This wording is fine, though, in the computer science sense.
 
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===  ku'e (KUhE) ===
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====  Proposed Definition ====
=== cmavo: ku'e (KUhE) ===


==== Proposed Definition ====
This is the elidable terminator of operators when they are acting in forethought mode. It serves to distinguish where the operands of one operator end and another begin.
This is the elidable terminator of operators when they are acting in forethought mode. It serves to distinguish where the operands of one operator end and another begin.


==== Proposed Keywords ====
==== See Also ====
 
* Forethought operator terminator
 
====  See Also ====
 
* {pe'o} Forethought operator flag
* {pe'o} Forethought operator flag


==== Usage Examples ====
==== Proposed Keywords ====
* forethought operator terminator


==== Usage Examples ====
;li py. su'i va'a ny. ku'e su'i zy du li xy.: p + (''negative'' n) + z = x (CLL, 18.6.2)
;li py. su'i va'a ny. ku'e su'i zy du li xy.: p + (''negative'' n) + z = x (CLL, 18.6.2)
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=== cmavo: ma'o (MAhO) ===
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=== ma'o (MAhO) ===
 
====  Proposed Defintion ====


==== Proposed Defintion ====
This flag converts letteral string or other mathematical expression (mex) operand into a mex operator. Its elidable terminator is {te'u}.
This flag converts letteral string or other mathematical expression (mex) operand into a mex operator. Its elidable terminator is {te'u}.


==== Proposed Keywords ====
==== See Also ====


* Operand to Operator flag
==== Proposed Keywords ====
 
* operand to operator flag
==== Usage Examples ====


==== Usage Examples ====
;li zy du li ma'o fy.boi xy.: z = f(x) (CLL, 18.6.3)
;li zy du li ma'o fy.boi xy.: z = f(x) (CLL, 18.6.3)


==== Notes ====
==== Notes ====
 
The CLL has the following observation: There is a potential semantic ambiguity in ''ma'o fy. ~91~te'u~93~'' if ''fy.'' is already in use as a variable: it comes to mean "the function whose value is always 'f' ". However, mathematicians do not normally use the same lerfu words or strings as both functions and variables, so this case should not arise in practice.
The CLL has the following observation: There is a potential semantic ambiguity in ''ma'o fy. ~91~te'u~93~'' if ''fy.'' is already in use as a variable: it comes to mean "the function whose value is always 'f' ". However, mathematicians do not normally use the same lerfu words or strings as both functions and variables, so this case should not arise in practice.
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=== cmavo: mo'e (MOhE) ===
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=== mo'e (MOhE) ===
 
====  Proposed Definition ====


==== Proposed Definition ====
Converts a sumti to a mex operand. Intended to allow dimensions to be embedding into mex expressions. It is also used for "folk quantifiers", also known as collective nouns. It precedes the sumti. Its elidible terminator is {te'u}.
Converts a sumti to a mex operand. Intended to allow dimensions to be embedding into mex expressions. It is also used for "folk quantifiers", also known as collective nouns. It precedes the sumti. Its elidible terminator is {te'u}.


==== See Also ====
==== See Also ====
 
* {na'u} — selbri to operator
* {na'u} Selbri to operator
* {ni'e} — selbri to operand
* {ni'e} Selbri to operand
 
====  Proposed Keywords ====


==== Proposed Keywords ====
* Sumti to mex operand
* Sumti to mex operand


==== Usage Examples ====
==== Usage Examples ====
 
;li mo'e re ratcu su'i mo'e re ractu du li mo'e vo danlu: (2 rats) + (2 rats) = (4 animals)  (CLL, 18.18.3)
;li mo'e re ratcu su'i mo'e re ractu du li mo'e vo danlu: (2 rats) + (2 rats) = (4 animals)  (CLL, 18.18.3)
;mi viska vei mo'e lo'e lanzu ve'o cinfo: I see (a typical family) of lions  (CLL, 18.18.4)
;mi viska vei mo'e lo'e lanzu ve'o cinfo: I see (a typical family) of lions  (CLL, 18.18.4)
;:I see a pride of lions
;:I see a pride of lions
;li mo'e lo spaji su'i mo'e lo spaji du li mo'e lo mutce spaji: A suprise + a suprise = a big suprise    (Re: mo'e (was: RE: ~91~lojban~93~ useless selmaho?, Sun, 2 Sep 2001 03:19:28 +0200, Adam Raizen, [http://www.lojban.org/sv/lists/lojban-list/msg21261.html link])


;li mo'e lo spaji su'i mo'e lo spaji du li mo'e lo mutce spaji: A suprise + a suprise = a big suprise    (Re: mo'e (was: RE: ~91~lojban~93~ useless selmaho?, Sun, 2 Sep 2001 03:19:28 +0200, Adam Raizen, [http://www.lojban.org/sv/lists/lojban-list/msg21261.html ink])
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=== cmavo: na'u (NAhU) ===
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=== na'u (NAhU) ===
 
====  Proposed Definition ====


==== Proposed Definition ====
The cmavo "na'u" makes a selbri into an operator. In general, the first place of the selbri specifies the result of the operator, and the other unfilled places specify the operands. Its elidible terminator is {te'u}. It is also used to construct questions about operators.
The cmavo "na'u" makes a selbri into an operator. In general, the first place of the selbri specifies the result of the operator, and the other unfilled places specify the operands. Its elidible terminator is {te'u}. It is also used to construct questions about operators.


