History: BPFK Section: MEX Operators

Preview of version: 37 (current)

First Version Version

Proposed Definitions And Examples

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Impact

There is no changes to the definitions. I've tried to make them follow the CLL as closely as possible. Further since there is so little mekso literature, there is almost nothing to 'break' anyway. I have made a few suggestions to extend the definitions to expand the functionality some operators. This can be ratified formally if the bpfk/community feels that they add to utility more than they subtract in flexibility.

I (mi'e Ross) am not the first person to take up this section. Minimiscience did some work before I came along. He (She?) is obviously a programmer and seem to have been caught up in designing a consistent type system. Evidence of the beginnings of the system has been moved to the section below this. I am of the opinion that we will never be able to describe how these operators work in every context and so we should stick to giving the base definition and allow authors/speakers to use the operators in other contexts in accordance with common mathematical convention. For the moment, the only hangover of Minimiscience's type system in the above definitions is for {pi'i}.

This said, I think there is merit in the idea to specify default values for omitted arguments or alternatively treat the functions as polymorphic and give definitions of different combinations of arguments it gets given. The latter seems blotted/ overkill but would give definite meanings to operators that get passed tu'o. I haven't done either above.

Minimiscience's Type System

 

  • When an expression is here said to be "undefined," it means that, in the absence of external information about the interpretation of the expression, it is semantically void, meaningless, and/or nonsensical.
  • Mathematical operators take one or more operands, which are here referred to by an 'x' subscripted with a number.
  • Operators defined here as "unary" are defined as operating on their first operand that is not equal to tu'o (referred to as "the operand" within the respective definitions), regardless of where it occurs in the operand list.
    • See also: CLL section 18.16, example 16.3 and the paragraph before it, in which the operand of va'a is in the x_1 place; CLL section 18.14, example 14.1, in which the operand of va'a is in the x_2 place.
  • If all operands of an operator are tu'o, the value of the expression is equal to tu'o.
  • If an operand described in an operator's definition is missing from the operator's operand list and there is no default value given, the missing operand shall be interpreted as tu'o.
  • If one or more extra operands not described in an operator's definition are present in the operator's operand list, they affect the evaluation in an undefined or unspecified manner analogous to sumti attached to a selbri with do'e.
  • Lojban mathematical operators are defined in terms of conventional mathematical operators, and thus there is an implicit type system used in determining the value of an expression. Mekso operands may be of any of the following types:
    • number — a "number" production in the formal grammar, usually corresponding to an element of the complex plane
    • array — an array, vector, ordered list/set, or tuple of one or more mekso values, constructed using jo'i
    • matrix — a composition of one or more arrays of numbers, all of the same size, constructed using pi'a or sa'i
    • function
  • If an operator is applied to operands of a type which its definition does not address, the expression is undefined.
  • The operand tu'o is polymorphic; its type in an expression is determined by its surrounding context.
  • Operator-specific type information (currently in the "Notes" subsections) needs to be included in the main definitions somehow without being too clunky.

History

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Date User IP Edit Comment Version   Action
Thu 21 of Aug., 2014 15:19 GMT Ilmen 95.210.209.219 Fixing a typo 37
Current
v  s
Thu 21 of Aug., 2014 15:17 GMT Ilmen 95.210.209.219 Template + notes 36 v  s
Sun 08 of June, 2014 19:30 GMT mukti 216.194.27.154   35 v  s
Tue 19 of Oct., 2010 01:02 GMT lindarthebard 32.172.136.135   34 v  s
Wed 15 of Sep., 2010 08:12 GMT RossOgilvie 210.84.42.221 Wrote up impact section 33 v  s
Wed 15 of Sep., 2010 07:48 GMT RossOgilvie 210.84.42.221 Tidy up and some standardisation 32 v  s
Mon 13 of Sep., 2010 02:32 GMT RossOgilvie 210.84.4.4   31 v  s
Mon 13 of Sep., 2010 02:32 GMT RossOgilvie 210.84.4.4 sa'o 30 v  s
Sat 11 of Sep., 2010 05:16 GMT RossOgilvie 220.239.170.184   29 v  s
Sat 11 of Sep., 2010 04:54 GMT RossOgilvie 220.239.170.184 ri'o 28 v  s
Fri 10 of Sep., 2010 10:47 GMT RossOgilvie 210.84.4.4   27 v  s
Fri 10 of Sep., 2010 10:36 GMT RossOgilvie 210.84.4.4   26 v  s
Fri 10 of Sep., 2010 08:29 GMT RossOgilvie 210.84.4.4 va'a 25 v  s
Fri 10 of Sep., 2010 08:10 GMT RossOgilvie 210.84.4.4 ne'o 24 v  s
Fri 10 of Sep., 2010 06:00 GMT RossOgilvie 220.239.170.184 fe'a 23 v  s
Fri 10 of Sep., 2010 05:50 GMT RossOgilvie 220.239.170.184 de'o 22 v  s
Fri 10 of Sep., 2010 05:46 GMT RossOgilvie 220.239.170.184   21 v  s
Thu 09 of Sep., 2010 07:23 GMT RossOgilvie 210.84.4.4 did te'a 20 v  s
Thu 09 of Sep., 2010 07:18 GMT RossOgilvie 210.84.4.4   19 v  s
Thu 09 of Sep., 2010 07:11 GMT RossOgilvie 210.84.4.4 did pa'i 18 v  s
Thu 09 of Sep., 2010 05:01 GMT RossOgilvie 172.17.36.41 did ju'u 17 v  s
Thu 09 of Sep., 2010 04:42 GMT RossOgilvie 172.17.36.41 added a keyword to gei 16 v  s
Thu 09 of Sep., 2010 04:40 GMT RossOgilvie 172.17.36.41 Several definitions 15 v  s
Wed 08 of Sep., 2010 04:01 GMT RossOgilvie 172.17.36.37 Did fe'i 14 v  s
Tue 07 of Sep., 2010 14:30 GMT RossOgilvie 220.239.170.184 Did ge'a 13 v  s
Tue 07 of Sep., 2010 14:18 GMT RossOgilvie 220.239.170.184 Added boxes to the page 12 v  s
Tue 07 of Sep., 2010 14:13 GMT RossOgilvie 220.239.170.184 Did vu'u 11 v  s
Wed 16 of June, 2010 14:02 GMT RossOgilvie 220.239.170.184 Repealed earlier change (don't know what I was thinking) and minor formatting of CLL refererences 10 v  s
Sun 18 of Apr., 2010 14:17 GMT RossOgilvie 220.239.170.184   9 v  s
Wed 14 of Apr., 2010 02:12 GMT Minimiscience 129.21.72.20 Put boxes around the edited cmavo to make them stand out more 8 v  s
Wed 14 of Apr., 2010 02:05 GMT Minimiscience 129.21.72.20 Described fe'i and pi'i 7 v  s
Wed 14 of Apr., 2010 01:49 GMT Minimiscience 129.21.72.20 Added in a forgotten subsection heading 6 v  s
Wed 14 of Apr., 2010 01:48 GMT Minimiscience 129.21.72.20 Began describing the implicit type system 5 v  s
Wed 14 of Apr., 2010 01:28 GMT Minimiscience 129.21.72.20 Specified fu'u 4 v  s
Wed 14 of Apr., 2010 01:21 GMT Minimiscience 129.21.72.20 Fixed formatting 3 v  s
Wed 14 of Apr., 2010 01:17 GMT Minimiscience 129.21.72.20 Descibed "gei" and some general things about VUhU 2 v  s
Wed 17 of Nov., 2004 02:47 GMT rlpowell 64.81.49.171   1 v  s