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Re: [Texmacs-dev] (For the Wikipedia article) Algorithms and format

 From: Giovanni Piredda Subject: Re: [Texmacs-dev] (For the Wikipedia article) Algorithms and format Date: Mon, 30 Nov 2020 13:56:13 +0100 User-agent: Mozilla/5.0 (X11; Linux x86_64; rv:78.0) Gecko/20100101 Thunderbird/78.5.0

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On 30.11.20 08:16, Massimiliano Gubinelli wrote:
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```Dear Giovanni,

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On 28. Nov 2020, at 23:16, Giovanni Piredda <pireddag@posteo.de <mailto:pireddag@posteo.de>> wrote:
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On 28.11.20 22:57, TeXmacs wrote:
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```On Sat, Nov 28, 2020 at 07:20:15PM +0100, Giovanni Piredda wrote:
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```I have in mind that the "Turing complete" expression describes a
system of manipulation of symbols (I helped now myself with
Wikipedia for finding the word "manipulation" in this context), by
which starting with a set of symbols and applying the manipulation
rules I obtain another set of symbols.
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```This is just to say that the parser of TeX is a complete programming
language on its own.  This means that it is undecidable whether
a given program is parsable.  TeX has no well-defined grammar,
contrary to *ML languages (HTML, SGML, MathML) or TeXmacs.
This is actually a very serious problem (it makes it impossible to
write 100% reliable convertes)
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So "possibility to write converters that work always" is one point that I am going to write in the Wiki page I think.
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```While I see a grammar as a set of rules that determine allowable
compositions of symbols, but they do not tell how to compose any set
of symbols.

But you wrote that the grammar is Turing complete. Could you explain
more? Maybe a pointer to something to read, if it is to long to
write here.
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```See also The Jolly Writer, section 1.8.
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Thanks, here it will take a bit (the explanation on top helped).

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```I have thought a bit on why LaTeX/TeX is so successful,
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```One of the keys is that it cannot easily be converted to something else.
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Proprietary formats such as early M\$ Word are another way to make this task hard.
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Right. Once that you have many pages written in the format, it is difficult to switch to something different. This is also (perhaps) one of the reasons why the LaTeX code written by programs looks usually quite different from the one written by people---there are too many ways to do the same thing.
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The comparison between PS and PDF can be cited in this context. PDF was indeed introduced (as far as I understand) to reduce the wilderness of PS documents (PS is a full-fledged programming language) to a "description language" where arbitrary computations are no more possible.
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I understood it in this way so far (it will take more time before I am able to write it up on Wikipedia)---I write it here in the TeX/TeXmacs format conversion case, but it is more general---please let me know if the description is sensible, it is part of the understanding I know in order to write:
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TeX is a programming language, and the TeXmacs format is description of an abstract object, which is the *output* of a programming language. The theorem on undecidability of the halting problem says that (expressed in a more general way than the formulation "you cannot know if a program halts for all programs") in order to know the output of a program (again, for all programs) you need to run the program; there may be programs for which you can know the output with a simpler calculation.
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Applying this to the conversion between a TeX _program that generates a document_ and a TeXmacs _description of a document_: you cannot do it for all TeX programs.
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Now the difficult and interesting part: for a reasonable converter, one needs to define (and mechanically, with an algorithm, to decide whether the program belongs to the subset or not) a subset of TeX programs for which one can do the conversion. The problem of definition looks to me difficult because the subset has to be "large enough to be useful" and "small enough that the conversion is possible" at the same time. The decision itself might be easy if the criteria for "belonging to the set" make it so (but finding criteria that help from this point of view might be again difficult).
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It would be interesting to know on this topic what is the status of the "conservative conversion" described in "Conservative conversion between LaTeX and TeXmacs" (a good topic to include in an article in an encyclopedia).
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Finally on this topic

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However you need also to add that the \extern primitive allows to access these computational capabilities with an underlying scripting language. Here the comparison can be made with HTML/JS.
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And the native macro system too pushes one outside the markup system, right?

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```The "markup" of TeX (I call it that way even if it is not markup)
for me is the easiest to read among all of the markup languages I
have seen (for mathematics especially, for other things too).
Perhaps this has been also one factor for success.
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```Easy in appearance.

If it is that easy, try writing a converter to some other format.
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I meant "easy to read for me". This is subjective *and* only loosely related to how easy is to read it mechanically, i.e. with an algorithm---I saw this position that I am taking now only taken once by another person on the Internet, and a similar position ("reading TeX is second nature after a while", but without comparison to other markup) taken by other two persons (one in flesh and blood, one on the Internet). By the way I can read at sight only simple mathematical formulae written in TeX, but I do worse with all of the other markup systems I know.
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In the context of markup languages you may want to link to general pages like:
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https://en.wikipedia.org/wiki/Markup_language <https://en.wikipedia.org/wiki/Markup_language>
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Thanks, this link belongs there. Moreover one can write up *inside this article* a paragraph on the TeXmacs format; in this case it would be helpful (I feel it necessary in this moment) to describe in a sentence what distinguishes it from SGML (what makes it not a particular SGML like DocBook) and maybe also why it was chosen that the TeXmacs format would not be SGML.
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and also it could be mentioned that there are other interesting systems like
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https://en.wikipedia.org/wiki/Lout_(software) <https://en.wikipedia.org/wiki/Lout_(software)>
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which is a lazy functional description language for pages.

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Thanks, I downloaded the system and looked at a few pages of the manual ... now I need to understand why it is a lazy functional description language, but that I have to postpone :-)
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Finally, for my remark that TeX is the easiest to read "markup" that I know, it occurred to me that the format of computer algebra systems is still easier to read; but perhaps it is not comprehensive enough to be used for typesetting a document, and if you include more syntactic expressions so that it is, it becomes as difficult to read as TeX at least. Maybe I will experiment a bit with Mathematica, which as far as I remember can format mathematical expressions as well; I need to express all input in linear form of course otherwise it is easier to read but the comparison is unfair ;-)
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G.

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