==== See Also ====
==== See Also ====
 
* {ni'e} selbri to operand
* {ni'e} selbri to operand
* {mo'e} sumti to operand
* {mo'e} sumti to operand
* {te'u} terminator
 
* {te'u} terminator
 
====  Proposed Keywords ====


==== Proposed Keywords ====
* selbri to operator
* selbri to operator


==== Usage Examples ====
==== Usage Examples ====


;li na'u tanjo te'u vei pai fe'i vo ~91~ve'o~93~ du li pa : tan ( pi / 4 ) = 1 (similar to CLL, 18.18.1)
;li na'u tanjo te'u vei pai fe'i vo ~91~ve'o~93~ du li pa : tan ( pi / 4 ) = 1 (similar to CLL, 18.18.1)
;li re na'u mo re du li vo: 2 what-operator? 2 = 4 (CLL, 18.19.4)
;li re na'u mo re du li vo: 2 what-operator? 2 = 4 (CLL, 18.19.4)
 
;.i go li cy. na'u klesi .abu lo'o.eli cy. na'u klesi by. jetnu gi cy. kampu klesi .abu joi by:If C ''subset'' A and C ''subset'' B, then C is called a common subset of A and B. (Fundamental Concepts Of Higher Algebra, Translation by Nick Nicholas, [http://www.lojban.org/cgi-bin/corpus/show/Fundamental%20Concepts%20Of%20Higher%20Algebra link] )
;.i go li cy. na'u klesi .abu lo'o.eli cy. na'u klesi by. jetnu gi cy. kampu klesi .abu joi by:If C ''subset'' A and C ''subset'' B, then C is called a common subset of A and B. (Fundamental Concepts Of Higher Algebra, Translation by Nick Nicholas, [http://www.lojban.org/cgi-bin/corpus/show/Fundamental%20Concepts%20Of%20Higher%20Algebra ink] )
 
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==== Notes ====
==== Notes ====
 
This comment applies exclusively to CLL example 18.18.1. I'm not sure if it therefore belongs here. The CLL example of this seems to be needlessly complicated (using the value of pi/2 where the function is undefined). I've changed the example here slightly to avoid any disputes about validity.
This comment applies exclusively to CLL example 18.18.1. I'm not sure if it therefore belongs here. The CLL example of this seems to be needlessly complicated (using the value of pi/2 where the function is undefined). I've changed the example here slightly to avoid any disputes about validity.
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=== cmavo: ni'e (NIhE) ===


=== ni'e (NIhE) ===
==== Proposed Definition ====
 
====  Proposed Definition ====
 
The cmavo "ni'e" makes a selbri into an operand. The x1 place of the selbri generally represents a number, and therefore is often a ``ni'' abstraction. The "ni'e" makes that number available as a mekso operand. A common application is to make equations relating pure dimensions.
The cmavo "ni'e" makes a selbri into an operand. The x1 place of the selbri generally represents a number, and therefore is often a ``ni'' abstraction. The "ni'e" makes that number available as a mekso operand. A common application is to make equations relating pure dimensions.


==== Proposed Keywords ====
==== See Also ====
* {na'u} — selbri to operator
* {mo'e} — sumti to operand


==== Proposed Keywords ====
* selbri to operand
* selbri to operand


==== See Also ====
==== Usage Examples ====
 
* {na'u} selbri to operator
* {mo'e} sumti to operand
 
====  Usage Examples ====
 
;li ni'e ni clani ~91~te'u~93~ pi'i ni'e ni ganra ~91~te'u~93~ pi'i ni'e ni condi te'u du li ni'e ni canlu: Length x Width x Depth = Volume (CLL 18.18.2)
;li ni'e ni clani ~91~te'u~93~ pi'i ni'e ni ganra ~91~te'u~93~ pi'i ni'e ni condi te'u du li ni'e ni canlu: Length x Width x Depth = Volume (CLL 18.18.2)
;ibabo le jinga korbi goi jyky cu du le cmarai mulna'u poi zmadu li ni'e ni ce'u cuxna fe'i ni'e zmarai ni cumki jinga: A winning threshold is determined as follows: divide the number of voters by the maximum number of slots to fill, and take the lowest integer larger than this number. (Single Transferrable Vote, pycyn?, Saturday 21/6/2003 22:48:27 UTC?, [http://www.lojban.org/tiki/Single+Transferrable+Vote link])


;ibabo le jinga korbi goi jyky cu du le cmarai mulna'u poi zmadu li ni'e ni ce'u cuxna fe'i ni'e zmarai ni cumki jinga: A winning threshold is determined as follows: divide the number of voters by the maximum number of slots to fill, and take the lowest integer larger than this number. (Single Transferrable Vote, pycyn?, Saturday 21/6/2003 22:48:27 UTC?, [http://www.lojban.org/tiki/Single+Transferrable+Vote ink])
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=== cmavo: nu'a (NUhA) ===
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=== nu'a (NUhA) ===
 
====  Proposed Definition ====


==== Proposed Definition ====
The cmavo "nu'a" is the inverse of {na'u}, and allows a mekso operator to be used as a normal selbri, with the first place being the result of applying the operator to the other places.  
The cmavo "nu'a" is the inverse of {na'u}, and allows a mekso operator to be used as a normal selbri, with the first place being the result of applying the operator to the other places.  


