The thing is: LaTeX might try hard to look like a declarative language for structured documents, but it is not. It is a set of TeX macros. And TeX is a type setting system.
There is no good reason to put the accessibility into the type setting. Instead, use a declarative (e.g., any markup) language, translate that a) to (LaTeX) and b) to accessibility annotations and then combine the two results. Problem solved.
Unfortunately you will either lose a lot of expressiveness along the way or you have to find a very sophisticated markup language.
Yeah, one could do that. But then again, one could do that with any other scripting language. A true declarative document would mean a single source of truth and freedom from those technical matters.
An answer, particularly in the sciences, is to also distribute the source *.tex files, which being plain text with markup, can be handled just fine by things like emacspeak, or accessibility tooling for other sensible editors.
This comes up a bit around the blind accessibility issue for mathematics, which is why I suspect it's bubbling up this week on HN.
There's a bunch of counter-argument here from working practising blind mathematicians who read and write raw TeX every day, so there's at least a non-zero audience.
There were a bunch of mathematicians who used roman numerals for arithmetic between 0 AD and 1200AD. That they existed is not a counter-argument to the fact roman numerals are terrible to do arithmetic in. That is an argument that people can get used to anything, and become proficient enough at it that changing to a new - and better - system will set them back enough for it to be not worth while doing - for them. The same is true for modern maths notation.
I read more than one or two IT papers which donated variable types by using a different font between A and A and that difference was essential for reasonable understanding the papers.
Then the notation is overloaded.
Brackets are not even necessary enclosing something or are not necessary well balanced.
"Bar" based brackets and bars used for non bracket purpose are not necessary differentiate by noon visual clues. Etc.
It's already often confusing for people which can read the formula so I'm not surprised that really annoying for people which can't normally read the formula.
A super simple example is that [a;b[ is that "German"/(EU?) still to write an range with inclusive start and exclusive end. In the US [a;b) is used instead. But let's be honest something like rangeIE(a, b) or similar (Latex range_{ie}) is much better for a screen reader I thing and that's a trivial example not one of the really bad ones.
I think all formula should be written in a way which represents semantics not visuals and then be compiler to a classical visual representation (maybe using some additional non-semantic style annotation block).
A friend of mine works with a professor that defines:
\be -> \begin{equation}, \ee -> \end{equation}, \ga -> \gamma, \gm -> \gamma, \s -> \section, and so on
Personally I think that latex should produce pdf documents with better mappings so that copy-paste and latex-paragraphs are preserved, even if obviously it will still get messed up in complex layouts
I am using the former for some personal documents and found that it improves text selection and copying on Apple devices. (This could be related to how PDFKit handles text.)
If you want accessibility, it would be better to convert your content to XML and run the LaTeX through MathJax first, using accessibility extensions (https://mathjax.github.io/MathJax-a11y/docs/). Then use a third-party converter such as PrinceXML to generate the PDF from the XML.
One pattern I like to use is to write my documents using markdown which can be compiled into pdf via latex with a template of my choosing. It is also capable of compiling to other formats which may be more accessible such as plain text, html and docx.
Why must the PDF encapsulate all requirements? My understanding of accessibility requirements it that you must have a version that is amenable to automatic speech, not that all versions must be.
It doesn't have to. But ideally you only want to have to produce and distribute a single file.
Also, a lot of people don't consider accessibility when generating PDFs. If LaTeX produced accessible PDFs, the PDFs would be tagged automatically without the author even thinking about it. Of course, it might still not be perfect, but it would be a lot better than the status quo.
2. Even by 2016, pdfTeX had been largely superseded by LuaTeX.
3. The author bizzarely links to "the mess" of the literate source of TeX the program as a WEB file rather than as a typeset document.
4. AIUI, the source code of the TeX engine has nothing/very little to do with adding tags to PDFs, which it is the job for LaTeX packages. Admittedly, understanding and writing their source code is a rarer skill than reading the literate source of TeX.
The overwhelming majority of people writing today use pdflatex. But at this point lualatex is pretty fast, and is starting to accumlate packages that leverage it to do good things. It is starting to build momentum.
MathML isn't dead! Igalia have been doing some pretty great work on getting it upstreamed into Chromium, where there has been no MathML implementation (in contrast to Firefox) for some time.
I had never learned Pascal but I've managed to edit and compile TeX successfully, and it was easier than trying to understand any of my own non-literate programs.
>My point being that if we wouldn’t rely on TeX itself and use ANT (or whatever alternative) which is written in the quite elegant OCaml, than hacking it would be at least possible for mere mortals. Although I have to admit, despite being in love with OCaml since my PhD days, it’s also a quite niche language. But imagine if the whole thing was written in Python, or at least C.
Imagine if software engineers were actual engineers instead of glorified script kiddies.
