https://mw-live.lojban.org/index.php?title=Proposal:_distinguishing_digits_from_numbers&feed=atom&action=historyProposal: distinguishing digits from numbers - Revision history2024-03-29T10:39:36ZRevision history for this page on the wikiMediaWiki 1.38.4https://mw-live.lojban.org/index.php?title=Proposal:_distinguishing_digits_from_numbers&diff=121195&oldid=prevKrtisfranks: /* Clean-Up */2016-09-09T06:53:12Z<p><span dir="auto"><span class="autocomment">Clean-Up</span></span></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>"boi'ai" is meant to immediately convert a number back into a single digit (NUM-to-SYM). For example, in base n (for integer n greater than 2), the number n-1 multiplied a single-digit (in base n) number x results in the number (x-1, n-x). (So, in decimal, n = 10l thus n-1 = 9; and if x = 3, then (n-1)*x = 9*3 = 27 = (2, 7) = (3-1, 10-3) = (x-1, n-x).) But how do we express "(x-1, n-x)" if it has complicated digits like these (namely, "x-1" and "n-x"), and is a number to boot? Well, x-1 and n-x are both numbers (each is a single number because the operator "vuhu"/"-" produces such a thing), so we can act on them each with the unary operator "boi'ai". It takes these numbers and turns them into a single digit SYM each, with their appropriate and respective meanings. Now that we have digits, they do what digits do, automatically concatenating into the digit string "r s", where "r" is the single digit that means the number x-1 and "s" is the single digit that means the number n-x. In time, this string "r s" will filter through the order of precedence in interpretation to become the number (x-1, n-x).</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>"boi'ai" is meant to immediately convert a number back into a single digit (NUM-to-SYM). For example, in base n (for integer n greater than 2), the number n-1 multiplied a single-digit (in base n) number x results in the number (x-1, n-x). (So, in decimal, n = 10l thus n-1 = 9; and if x = 3, then (n-1)*x = 9*3 = 27 = (2, 7) = (3-1, 10-3) = (x-1, n-x).) But how do we express "(x-1, n-x)" if it has complicated digits like these (namely, "x-1" and "n-x"), and is a number to boot? Well, x-1 and n-x are both numbers (each is a single number because the operator "vuhu"/"-" produces such a thing), so we can act on them each with the unary operator "boi'ai". It takes these numbers and turns them into a single digit SYM each, with their appropriate and respective meanings. Now that we have digits, they do what digits do, automatically concatenating into the digit string "r s", where "r" is the single digit that means the number x-1 and "s" is the single digit that means the number n-x. In time, this string "r s" will filter through the order of precedence in interpretation to become the number (x-1, n-x).</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>It might also be the case that we wish to endow this word with an additional property: that it halts the interpretation immediately after JUhU, meaning that the XPR gains some meaning internally but never gets evaluated as a number. I personally prefer that this property be included and will assume that it is throughout the rest of this article. (This means that "r s" will not naturally filter down to the number (r, s); it gets stuck at what the meaning of the positions of each "r" and "s" mean. It must be forced down using other operators. So, the last paragraph maybe should be reread with this thought in the forefront of your mind.) I did think that it was necessary to explicitly recognize and adopt this property though. The community deserves to know what it is getting.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>It might also be the case that we wish to endow this word with an additional property: that it halts the interpretation immediately after JUhU, meaning that the XPR gains some meaning internally but never gets evaluated as a number. I personally prefer that this property be included and will assume that it is throughout the rest of this article. (This means that "r s" will not naturally filter down to the number (r, s); it gets stuck at what the meaning of the positions of each "r" and "s" mean. It must be forced down using other operators. So, the last paragraph maybe should be reread with this thought in the forefront of your mind.) <ins style="font-weight: bold; text-decoration: none;">Another example of a justification for this halting property: saying that <math>x \in \{ ''2'', ''3'' \}</math>, meaning that x is one of the digits "2" xor "3" (which are distinct, even if they were to represent the same value), would not be possible unless the interpretation process were indefinitely suspended, since otherwise, the digits would immediately be evaluated and x would equal either the number two or the number three (which could be the same number if the distinct digits do not have distinct meaning, such as is thebcase with decimal "10", Roman "X", and base-greater-than-ten "A"). </ins>I did think that it was necessary to explicitly recognize and adopt this property though<ins style="font-weight: bold; text-decoration: none;">. So, I propose that '''"boi'ai" immediately forces the conversion from NUM to SYM, and that the interpretation process continues to and including JUhU but inmediately pauses thereäfter so that no further interpretation occurs'''</ins>. The community deserves to know what it is getting.