==== See Also ====
==== See Also ====
 
* {na'u} selbri to operator
* {na'u} selbri to operator
* {me} sumti to selbri
* {me} sumti to selbri
 
====  Proposed Keywords ====


==== Proposed Keywords ====
* operator to selbri
* operator to selbri


==== Usage Examples ====
==== Usage Examples ====
 
;li ni'umu cu nu'a va'a li ma'umu: -5 is the negative of +5 (CLL, 18.19.3)
;li ni'umu cu nu'a va'a li ma'umu: -5 is the negative of +5 (CLL, 18.19.3)


==== Issues ====
==== Issues ====
 
It's been pointed out by Xorxes that {me} could be expanded to do this. {nu'a} could be moved to ME for backwards compatibility. It has had (almost) no usage in the wild (corpora + mailing list) (literally 6 mentions on IRC). But it does have a nice symmetry with na'u
It's been pointed out by Xorxes that {me} could be expanded to do this. {nu'a} could be moved to ME for backwards compatibility. It has had (almost) no usage in the wild (corpora + mailing list) (literally 6 mentions on IRC). But it does have a nice symmetry with na'u
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=== pe'o (PEhO) ===
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=== cmavo: pe'o (PEhO) ===
====  Proposed Definition ====


==== Proposed Definition ====
The optional flag that indicates a forethought mekso operator. Forethought mode is also known as Polish notation. When used in conjunction with {ku'e}, it acts like brackets around the function and its arguments.
The optional flag that indicates a forethought mekso operator. Forethought mode is also known as Polish notation. When used in conjunction with {ku'e}, it acts like brackets around the function and its arguments.


==== See Also ====
==== See Also ====
* {fu'a} — Reverse Polish flag
* {ku'e} — forethought operator terminator


* {fu'a} Reverse Polish flag
==== Proposed Keywords ====
* {ku'e} Forethought operator terminator
* forethought flag
 
==== Proposed Keywords ====
 
* Forethought Flag
 
====  Usage Examples ====


==== Usage Examples ====
;li pe'o su'i paboi reboi ciboi ku'e du li xa: (+ 1 2 3 ) = 6  (CLL 18.6.4)
;li pe'o su'i paboi reboi ciboi ku'e du li xa: (+ 1 2 3 ) = 6  (CLL 18.6.4)
;li py. su'i pe'o va'a ny. ku'e su'i zy du li xy.: p + ( -n) + z = x  (CLL 18.6.5)
;li py. su'i pe'o va'a ny. ku'e su'i zy du li xy.: p + ( -n) + z = x  (CLL 18.6.5)
;li zy du li pe'o ma'o fy.boi xy. ku'e: z = ( f(x) )  (CLL 18.6.6)
;li zy du li pe'o ma'o fy.boi xy. ku'e: z = ( f(x) )  (CLL 18.6.6)


==== Notes ====
==== Notes ====
 
When using forethought mekso, be sure that the operands really are operands: they cannot contain regular infix expressions unless parenthesized with {vei} and {ve'o}. Eg li + 2 x 3 4 parses as 2 + ( 3 x 4 ) and not ( 2 x 3 ) + 4.
When using forethought mekso, be sure that the operands really are operands: they cannot contain regular infix expressions unless parenthesized with {vei} and {ve'o}. Eg li + 2 x 3 4 parses as 2 + ( 3 x 4 ) and not ( 2 x 3 ) + 4.
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=== cmavo: ti'o (SEI) ===
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=== ti'o (SEI) ===
 
====  Proposed Definition ====


==== Proposed Definition ====
This, like {sei}, attaches a commentary about the text. The purpose of this is to define a heirarchy of precedence for mex operators.  
This, like {sei}, attaches a commentary about the text. The purpose of this is to define a heirarchy of precedence for mex operators.  
 
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The format of a {ti'o} declaration has not been formally established, but presumably would take the form of mentioning a mekso operator and then giving it either an absolute numerical precedence on some pre-established scale, or else specifying relative precedences between new operators and existing operators. Typically only operators of selma'o VUhU would be given higher precedence, whereas operators created with {na'u}, {ni'e} or {ma'o} would remain at the lowest level of precedence.  
The format of a {ti'o} declaration has not been formally established, but presumably would take the form of mentioning a mekso operator and then giving it either an absolute numerical precedence on some pre-established scale, or else specifying relative precedences between new operators and existing operators. Typically only operators of selma'o VUhU would be given higher precedence, whereas operators created with {na'u}, {ni'e} or {ma'o} would remain at the lowest level of precedence.  
 
