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Lambda Operator in LaTeX

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Re: Lambda Operator in LaTeX

#11

Post by zauguin »

You don't have to define `\First` and `\Second` since these are predefined as `\@firstoftwo` and `\@secondoftwo`. Also the Unicode bytes are already active so setting their catcode is useless. Also redefining the first octet breaks LaTeX's UTF-8 handling and the else case forms an infinite loop. Changing the catcodes of `(` and `)` means that this command doesn't work in the arguments of other commands and it breaks other uses of `(` and `)` in the argument.

Instead you could do this as

  \documentclass{article}
  \usepackage{xparse}

  \NewDocumentCommand \LambdaCalc {u{.} r()} {%
    [arg:(#1) body:(#2)]
  }
  \DeclareUnicodeCharacter {03BB} {\LambdaCalc}

  \begin{document}

  λx.(2x)

  \end{document}

Re: Lambda Operator in LaTeX

#12

Post by c7b »

Sums up the LaTeX experience quite well imho:

> LaTeX is great for typesetting math.

Q: Ok, great! So how do I typeset this bit of common math?

A: a 20-line barrage of import statements, makeatletter's and definitions that you copy-paste into your preamble and cross your fingers that it won't conflict with the half-dozen other barrages that you copied there to do other bits of common math, often hidden between other Google results with wildly different answers.

Re: Lambda Operator in LaTeX

#14

Post by bradrn »

c7b wrote: post #12

Sums up the LaTeX experience quite well imho: > LaTeX is great for typesetting math. Q: Ok, great! So how do I typeset this bit of common math? A: a 20-line barrage of import statements, makeatletter's and definitions that you copy-paste into your preamble and cross your fingers that it won't conflict with the half-dozen other barrages that you copied there to do other bits of common math, often hidden between other…

I tend to disagree with this. In my experience most common constructs are supported pretty well, especially for maths. The complex stuff comes when you want to do slightly less common stuff — like, for instance, turning the character ‘λ’ into a command for custom typesetting of lambda expressions (as in the article).

Re: Lambda Operator in LaTeX

#15

Post by todd8 »

slavapestov wrote: post #10
bradrn wrote: post #7

Earlier quoted context omitted.

> There are very few bits of software that are more arcane and broken by default than this absolute crapstraction of a platform. And that is exactly why a more programmable platform would be good! These issues arise in the first place largely because TeX is not easily programmable, so people have to find arcane workarounds to do anything complex in it.

The weirdness is totally expected for something originally designed in 1983. What is unexpected is that there is still no good replacement for writing math…

LaTeX and Emacs share a feature, they are both contain a core written in a low level language (For TeX it was Pascal originally, and for Emacs it is C). Anticipating the need for extensions, both systems are open source and include user programmability, a powerful macro based programming language for TeX and a fully integrated Lisp system in Emacs.

This has allowed both to grow in functionality, year after year. Code written by users wanting particular capabilities has led to so many fantastic enhancements. No one user or committee could anticipate the many ways that these programs could be extended. Although, it would be nice if these systems could be cleaned up and modernized, this is only a dream. In practice, nobody has the time to start over on these enormous bodies of work comprising millions of lines of code.

It's too bad, because it's a joy to use ether of these system once you've spent enough time reading their extensive documentation and puttered around with them for a few years, but their eccentricities and anachronisms keep them out of the hands of many users.

Re: Lambda Operator in LaTeX

#16

Post by svat »

c7b wrote: post #12

Sums up the LaTeX experience quite well imho: > LaTeX is great for typesetting math. Q: Ok, great! So how do I typeset this bit of common math? A: a 20-line barrage of import statements, makeatletter's and definitions that you copy-paste into your preamble and cross your fingers that it won't conflict with the half-dozen other barrages that you copied there to do other bits of common math, often hidden between other…

I'll agree that not the posted article but your comment does sum up the way many users experience LaTeX (without taking a few minutes to understand what's going on), and it's interesting to think about what factors of TeX/LaTeX and its documentation/ecosystem lead to this outcome.

About the posted article: if all one wanted to do was "typeset this bit of common math", one can just type "\lambda x.(2x)" in math mode. Or, if not constrained to keep it old school i.e. pdfTeX, use XeTeX/LuaTeX with \usepackage{unicode-math}, to type "λ x.(2x)" directly.

The posted article is actually about doing some parsing using TeX, namely the author wants to type "λ x.(2x)" into their .tex file and have it be parsed into, say, [arg:(x) body:(2x)] to be used later for whatever they're building. This is not related to typesetting at all, so why do they want to do such a thing in TeX, instead of doing it outside and using TeX just for typesetting? The motivation seems to be, as their footnote 2 indicates, that some people just enjoy being perverse. That's fine!

Even there, if you compare the author's approach with that in the comment here https://news.ycombinator.com/item?id=33296527 (by someone who knows what they're doing; cf. https://www.latex-project.org/about/team/), you'll see how the "right" way is less forbidding-looking, and also less breakage-prone. What's going on is that the author has just learned something new (how Unicode is handled in pdfTeX even though it only works with 8-bit bytes), become excited at the possibilities, and hacked their own solution using the primitives, without bothering to integrate with the broader ecosystem of other packages and conventions — which is also fine; TeX will let you do that and not get in the way.

The real interesting question raised by your comment IMO is not at all about the posted article but about experiences such as those in your comment: I can easily imagine many people doing what you did (not understanding the context, and possibly even copying ad-hoc code like this into one's document and crossing one's fingers): here we start to get into the actual problems with the LaTeX ecosystem and the mismatch between users' mental models and that of the (too many!) pieces of software involved, but I've exceeded the time limit I set to comment here so I'll stop :)

Re: Lambda Operator in LaTeX

#17

Post by svat »

slavapestov wrote: post #10
bradrn wrote: post #7

Earlier quoted context omitted.

