What is (*>*) in Isabelle? - symbols

I have downloaded several .thy files in Isabelle that use (*<*) and (*>*).They seem to have no effect as far as I can tell, but they must have a purpose. Does anyone know what they are used for?

The special comments (*<*) and (*>*) tell the document preparation system of Isabelle to not include the enclosed theory text in the generated PDF documents. They are the predecessors of the more structured tags like %invisible, which also control what appears in the generated documents. For example,
lemma %invisible silly: "0 = 0" by simp
and
(*<*)
lemma silly: "0 = 0" by simp
(*>*)
have roughly the same effect, namely the whole lemma and its proof will not show up in the document. However, tags can only be attached to top-level commands like definition, lemma, proof, by. Hence, you cannot hide just parts of a command like in
by(simp add: take_map(*<*) drop_map(*>*))
which will yield by(simp add: take_map) in the PDF, i.e., the drop_map is omitted.

Related

How to properly do custom markdown markup

I currently work on a personal writing project which has ended up with me maintaining a few different versions due to the differences of the relevant platforms and output formats I want to support that are not trivially solved. After several instances of me glancing at pandoc and the sheer forest that it represents, I have concluded mere templates don't do what I need, and worse, that I seem to need a combination of a custom filter and writer... suffice to say: messing with the AST is where I feel way out of my depth. Enough so that, rather than asking specific questions of 'how do I do X' here, this is a question of 'is X the right way to go about it, or what is the proper way to do it, and can you give an example of how it ties together?'... so if this question is rather lengthy: my apologies.
My current goal is to have custom markup like the following which is supposed to 'track' which character says something:
<paul|"Hi there">
If I convert to HTML, I'd want something similar to:
<span class="speech paul">"Hi there"</span>
to pop out (and perhaps the <p> tags), whereas if it is just pure markdown / plain text, I'd want it to silently disappear:
"Hi there"
Looking at the JSON AST structures I've studied, it would make sense that I'd want a new structure type similar to the 'Emph' tag called 'Speech' which allows whole blobs of text to be put inside of it with a bit of extra information attached (the person speaking). So something like this:
{"t":"Speech","speaker":"paul","c":[ ... ] }
Problem #1: At the point a lua-filter sees the document, it is obviously already distilled to an AST. This means replacing the items in a manner similar to what most macro expander samples do cannot really work since it would require reading forward. With this method, I just replace bits and pieces in place (<NAME| becomes a StartSpeech and the first solitary > that follows becomes an EndSpeech, but that would make malformed input a bigger potential problem because of silent-ish failures. Additionally, these tags would be completely out of sorts with how an AST is supposed to look.
To complicate matters even further, some of my characters end up learning a secondary language throughout the story, for which I apply a different format that contains a simplified understanding of the spoken text with perspective-characters understanding of what was said. Example:
<paul|"Heb je goed geslapen?"|"Did you ?????">
I could probably add a third 'UnderstoodSpeech' group to my filter, but (problem #2) at this point, the relationship between the speaker, the original speech, and the understood translation is completely gone. As long as the final documents need these values in these respective orders and only in these orders, it is fine... but what if I want my HTML version to look like
"Did you?????"
with a tool-tip / hover-over effect containing the original speech? That would be near impossible to achieve because the AST does not contain that kind of relational detail.
Whatever kind of AST I create in the filter is what I need to understand in my custom writer. Ideally, I want to re-use as much stock functionality of pandoc as possible for the writer, but I don't even know if that is feasible at this point.
So now my question: could someone with great pandoc understanding please give me an example on how to keep relevant data-bits together and apply them in the correct manner? By this I mean show a basic example of what needs to be put in the lua-filter and lua-writer scripts in the following toolchain
[CUSTOMIZED MARKDOWN INPUT] -> lua-filter -> lua-writer -> [CUSTOMIZED HTML5 OUTPUT]

Is Pug context free?