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If such a system was created, there would most likely be a predefined set of precedence levels that would match common mathematics conventions and which could easily be referenced. In such a system one would expect that multiplication would be of higher precedence than addition
If such a system was created, there would most likely be a predefined set of precedence levels that would match common mathematics conventions and which could easily be referenced. In such a system one would expect that multiplication would be of higher precedence than addition


==== Proposed Keywords ====
==== See Also ====


* Metalinguistic Operator Precedence Declaration
==== Proposed Keywords ====
* Mex precedence
* metalinguistic operator precedence declaration
 
* mex precedence
==== Usage Examples ====


==== Usage Examples ====
;ti'o zo pi'i ce'o zo su'i porsi li pa su'i re pi'i ci du li ze: ("x" and "+" is an ordered sequence) 1 + 2 x 3 = 7 (created for this, mi'e RossOgilvie, 16/6/10)
;ti'o zo pi'i ce'o zo su'i porsi li pa su'i re pi'i ci du li ze: ("x" and "+" is an ordered sequence) 1 + 2 x 3 = 7 (created for this, mi'e RossOgilvie, 16/6/10)


==== Issues ====
==== Issues ====
 
This isn't really a definition; more a suggestion of what the intention of this cmavo should be. A good system needs to be worked out. I could find no mention of it in the mailing list.
This isn't really a definition; more a suggestion of what the intention of this cmavo should be. A good system needs to be worked out. I could find no mention of it in the mailing list.


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=== cmavo: te'u (TEhU) ===
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=== te'u (TEhU) ===
 
====  Proposed Definition ====


==== Proposed Definition ====
An elidable terminator for several mex related {selma'o}, namely NAhU, NIhE, MOhE, MAhO, and JOhI. These {selma'o} are generally conversion tags.
An elidable terminator for several mex related {selma'o}, namely NAhU, NIhE, MOhE, MAhO, and JOhI. These {selma'o} are generally conversion tags.


==== See Also ====
==== See Also ====
 
* {na'u}
* {na'u}
* {ni'e}
* {ni'e}
* {mo'e}
* {mo'e}
* {ma'o}
* {ma'o}
* {jo'i}
* {jo'i}


==== Proposed Keywords ====
==== Proposed Keywords ====
 
* mex conversion terminator
* Mex Conversion Terminator


==== Usage Examples ====
==== Usage Examples ====


;li jo'i paboi reboi te'u su'i jo'i ciboi voboi du li jo'i voboi xaboi: the-number array( one, two ) plus array( three, four) equals the-number array( four, six)  (CLL 18.15.1)
;li jo'i paboi reboi te'u su'i jo'i ciboi voboi du li jo'i voboi xaboi: the-number array( one, two ) plus array( three, four) equals the-number array( four, six)  (CLL 18.15.1)
;li na'u tanjo te'u vei pai fe'i vo ~91~ve'o~93~ du li pa: the-number the-operator tangent( pi / 4 ) = the-number 1  (CLL 18.18.1)
;li na'u tanjo te'u vei pai fe'i vo ~91~ve'o~93~ du li pa: the-number the-operator tangent( pi / 4 ) = the-number 1  (CLL 18.18.1)
;li ni'e ni clani ~91~te'u~93~ pi'i ni'e ni ganra ~91~te'u~93~ pi'i ni'e ni condi te'u du li ni'e ni canlu:Length × Width × Depth = Volume  (CLL 18.18.2)
;li ni'e ni clani ~91~te'u~93~ pi'i ni'e ni ganra ~91~te'u~93~ pi'i ni'e ni condi te'u du li ni'e ni canlu:Length × Width × Depth = Volume  (CLL 18.18.2)
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<br>
 
<br>
<br />
 
<br />
 
<br />
 
 
===  vei (VEI) ===


====  Proposed Definition ====
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=== cmavo: vei (VEI) ===


==== Proposed Definition ====
This is the mathematical left bracket. Used to group mex expressions. For example, brackets are used to turn a mex expression into an operand for use by a forethought operator, or to place a mex expression in a subscript. The right bracket {ve'o} is elidable. {vei} and {ve'o} are necessary for any non-simple mekso used as a quantifier.
This is the mathematical left bracket. Used to group mex expressions. For example, brackets are used to turn a mex expression into an operand for use by a forethought operator, or to place a mex expression in a subscript. The right bracket {ve'o} is elidable. {vei} and {ve'o} are necessary for any non-simple mekso used as a quantifier.


==== See Also ====
==== See Also ====
* {ve'o} — right bracket
* {ku'e} — forethought operator teminator


* {ve'o} Right bracket
==== Proposed Keywords ====
* {ku'e} Forethought operator teminator
* left bracket


==== Proposed Keywords ====
==== Usage Examples ====
 
* Left bracket
 
====  Usage Examples ====


;li vei ny. su'i pa ve'o pi'i vei ny. su'i pa ~91~ve'o~93~ du li ny. ~91~bi'e~93~ te'a re su'i re bi'e pi'i ny. su'i pa: (n+1)(n+1) = n~94~2 + 2n + 1  (CLL 18.5.10)
;li vei ny. su'i pa ve'o pi'i vei ny. su'i pa ~91~ve'o~93~ du li ny. ~91~bi'e~93~ te'a re su'i re bi'e pi'i ny. su'i pa: (n+1)(n+1) = n~94~2 + 2n + 1  (CLL 18.5.10)
;xy.boixi vei ny. su'i pa ~91~ve'o~93~: x sub ( n + 1)  (CLL 18.13.4)
;xy.boixi vei ny. su'i pa ~91~ve'o~93~: x sub ( n + 1)  (CLL 18.13.4)
;vei ci .a vo ve'o prenu cu klama le zarci: ( three or four ) people go-to the market.  (CLL 18.17.1)
;vei ci .a vo ve'o prenu cu klama le zarci: ( three or four ) people go-to the market.  (CLL 18.17.1)
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<br />
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=== cmavo: ve'o (VEhO) ===
<br />
 