> There are very few bits of software that are more arcane and broken by default than this absolute crapstraction of a platform. And that is exactly why a more programmable platform would be good! These issues arise in the first place largely because TeX is not easily programmable, so people have to find arcane workarounds to do anything complex in it.

The weirdness is totally expected for something originally designed in 1983. What is unexpected is that there is still no good replacement for writing math…

TeX was designed even earlier (in 1977), and most of the weirdness is from people trying to do things inside TeX — the actual "writing math" part is still mostly fine. (E.g. people don't run into much of the weirdness when using MathJax/KaTeX, which are reimplementations of just the typical math typesetting concerns.)

My understanding, from reading some of the history, is that in the early 1980s when Lamport wrote the set of TeX macros that became LaTeX, already TeX had spread like wildfire among math/CS departments, and it so happened that TeX itself was a more widely available and reliable (see "trip test") programming "language"/platform than any actual programming language. (This was when C was yet to become available outside of a handful of labs and universities, and what most people had was a variety of mediocre Pascal compilers that supported differing sets of Pascal and extensions, which is why Knuth wrote TeX in a very tiny subset of Pascal extended with his own preprocessing system (WEB/tangle/weave) — and still it is said that compiling and testing TeX uncovered at least one bug in every Pascal compiler encountered.)

So at that time, it made sense to "do everything in TeX", and LaTeX's approach of hiding a lot of insane macro-hell complexity behind innocent-looking boxes, an approach since taken up by zillions of "packages" of varying quality, leads us to the situation we're in today.

But there's hope: with LuaTeX inside the TeX world, and things like markdown/pandoc outside of it, people are slowly beginning to get used to doing the programming part in an actual programming language (Lua or whatever), and using TeX merely for typesetting, in which area it is still good / a reasonable and not-too-weird piece of software.

Re: Lambda Operator in LaTeX

#18

Post by miguelmurca »

zauguin wrote: post #11

You don't have to define `\First` and `\Second` since these are predefined as `\@firstoftwo` and `\@secondoftwo`. Also the Unicode bytes are already active so setting their catcode is useless. Also redefining the first octet breaks LaTeX's UTF-8 handling and the else case forms an infinite loop. Changing the catcodes of `(` and `)` means that this command doesn't work in the arguments of other commands and it breaks…

Thanks, and ouch. I have some follow-up questions/comments, if you have the time:

> these are predefined as `\@firstoftwo` and `\@secondoftwo`

I do wish LaTeX kernel commands (which I'm assuming these are) were more widely documented. As it stands, it's pretty hard to keep track of what already exists. Is there a nice reference for those?

> Also the Unicode bytes are already active so setting their catcode is useless.

This is true for LaTeX and not TeX, correct? Originally, I'd `\expandafter\let\expandafter\@firstoct\@firstoftwoλ`, but I decided not to assume that that character was already active.

> Also redefining the first octet breaks LaTeX's UTF-8 handling...

How so? (If the else case wasn't broken)

>...and the else case forms an infinite loop.

If `\Firstλ` was not an active character, would this still be true? Since I store `\Firstλ` in `\lambda@first@oct` before it's declared an active character.

> and it breaks other uses of `(` and `)` in the argument.

This is not a concern for the DSL, but...

> Changing the catcodes of `(` and `)` means that this command doesn't work in the arguments of other commands

...this is. Thanks.

> Instead you could do this as

Damn :)

Thanks for the nice feedback. I suppose I should read up on xparse. In any case I feel like it's not moot to try to achieve the same results with primitives, to have some idea of what's breaking when a given program doesn't compile (usually at that point the primitives surface).

Re: Lambda Operator in LaTeX

#19

Post by dhosek »

jcelerier wrote: post #8
titzer wrote: post #5

Having spent most of the day stepping on LaTeX rakes, I am really at a loss how anyone could think that making it more programmable would think that's a good idea. There are very few bits of software that are more arcane and broken by default than this absolute crapstraction of a platform.

wish granted, advanced LaTeX macro programming will now have to be done in ksh

I’ve occasionally contemplated the idea of creating a TeXasm target that one could compile programs in higher-level languages to. Then, one could bootstrap a C compiler that compiles to TeX and runs in TeX.

Re: Lambda Operator in LaTeX

#20

Post by miguelmurca »

svat wrote: post #16
c7b wrote: post #12

Sums up the LaTeX experience quite well imho: > LaTeX is great for typesetting math. Q: Ok, great! So how do I typeset this bit of common math? A: a 20-line barrage of import statements, makeatletter's and definitions that you copy-paste into your preamble and cross your fingers that it won't conflict with the half-dozen other barrages that you copied there to do other bits of common math, often hidden between other…

I'll agree that not the posted article but your comment does sum up the way many users experience LaTeX (without taking a few minutes to understand what's going on), and it's interesting to think about what factors of TeX/LaTeX and its documentation/ecosystem lead to this outcome. About the posted article: if all one wanted to do was "typeset this bit of common math", one can just type "\lambda x.(2x)" in math mode.…

It's true, I do enjoy being perverse. However, I think it's a bit unfair to say I have "picked up a few pieces of knowledge, become excited, and tried to hack their way through by themselves, without understanding the broader ecosystem of other packages and conventions". I'm aware of xparse, and other tools in the ecosystem (etoolbox, ifthenelse). This doesn't mean that I shouldn't try to get a given result with the provided primitives, rather than use an existing codebase. Very analogous to writing your own X programming lib rather than using an existing one: good for experimenting and learning, but maybe not something you should go for in production. (Of course, I'm certainly not at the level of a LaTeX team member.)
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