I was thinking to make a Pug parser but besides the indents are well-known to be context-sensitive (that can be trivially hacked with a lexer feedback loop to make it almost context-free which is adopted by Python), what otherwise makes it not context-free?
XML tags are definitely not context-free, that each starting tag needs to match an end tag, but Pug does not have such restriction, that makes me wonder if we could just parse each starting identifier as a production for a tag root.
The main thing that Pug seems to be missing, at least from a casual scan of its website, is a formal description of its syntax. Or even an informal description. Perhaps I wasn't looking in right places.
Still, based on the examples, it doesn't look awful. There will be some challenges; in particular, it does not have a uniform tokenisation context, so the scanner is going to be complicated, not just because of the indentation issue. (I got the impression from the section on whitespace that the indentation rule is much stricter than Python's, but I didn't find a specification of what it is exactly. It appeared to me that leading whitespace after the two-character indent is significant whitespace. But that doesn't complicate things much; it might even simplify the task.)
What will prove interesting is handling embedded JavaScript. You will at least need to tokenise the embedded JS, and the corner cases in the JS spec make it non-trivial to tokenise without parsing. Anyway, just tokenising isn't sufficient to know where the embedded code terminates. (For the lexical challenge, consider the correct identification of regular expression literals. /= might be the start of a regex or it might be a divide-and-assign operator; how a subsequent { is tokenised will depend on that decision.) Template strings present another challenge (recursive embedding). However, JavaScript parsers do exist, so you might be able to leverage one.
In other words, recognising tag nesting is not going to be the most challenging part of your project. Once you've identified that a given token is a tag, the nesting part is trivial (and context-free) because it is precisely defined by the indentation, so a DEDENT token will terminate the tag.
However, it is worth noting that tag parsing is not particularly challenging for XML (or XML-like HTML variants). If you adopt the XML rule that close tags cannot be omitted (except for self-closing tags), then the tagname in a close tag does not influence the parse of a correct input. (If the tagname in the close tag does not match the close tag in the corresponding open tag, then the input is invalid. But the correspondence between open and close tags doesn't change.) Even if you adopt the HTML-5 rule that close tags cannot be omitted except in the case of a finite list of special-case tagnames, then you could theoretically do the parse with a CFG. (However, the various error recovery rules in HTML-5 are far from context free, so that would only work for input which did not require rematching of close tags.)
Ira Baxter makes precisely this point in the cross-linked post he references in a comment: you can often implement context-sensitive aspects of a language by ignoring them during the parse and detecting them in a subsequent analysis, or even in a semantic predicate during the parse. Correct matching of open- and close tagnames would fall into this category, as would the "declare-before-use" rule in languages where the declaration of an identifier does not influence the parse. (Not true of C or C++, but true in many other languages.)
Even if these aspects cannot be ignored -- as with C typedefs, for example -- the simplest solution might be to use an ambiguous CFG and a parsing technology which produces all possible parses. After the parse forest is generated, you could walk the alternatives and reject the ones which are inconsistent. (In the case of C, that would include an alternative parse in which a name was typedef'd and then used in a context where a typename is not valid.)