<br />
 
 
=== ve'o (VEhO) ===
 
====  Proposed Definition ====


==== Proposed Definition ====
This is the mathematical right bracket. Used to group mex expressions. For example, brackets are used to turn a mex expression into an operand for use by a forethought operator, or to place a mex expression in a subscript. As a terminator, it is elidable. The corresponding left bracket is {vei}. {vei} and {ve'o} are necessary for any non-simple mekso used as a quantifier.
This is the mathematical right bracket. Used to group mex expressions. For example, brackets are used to turn a mex expression into an operand for use by a forethought operator, or to place a mex expression in a subscript. As a terminator, it is elidable. The corresponding left bracket is {vei}. {vei} and {ve'o} are necessary for any non-simple mekso used as a quantifier.


==== See Also ====
==== See Also ====
 
* {vei} —left bracket
* {vei} Left bracket
* {tu'e} — mex conversion terminator
* {tu'e} Mex Conversion Terminator
 
====  Proposed Keywords ====


* Right bracket
==== Proposed Keywords ====
* right bracket


==== Usage Examples ====
==== Usage Examples ====


;li vei ny. su'i pa ve'o pi'i vei ny. su'i pa ~91~ve'o~93~ du li ny. ~91~bi'e~93~ te'a re su'i re bi'e pi'i ny. su'i pa: (n+1)(n+1) = n~94~2 + 2n + 1 (CLL 18.5.10)
;li vei ny. su'i pa ve'o pi'i vei ny. su'i pa ~91~ve'o~93~ du li ny. ~91~bi'e~93~ te'a re su'i re bi'e pi'i ny. su'i pa: (n+1)(n+1) = n~94~2 + 2n + 1 (CLL 18.5.10)
;xy.boixi vei ny. su'i pa ~91~ve'o~93~: x sub ( n + 1) (CLL 18.13.4)
;xy.boixi vei ny. su'i pa ~91~ve'o~93~: x sub ( n + 1) (CLL 18.13.4)
;vei ci .a vo ve'o prenu cu klama le zarci: ( three or four ) people go-to the market. (CLL 18.17.1)
;vei ci .a vo ve'o prenu cu klama le zarci: ( three or four ) people go-to the market. (CLL 18.17.1)
 
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{BOX}
== Issues ==
 
The write up above pretty much follows the CLL. However there has been at least one [http://www.lojban.org/tiki/MEX+grammar+proposal proposal] (and I suspect there might be others) to reform the mex grammar to simplify it, mostly by merging selma'o. I myself am unhappy by the complexity of mex; specifically the limitations of {fu'a}, and the current uses of {tu'o} and {ge'a} (as noted above).
== Issues ==
 
The write up above pretty much follows the CLL. However there has been at least one [http://www.lojban.org/tiki/MEX+grammar+p proposal] (and I suspect there might be others) to reform the mex grammar to simplify it, mostly by merging selma'o. I myself am unhappy by the complexity of mex; specifically the limitations of {fu'a}, and the current uses of {tu'o} and {ge'a} (as noted above).


Also, the definition of {ti'o} is almost apologetic in its uselessness. As the CLL suggests, a working party needs to hammer out a standardised format for {ti'o}, put together a common convention precedence list for VUhU and publish it for reference. (In fact if such a list were published, then perhaps it should apply by default. The CLL suggests that the common convention for order of operations applies in mex already, and that would provide a sound way to implement this)
Also, the definition of {ti'o} is almost apologetic in its uselessness. As the CLL suggests, a working party needs to hammer out a standardised format for {ti'o}, put together a common convention precedence list for VUhU and publish it for reference. (In fact if such a list were published, then perhaps it should apply by default. The CLL suggests that the common convention for order of operations applies in mex already, and that would provide a sound way to implement this)


== Impact ==
== Impact ==
There is little impact from this, as mex is so underused. The only substantial work involving mex that I could find was [http://www.lojban.org/cgi-bin/corpus/show/Fundamental%20Concepts%20Of%20Higher%20Algebra
Fundamental Concepts Of Higher Algebra], by Nick Nicholas. Regardless, there is no recommendation to change the CLL definitions.


There is little impact from this, as mex is so underused. The only substantial work involving mex that I could find was [http://www.lojban.org/cgi-bin/corpus/show/Fundamental%20Concepts%20Of%20Higher%20Algebra Fundamental Concepts Of Higher Algebra], by Nick Nicholas. Regardless, there is no recommendation to change the CLL definitions.
[[Category:BPFK Sections including selma'o BIhE|M]]
[[Category:BPFK Sections including selma'o FUhA|M]]
[[Category:BPFK Sections including selma'o JOhI|M]]
[[Category:BPFK Sections including selma'o KUhE|M]]
[[Category:BPFK Sections including selma'o MAhO|M]]
[[Category:BPFK Sections including selma'o MOhE|M]]
[[Category:BPFK Sections including selma'o NAhU|M]]
[[Category:BPFK Sections including selma'o NIhE|M]]
[[Category:BPFK Sections including selma'o NUhA|M]]
[[Category:BPFK Sections including selma'o PEhO|M]]
[[Category:BPFK Sections including selma'o SEI|M]]
[[Category:BPFK Sections including selma'o TEhU|M]]
[[Category:BPFK Sections including selma'o VEI|M]]
[[Category:BPFK Sections including selma'o VEhO|M]]

Latest revision as of 23:24, 3 April 2020

This page is imported from version 84 of the page BPFK Section: MEX from the lojban Tiki.