>I wish someone would design a new space shuttle because while it's a neat project I only understand MKS units and it's too much effort to use a calculator for converting between them and Imperial units.
It does seem that the OP constructs a bit of a strawman by claiming TeX's source code is too complicated for an average computer science graduate. I doubt even the top 5% of computer graduates could more readily understand the source code of most common programs.
Well, Knuth's programming style is idiosyncratic, to say the least. But in the early 80s, in advance of the publication of The TeXBook, I learned enough TeX from reading the literate source for TeX to put together a 100-page software manual.
I don't really agree with Knuth's version of literate programming, but one can hardly fault the TeX source for being unreadable.
We're not talking about the difficulty of writing a document using LaTeX, which I think we can agree is more or less proportional to the degree of control one has over the finished product.
What's at stake here is the difficulty of editing the source code of LaTeX, which would be necessary in order to make the resulting pdf files more compatible with screen readers for the visually impaired.
Back in the day we had engineers writing documents from markup. We called them typesetters. It was a qualified job, you don't expect the task to be something Joe Random could to with 6 weeks of training.
> Back in the day we had engineers writing documents from markup.
Back in the day secretaries were creating electronic documents with troff and nroff:
> The first version of Unix was developed on a PDP-7 which was sitting around Bell Labs. In 1971 the developers wanted to get a PDP-11 for further work on the operating system. In order to justify the cost for this system, they proposed that they would implement a document-formatting system for the Bell Labs patents department[1]. This first formatting program was a reimplementation of McIllroy's roff, written by Joe F. Ossanna.
The problem with maths notation is that it was invented by sighted people for sighted people as a short hand for very complex ideas, which at the time weren't fully understood.
If you want to type equations use s-expressions, the clarity you get from saying what you mean is astonishing.
(define integral
(lambda (function)
;; Implementation of Risch algorithm left
;; as an exercise to the motivated reader.
))
(define definite-integral
(lambda (lower-bound upper-bound function)
(let ((anti-derivative (integral function)))
(- (anti-derivative upper-bound)
(anti-derivative lower-bound)))))
Hey look, you don't need the dummy variable explicitly any more. It's almost like it's a relic from a time before people understood what function application actually was.
If you want the implicit mess (and incredible power) of higher maths, be prepared to deal with the the mess of typography. Which is why you need TeX, or worse.
> Hey look, you don't need the dummy variable explicitly any more. It's almost like it's a relic from a time before people understood what function application actually was.
If you actually perform definite integration, as a limit of Riemann (or Lebesgue, if you like) sums, or even try to approximate it numerically, you're going to have some dummy variable cropping back up again. As your comment indicates, when Risch's theorem proves that there is no elementary anti-derivative, you're going to be out of luck.
You're skimping on some of the complexity by equating a definition with a particular way of computing it, but that's completely inadequate for mathematics, as there are many things we can't compute (either in theory or in practice).
In particular, you definition of integral assumes that integrable functions always have an antiderivative, which is wrong.
I find it odd that you pretend a meta-mathematical question is a mathematical one.
You are dismissing constructivism as not mathematics, and you ignore that the halting problem is a way to deal with a class of results which include non-existence proofs by running an algorithm forever.
I can easily create calculations that will never return results which classical mathematics say are impossible by the simple fact they never return any results at all.
The Risch algorithm being a complex example, finding the square root of two in the rational number domain being a simple one. I can still deal with them as though they return results in all calculations though, without the need for baroque semi-mystical notation. Unless you want to claim some sort of divine human essence not present in Turing Machines and Lambda Calculus which lets us transcend their computational capabilities?
I literally don't understand what the hell you are talking about.
But this has nothing to do with constructivism. Even if you only allow constructive definitions and proofs, there is still the world of a difference between the definition of an integral and the result you get from evaluating it.
Yeah, sure, in theory you can represent an integral as a function that takes another function and two boundary points and returns a value...
But first, it may not be possible to determine the value of the integral exactly because there is no known method of doing so (the Risch algorithm, apart from it basically being so complex that it's implemented almost nowhere fully, only works for elementary functions!).
And second, if integrals are "just functions", you lose the ability to manipulate them according to known theorems, e.g. additivity, triangle inequality, Cauchy-Schwarz, convergence theorems, ...
So yeah, here's where I get the feeling that some people should do some more maths and spend good parts of their days proving theorems and playing with definitions before they start complaining about how dumb its language is.
> In particular, you definition of integral assumes that integrable functions always have an antiderivative, which is wrong.
I was objecting at the same time as you were, but I don't think this is the right objection. It's true that not every integrable function has an elementary anti-derivative, but every integrable function f does have an anti-derivative F, at least in the sense that F is almost everywhere differentiable, and the derivative is almost everywhere equal to f. (And, of course, if f is continuous, then F is everywhere differentiable, and its derivative everywhere equals f.)