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>"boi'au" forces the conversion of a single XPR to a number (immediately through all of the steps of the order of interpretation). This can be helpful for when the output of an operation is strictly a string and it might otherwise pass through the order of interpretation without being evaluated. It is also useful for emphasis or to quickly convert a string, by-passing the typical order of precedence. If we consider the example of the rule for multiplying x by 10 (in any base) to be to concatenate a zero onto the string which represents x in that base, then the expression of this rule might accidentally produce general strings instead of specifically digit strings, meaning that "x0" would pass through the order of precedence without being num-evalled. Then, whensoever one wants to use a VUhU on it (or even to assert an equality between x*10 and "x0"), doing so would be impossible due to typing. But with the help of our unary XPR-to-NUM converter, we are good to go. If the aforementioned additional property of "boi'ai" is adopted, then this word becomes even more useful, for it will force XPR produced by "boi'ai" beyond the JUhU phase of interpretation.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>"boi'au" forces the conversion of a single XPR to a number (immediately through all of the steps of the order of interpretation). This can be helpful for when the output of an operation is strictly a string and it might otherwise pass through the order of interpretation without being evaluated. It is also useful for emphasis or to quickly convert a string, by-passing the typical order of precedence. If we consider the example of the rule for multiplying x by 10 (in any base) to be to concatenate a zero onto the string which represents x in that base, then the expression of this rule might accidentally produce general strings instead of specifically digit strings, meaning that "x0" would pass through the order of precedence without being num-evalled. Then, whensoever one wants to use a VUhU on it (or even to assert an equality between x*10 and "x0"), doing so would be impossible due to typing. But with the help of our unary XPR-to-NUM converter, we are good to go. If the aforementioned additional property of "boi'ai" is adopted, then this word becomes even more useful, for it will force XPR produced by "boi'ai" beyond the JUhU phase of interpretation.</div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>There are a few costs to the latter, but these probably can be overcome (except for the more necessary use of "boi" in order to mean what one wants in some contexts). The upshot is that we now have an easy way to say "Plot3D", whereas if letters and numerals are treated as different and naturally separated by an implicit "boi", this would not be (easily) possible; we would have to resort to converting each of "Plot", "3", and "D" back to strings (possibly risking these being defined as numbers and thus have something like "D" = "9"; see below), concatenate them explicitly (because, remember, we are assuming that they do not naturally implicitly concatenate now), and the convert the string back into a number (which might be the Mathematica function Plot3D).</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>There are a few costs to the latter, but these probably can be overcome (except for the more necessary use of "boi" in order to mean what one wants in some contexts). The upshot is that we now have an easy way to say "Plot3D", whereas if letters and numerals are treated as different and naturally separated by an implicit "boi", this would not be (easily) possible; we would have to resort to converting each of "Plot", "3", and "D" back to strings (possibly risking these being defined as numbers and thus have something like "D" = "9"; see below), concatenate them explicitly (because, remember, we are assuming that they do not naturally implicitly concatenate now), and the convert the string back into a number (which might be the Mathematica function Plot3D).</div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Need to figure out ==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Need to figure out ==</div></td></tr>