Proposed Definitions And Examples

cmavo: bi'e (BIhE)

Proposed Definition

Indicates an operator has precedence over unmarked operators. When an operator is prefixed with this cmavo, it becomes automatically of higher precedence than other operators not so prefixed. If more than one operator has a bi'e prefix, grouping is to the right; multiple bi'e prefixes on a single operator are not allowed.

See Also

Proposed Keywords

  • high priority operator
  • precedence operator

Usage Examples

li ci su'i vo bi'e pi'i mu du li reci
3 + (4 × 5) = 23 (CLL, 18.5.9)

Notes

This is distinct from the use of mathematical brackets {vei} and {ve'o}.

Issues

Xorxes has a plan to replace this by expanding the use of {bo}





cmavo: fu'a (FUhA)

Proposed Definition

Marks the mekso expression as using Reverse Polish (RP) notation. RP notation is always marked by an explicit fu'a at the beginning of the expression. Operators acting in RP are required to have two operands (though {tu'o} and {ge'a} can assist when using unitary and ternary operators respectively).

See also

  • {pe'o} — forethought operator flag
  • {tu'o} — null operand
  • {ge'a} — null operator

Proposed Keywords

  • Reverse Polish flag

Usage Examples

(natural example: doi jbokaj li fu'a pa boi re su'i ci su'i)

li fu'a reboi ci su'i du li mu
(RP) (2 3 +) = 5 (CLL, 18.16.1)
li fu'a reboi ci pi'i voboi mu pi'i su'i du li rexa
(RP) (2 3 x) (4 5 x) + = 26 (CLL, 18.16.2)
li fu'a ciboi muboi vu'u du li fu'a reboi tu'o va'a
(RP) (3 5 -) = (RP) (2 null) negative (CLL, 18.16.3)
li cinoki'oki'o du li fu'a biboi ciboi panoboi ge'a gei
30,000,000 = (RP) 8 (3 10 null) exp (CLL, 18.16.4)

Issues

It seems quite arbitrary that operators acting in reverse polish notation are required to have exactly 2 operands. Especially considering that in polish notation, operators are allowed to have as many operands as they like. It does not make semantic sense for all operators (for example the negation operator, used in the example usage above). Though there is a problem in determining which operands belong to which operator, and the solution currently is quite elegant for usage, it lacks symmetry with forethought equivalent and seems arbitrary.





cmavo: jo'i (JOhI)

Proposed Definition

Joins a sequence of simple operands or bracketed full expressions into a vector. A vector may have any number of components. It's corresponding terminator {te'u} is elidable.

See also

  • {te'u} — Mekso terminator for NAhU, NIhE, MOhE, MAhO, and JOhI

Proposed Keywords

  • vector flag

Usage Examples

li jo'i paboi reboi te'u su'i jo'i ciboi voboi du li jo'i voboi xaboi
vector (1, 2) + vector (3, 4) = vector (4, 6) (CLL, 18.15.1)
li ma'o fy. boi pa jo'i re jo'i ci
f(1,[2,[3]]) (Re: ~91~lojban~93~ loi preti be fi lo nincli zo'u tu'e, Thu, 23 Jan 2003 11:10:25 -0800, Robin Lee Powell, link)

Notes

It is the only member of selma'o JOhI

"Vector" may not be the mathematically best way to describe it. "Ordered list" or "ordered tuple" is better. This wording is fine, though, in the computer science sense.





cmavo: ku'e (KUhE)

Proposed Definition

This is the elidable terminator of operators when they are acting in forethought mode. It serves to distinguish where the operands of one operator end and another begin.

See Also

  • {pe'o} Forethought operator flag

Proposed Keywords

  • forethought operator terminator

Usage Examples

li py. su'i va'a ny. ku'e su'i zy du li xy.
p + (negative n) + z = x (CLL, 18.6.2)





cmavo: ma'o (MAhO)

Proposed Defintion

This flag converts letteral string or other mathematical expression (mex) operand into a mex operator. Its elidable terminator is {te'u}.

See Also

Proposed Keywords

  • operand to operator flag

Usage Examples

li zy du li ma'o fy.boi xy.
z = f(x) (CLL, 18.6.3)

Notes

The CLL has the following observation: There is a potential semantic ambiguity in ma'o fy. ~91~te'u~93~ if fy. is already in use as a variable: it comes to mean "the function whose value is always 'f' ". However, mathematicians do not normally use the same lerfu words or strings as both functions and variables, so this case should not arise in practice.





cmavo: mo'e (MOhE)

Proposed Definition

Converts a sumti to a mex operand. Intended to allow dimensions to be embedding into mex expressions. It is also used for "folk quantifiers", also known as collective nouns. It precedes the sumti. Its elidible terminator is {te'u}.