If you say "at least in the sense that F is almost everywhere differentiable", you're already redefining "anti-derivative" to some extent, I feel. But this is just arguing over semantics. Even then, I think your claim that every integrable function has a "generalized antiderivative" is also only true for the Riemann integral. The Dirichlet function is Lebesgue integrable, but it doesn't have an antiderivative even in this weaker sense.[^1] And mathematicians generally prefer the Lebesgue integral.
I think the more important insight here is that integration fundamentally isn't defined through the anti-derivative, and that the two notions are actually related is a deep theorem, rather than just a definition.
And the fact that non-elementary antiderivatives exist is interesting in theory, but in practice you can't use them directly for anything. In particular, in practical situations you will often use numerical methods to integrate a function which will not be based on any notion of anti-derivative at all.
[^1] Edit: I think I was wrong here. If you take the function identically zero, then its derivative is identically zero and as such equal to the Dirichlet function almost everywhere. So this is not a counterexample. I still think it's weird to call than an "antiderivative" though.
It wasn’t because mathematicians were reluctant to change that math in HTML didn't take off. Rather, it was because browser developers were loathe to implement and maintain the enormous and complex pile of code that is MathML, and they said "Why should we, if you mathematicians already have LaTeX?" [0]
Firefox has had MathML support for a long time. Complain to Apple and Google (and vote with your browsing activity, by using the browser that is less driven by commercial considerations).
Believe it or not, HTML, CSS, and MathML are still going pretty strong in the educational publishing industry.
MathType supports TeX input. MathJax accepts TeX input. The technology is already there, there's just very little mindshare because no one cares about accessibility.
I had a realization a while back, that in my opinion LaTeX isnt really needed anymore. Pretty much anything you can do with LaTeX, you can do with HTML. Want a PDF? Most browsers will print to PDF now, or you can use a library like this:
> I had a realization a while back, that in my opinion LaTeX isnt really needed anymore
Am I correct in assuming that you are not working in academia/on research? In that case, I would argue that from your point of view latex was never needed. On the other hand, if you are working on math/cs/physics research latex is indispensable...
Not even considering the math formatting, Html is still lacking good footnotes, bibliographies, glossary generation, index generation, and table of context generation. Browsers also render things atrociously compared to a latex pdf.
> There are third-party tools that do all of this.
The things that today do this will be all gone in ten years, or replaced with other things that will in turn be replaced ... LaTeX has been here for a long time, and has been strikingly stable.
I wrote my bachelor thesis in markdown with inline mathtex(?) and compiler it from there with pandoc.
I also tried from/to HTML and the result is just bad. HTML isn't suited at all to write scientific documents with proper formatting.
Also I still need to do some things directly in latex and include them with inline latex in markdown.
So no HTML+CSS isn't suited for this at all.
At least for now where scientific papers are still DIN A4 real paper based/targeting.
Maybe it's time to change that. People read papers a lot in 24" Monitors, tablets, laptops and e-book readers for all of this the current formatting sucks.
You can definitely generate good scientific PDFs from HTML and CSS, combined with tools to generate SVGs from your LaTeX/MathML. I've converted a fair number of textbooks from print to high quality digital and print hybrid PDFs.
The learning curve is pretty high though. If you're not a web developer already, there are better options out there.
No need for (much) CSS, browsers already support vector graphics: SVG!
In Pandoc, what you would do is you would use a general Latex plugin, and then TikZ supports PNG or SVG output by 'standalone' (https://tex.stackexchange.com/questions/51757/how-can-i-use-...), and you can either save that to a file & use as an image or you can inline them.
This uses Latex at compile-time, but considering the extent to which TikZ is a graphics DSL, I wonder how hard it would be to implement a TikZ->SVG compiler as a standalone tool in a different language? (Or make it available in a variant like Mathjax? Like https://github.com/kisonecat/tikzjax except without running an entire TeX engine in the user's browser.)
Well, LaTeX is great for mathematical symbols. I have not seen a typesetting in the web space that can compare itself to LaTeX. This is why scientists from the exact sciences use it.
MathJax is routinely used for inserting equations into HTML documents [0]. A side benefit is that it uses LaTeX-like syntax for defining equations.
Static site generators like Sphinx, Hugo, and Jekyll have support for MathJax which allows for inline equations in Markdown/RsT docs. See a Sphinx example here [1].
There is no good reason to put the accessibility into the type setting. Instead, use a declarative (e.g., any markup) language, translate that a) to (LaTeX) and b) to accessibility annotations and then combine the two results. Problem solved.
Unfortunately you will either lose a lot of expressiveness along the way or you have to find a very sophisticated markup language.