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</table>Krtisfrankshttps://mw-live.lojban.org/index.php?title=Proposal:_distinguishing_digits_from_numbers&diff=116502&oldid=prevKrtisfranks: /* "ma'o" and strings for names */2015-07-22T08:10:15Z<p><span dir="auto"><span class="autocomment">"ma'o" and strings for names</span></span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 08:10, 22 July 2015</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Can xo'e refer to letterals? Letterals form strings and sometimes might even occur in "numbers" or function names. What if we want the option of swapping a dummy symbol out for either a letteral or a number (maybe "sin" and "si8" are both defined, maybe they are functions)? It could be useful to refer to any SYM, but it might also be annoying. (I have, I believe proposed a tentative fix to this problem by restricting "xo'e" to PA and inventing two new cmavo: one refers to BY and the other refers to any SYM)</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Can xo'e refer to letterals? Letterals form strings and sometimes might even occur in "numbers" or function names. What if we want the option of swapping a dummy symbol out for either a letteral or a number (maybe "sin" and "si8" are both defined, maybe they are functions)? It could be useful to refer to any SYM, but it might also be annoying. (I have, I believe proposed a tentative fix to this problem by restricting "xo'e" to PA and inventing two new cmavo: one refers to BY and the other refers to any SYM)</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br/></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>== "ma'o" and strings for names ==</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">=</ins>== "ma'o" and strings for names <ins style="font-weight: bold; text-decoration: none;">=</ins>==</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>In "ma'o si8 boi xy", does "8" work as a digit? (I think so)</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>In "ma'o si8 boi xy" <ins style="font-weight: bold; text-decoration: none;">(using loose language; do not interpret rigorously as Lojban yet)</ins>, does "8" work as a digit? (I think so)</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>How do we distinguish it from the actual input (which may be an XPR or a NUM)? (I think that "boi" should be fine. But both of my responses are contingent on assuming many standards established within this article)</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>How do we distinguish it from the actual input (which may be an XPR or a NUM)? (I think that "boi" should be fine. But both of my responses are contingent on assuming many standards established within this article)</div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>How can we restrict the domain of possible referents? Maybe I want x<sub>1</sub> (notice that I did not quote it; it is a number here, for strings do not have the same properties as what are about to be mentioned) to only be even single-digited numbers (in some base). Do I need to do this ahead of time? If so how? If in the present moment/as an afterthought, how do I handle it?</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>How can we restrict the domain of possible referents? Maybe I want x<sub>1</sub> (notice that I did not quote it; it is a number here, for strings do not have the same properties as what are about to be mentioned) to only be even single-digited numbers (in some base). Do I need to do this ahead of time? If so how? If in the present moment/as an afterthought, how do I handle it?</div></td></tr>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Another Problem? ==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== Another Problem? ==</div></td></tr>
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</table>Krtisfrankshttps://mw-live.lojban.org/index.php?title=Proposal:_distinguishing_digits_from_numbers&diff=116501&oldid=prevKrtisfranks: /* Summary of New cmavo */2015-07-22T08:07:50Z<p><span dir="auto"><span class="autocomment">Summary of New cmavo</span></span></p>
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<td colspan="2" class="diff-lineno">Line 212:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* "boi'oi": forces "formal" reading of symbols only, with no substitutions. (Vaguely defined at best)</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* "boi'oi": forces "formal" reading of symbols only, with no substitutions. (Vaguely defined at best)</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* "ku'oi'u": terminator for at least one BOI'VG.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>* "ku'oi'u": terminator for at least one BOI'VG.</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">* "li": one of several mekso expression introducers; a gadri. Means "the evaluated result of the whole mekso expression".</ins></div></td></tr>
</table>Krtisfrankshttps://mw-live.lojban.org/index.php?title=Proposal:_distinguishing_digits_from_numbers&diff=116500&oldid=prevKrtisfranks: Created page with "{{jbocre/en}} ''Initially proposed by krtisfranks. Author: krtisfranks.'' A subtle but pervasive problem in Lojban at the moment is its utter disregard..."2015-07-22T08:06:23Z<p>Created page with "{{jbocre/en}} ''Initially proposed by <a href="/papri/User:Krtisfranks" title="User:Krtisfranks">krtisfranks</a>. Author: krtisfranks.'' A subtle but pervasive problem in Lojban at the moment is its utter disregard..."</p>
<a href="https://mw-live.lojban.org/index.php?title=Proposal:_distinguishing_digits_from_numbers&diff=116500">Show changes</a>Krtisfranks