See Also

  • {na'u} — selbri to operator
  • {ni'e} — selbri to operand

Proposed Keywords

  • Sumti to mex operand

Usage Examples

li mo'e re ratcu su'i mo'e re ractu du li mo'e vo danlu
(2 rats) + (2 rats) = (4 animals) (CLL, 18.18.3)
mi viska vei mo'e lo'e lanzu ve'o cinfo
I see (a typical family) of lions (CLL, 18.18.4)
I see a pride of lions
li mo'e lo spaji su'i mo'e lo spaji du li mo'e lo mutce spaji
A suprise + a suprise = a big suprise (Re: mo'e (was: RE: ~91~lojban~93~ useless selmaho?, Sun, 2 Sep 2001 03:19:28 +0200, Adam Raizen, link)





cmavo: na'u (NAhU)

Proposed Definition

The cmavo "na'u" makes a selbri into an operator. In general, the first place of the selbri specifies the result of the operator, and the other unfilled places specify the operands. Its elidible terminator is {te'u}. It is also used to construct questions about operators.

See Also

  • {ni'e} — selbri to operand
  • {mo'e} — sumti to operand
  • {te'u} — terminator

Proposed Keywords

  • selbri to operator

Usage Examples

li na'u tanjo te'u vei pai fe'i vo ~91~ve'o~93~ du li pa
tan ( pi / 4 ) = 1 (similar to CLL, 18.18.1)
li re na'u mo re du li vo
2 what-operator? 2 = 4 (CLL, 18.19.4)
.i go li cy. na'u klesi .abu lo'o.eli cy. na'u klesi by. jetnu gi cy. kampu klesi .abu joi by
If C subset A and C subset B, then C is called a common subset of A and B. (Fundamental Concepts Of Higher Algebra, Translation by Nick Nicholas, link )

'

Notes

This comment applies exclusively to CLL example 18.18.1. I'm not sure if it therefore belongs here. The CLL example of this seems to be needlessly complicated (using the value of pi/2 where the function is undefined). I've changed the example here slightly to avoid any disputes about validity.





cmavo: ni'e (NIhE)

Proposed Definition

The cmavo "ni'e" makes a selbri into an operand. The x1 place of the selbri generally represents a number, and therefore is often a ``ni abstraction. The "ni'e" makes that number available as a mekso operand. A common application is to make equations relating pure dimensions.

See Also

  • {na'u} — selbri to operator
  • {mo'e} — sumti to operand

Proposed Keywords

  • selbri to operand

Usage Examples

li ni'e ni clani ~91~te'u~93~ pi'i ni'e ni ganra ~91~te'u~93~ pi'i ni'e ni condi te'u du li ni'e ni canlu
Length x Width x Depth = Volume (CLL 18.18.2)
ibabo le jinga korbi goi jyky cu du le cmarai mulna'u poi zmadu li ni'e ni ce'u cuxna fe'i ni'e zmarai ni cumki jinga
A winning threshold is determined as follows: divide the number of voters by the maximum number of slots to fill, and take the lowest integer larger than this number. (Single Transferrable Vote, pycyn?, Saturday 21/6/2003 22:48:27 UTC?, link)





cmavo: nu'a (NUhA)

Proposed Definition

The cmavo "nu'a" is the inverse of {na'u}, and allows a mekso operator to be used as a normal selbri, with the first place being the result of applying the operator to the other places.

See Also

  • {na'u} — selbri to operator
  • {me} — sumti to selbri

Proposed Keywords

  • operator to selbri

Usage Examples

li ni'umu cu nu'a va'a li ma'umu
-5 is the negative of +5 (CLL, 18.19.3)

Issues

It's been pointed out by Xorxes that {me} could be expanded to do this. {nu'a} could be moved to ME for backwards compatibility. It has had (almost) no usage in the wild (corpora + mailing list) (literally 6 mentions on IRC). But it does have a nice symmetry with na'u





cmavo: pe'o (PEhO)

Proposed Definition

The optional flag that indicates a forethought mekso operator. Forethought mode is also known as Polish notation. When used in conjunction with {ku'e}, it acts like brackets around the function and its arguments.

See Also

  • {fu'a} — Reverse Polish flag
  • {ku'e} — forethought operator terminator

Proposed Keywords

  • forethought flag

Usage Examples

li pe'o su'i paboi reboi ciboi ku'e du li xa
(+ 1 2 3 ) = 6 (CLL 18.6.4)
li py. su'i pe'o va'a ny. ku'e su'i zy du li xy.
p + ( -n) + z = x (CLL 18.6.5)
li zy du li pe'o ma'o fy.boi xy. ku'e
z = ( f(x) ) (CLL 18.6.6)

Notes

When using forethought mekso, be sure that the operands really are operands: they cannot contain regular infix expressions unless parenthesized with {vei} and {ve'o}. Eg li + 2 x 3 4 parses as 2 + ( 3 x 4 ) and not ( 2 x 3 ) + 4.




cmavo: ti'o (SEI)

Proposed Definition

This, like {sei}, attaches a commentary about the text. The purpose of this is to define a heirarchy of precedence for mex operators.
The format of a {ti'o} declaration has not been formally established, but presumably would take the form of mentioning a mekso operator and then giving it either an absolute numerical precedence on some pre-established scale, or else specifying relative precedences between new operators and existing operators. Typically only operators of selma'o VUhU would be given higher precedence, whereas operators created with {na'u}, {ni'e} or {ma'o} would remain at the lowest level of precedence.
If such a system was created, there would most likely be a predefined set of precedence levels that would match common mathematics conventions and which could easily be referenced. In such a system one would expect that multiplication would be of higher precedence than addition

See Also

Proposed Keywords

  • metalinguistic operator precedence declaration
  • mex precedence

Usage Examples

ti'o zo pi'i ce'o zo su'i porsi li pa su'i re pi'i ci du li ze
("x" and "+" is an ordered sequence) 1 + 2 x 3 = 7 (created for this, mi'e RossOgilvie, 16/6/10)

Issues

This isn't really a definition; more a suggestion of what the intention of this cmavo should be. A good system needs to be worked out. I could find no mention of it in the mailing list.





cmavo: te'u (TEhU)

Proposed Definition

An elidable terminator for several mex related {selma'o}, namely NAhU, NIhE, MOhE, MAhO, and JOhI. These {selma'o} are generally conversion tags.

See Also

  • {na'u}
  • {ni'e}
  • {mo'e}
  • {ma'o}
  • {jo'i}

Proposed Keywords

  • mex conversion terminator

Usage Examples

li jo'i paboi reboi te'u su'i jo'i ciboi voboi du li jo'i voboi xaboi
the-number array( one, two ) plus array( three, four) equals the-number array( four, six) (CLL 18.15.1)
li na'u tanjo te'u vei pai fe'i vo ~91~ve'o~93~ du li pa
the-number the-operator tangent( pi / 4 ) = the-number 1 (CLL 18.18.1)
li ni'e ni clani ~91~te'u~93~ pi'i ni'e ni ganra ~91~te'u~93~ pi'i ni'e ni condi te'u du li ni'e ni canlu
Length × Width × Depth = Volume (CLL 18.18.2)





cmavo: vei (VEI)

Proposed Definition

This is the mathematical left bracket. Used to group mex expressions. For example, brackets are used to turn a mex expression into an operand for use by a forethought operator, or to place a mex expression in a subscript. The right bracket {ve'o} is elidable. {vei} and {ve'o} are necessary for any non-simple mekso used as a quantifier.

See Also

  • {ve'o} — right bracket
  • {ku'e} — forethought operator teminator

Proposed Keywords

  • left bracket

Usage Examples

li vei ny. su'i pa ve'o pi'i vei ny. su'i pa ~91~ve'o~93~ du li ny. ~91~bi'e~93~ te'a re su'i re bi'e pi'i ny. su'i pa
(n+1)(n+1) = n~94~2 + 2n + 1 (CLL 18.5.10)
xy.boixi vei ny. su'i pa ~91~ve'o~93~
x sub ( n + 1) (CLL 18.13.4)
vei ci .a vo ve'o prenu cu klama le zarci
( three or four ) people go-to the market. (CLL 18.17.1)





cmavo: ve'o (VEhO)

Proposed Definition

This is the mathematical right bracket. Used to group mex expressions. For example, brackets are used to turn a mex expression into an operand for use by a forethought operator, or to place a mex expression in a subscript. As a terminator, it is elidable. The corresponding left bracket is {vei}. {vei} and {ve'o} are necessary for any non-simple mekso used as a quantifier.

See Also

  • {vei} —left bracket
  • {tu'e} — mex conversion terminator

Proposed Keywords

  • right bracket

Usage Examples

li vei ny. su'i pa ve'o pi'i vei ny. su'i pa ~91~ve'o~93~ du li ny. ~91~bi'e~93~ te'a re su'i re bi'e pi'i ny. su'i pa
(n+1)(n+1) = n~94~2 + 2n + 1 (CLL 18.5.10)
xy.boixi vei ny. su'i pa ~91~ve'o~93~
x sub ( n + 1) (CLL 18.13.4)
vei ci .a vo ve'o prenu cu klama le zarci
( three or four ) people go-to the market. (CLL 18.17.1)

Issues

The write up above pretty much follows the CLL. However there has been at least one proposal (and I suspect there might be others) to reform the mex grammar to simplify it, mostly by merging selma'o. I myself am unhappy by the complexity of mex; specifically the limitations of {fu'a}, and the current uses of {tu'o} and {ge'a} (as noted above).

Also, the definition of {ti'o} is almost apologetic in its uselessness. As the CLL suggests, a working party needs to hammer out a standardised format for {ti'o}, put together a common convention precedence list for VUhU and publish it for reference. (In fact if such a list were published, then perhaps it should apply by default. The CLL suggests that the common convention for order of operations applies in mex already, and that would provide a sound way to implement this)

Impact

There is little impact from this, as mex is so underused. The only substantial work involving mex that I could find was [http://www.lojban.org/cgi-bin/corpus/show/Fundamental%20Concepts%20Of%20Higher%20Algebra Fundamental Concepts Of Higher Algebra], by Nick Nicholas. Regardless, there is no recommendation to change the CLL definitions.