CommonMark Parsing ***

Let's say I want to parse the string ***cat*** into Markdown using the CommonMark standard. The standard says (http://spec.commonmark.org/0.28/#phase-2-inline-structure):
....
If one is found:
Figure out whether we have emphasis or strong emphasis: if both closer
and opener spans have length >= 2, we have strong, otherwise regular.
Insert an emph or strong emph node accordingly, after the text node
corresponding to the opener.
Remove any delimiters between the opener and closer from the delimiter
stack.
Remove 1 (for regular emph) or 2 (for strong emph) delimiters from the
opening and closing text nodes. If they become empty as a result,
remove them and remove the corresponding element of the delimiter
stack. If the closing node is removed, reset current_position to the
next element in the stack.
....
Based on my reading of this the result should be <em><strong>cat</strong></em> since first the <strong> is added, THEN the <em>. However, all online markdown editors I have tried this in output <strong><em>cat</em></strong>. What am I missing?
Here is a visual representation of what I think should be happening
TextNode[***] TextNode[cat] TextNode[***]
TextNode[*] StrongEmphasis TextNode[cat] TextNode[*]
TextNode[] Emphasis StrongEmphasis TextNode[cat] TextNode[]
Emphasis StrongEmphasis TextNode[cat]
It's important to remember that Commonmark and Markdown are not necessarily the same thing. Commonmark is a recent variant of Markdown. Most Markdown parsers existed and established their behavior long before the Commonmark spec was even started.
While the original Markdown rules make no comment on whether the <em> or <strong> tag should be first in the given example, the reference implementation's (markdown.pl) actual behavior was to list the <strong> tag before the <em> tag in the output. In fact, the MarkdownTest package, which was created by the author of Markdown and markdown.pl) explicitly required that output (the original is no longer available online that I know of, but mdtest is a faithful copy with its history showing no modifications of that test since the initial import from MarkdownTest). AFAICT, every (non-Commonmark) Markdown parser has followed that behavior exactly.
The Commonmark spec took a different route. The spec specifically states in Rule 14 of Section 6.4 (Emphasis and strong emphasis):
An interpretation <em><strong>...</strong></em> is always preferred to <strong><em>...</em></strong>.
... and backs it up with example 444:
***foo***
<p><em><strong>foo</strong></em></p>
In fact, you can see that that is exactly the behavior of the reference implementation of Commonmark.
As an aside, the original question quotes from the Appendix to the spec which recommends how to implement a parser. While potentially useful to a parser creator, I would not recommend using that section to determine proper syntax handling and/or output. The actual rules should be consulted instead; and in fact, they clearly provide the expected output in this instance. But this question is about an apparent disparity between implementations and the spec, not interpretation of the spec.
For a more complete comparison, see Babelmark. With the exception of a few (completely) broken implementations, every "classic" Markdown parser follows markdown.pl, while every Commonmark parser follows the Commonmark spec. Therefore, there is no actual disparity between the spec and implementations. The disparity is between Markdown and Commonmark.
As for why the Commonmark authors chose a different route in this regard, or why they insist on calling Commonmark "Markdown" when it is clearly different are off topic here and better asked of the authors themselves.

Extracting from .bib file with Raku (previously aka Perl 6)

I have this .bib file for reference management while writing my thesis in LaTeX:
#article{garg2017patch,
title={Patch testing in patients with suspected cosmetic dermatitis: A retrospective study},
author={Garg, Taru and Agarwal, Soumya and Chander, Ram and Singh, Aashim and Yadav, Pravesh},
journal={Journal of Cosmetic Dermatology},
year={2017},
publisher={Wiley Online Library}
}
#article{hauso2008neuroendocrine,
title={Neuroendocrine tumor epidemiology},
author={Hauso, Oyvind and Gustafsson, Bjorn I and Kidd, Mark and Waldum, Helge L and Drozdov, Ignat and Chan, Anthony KC and Modlin, Irvin M},
journal={Cancer},
volume={113},
number={10},
pages={2655--2664},
year={2008},
publisher={Wiley Online Library}
}
#article{siperstein1997laparoscopic,
title={Laparoscopic thermal ablation of hepatic neuroendocrine tumor metastases},
author={Siperstein, Allan E and Rogers, Stanley J and Hansen, Paul D and Gitomirsky, Alexis},
journal={Surgery},
volume={122},
number={6},
pages={1147--1155},
year={1997},
publisher={Elsevier}
}
If anyone wants to know what bib file is, you can find it detailed here.
I'd like to parse this with Perl 6 to extract the key along with the title like this:
garg2017patch: Patch testing in patients with suspected cosmetic dermatitis: A retrospective study
hauso2008neuroendocrine: Neuroendocrine tumor epidemiology
siperstein1997laparoscopic: Laparoscopic thermal ablation of hepatic neuroendocrine tumor metastases
Can you please help me to do this, maybe in two ways:
Using basic Perl 6
Using a Perl 6 Grammar
TL;DR
A complete and detailed answer that does just exactly as #Suman asks.
An introductory general answer to "I want to parse X. Can anyone help?"
A one-liner in a shell
I'll start with terse code that's perfect for some scenarios[1], and which someone might write if they're familiar with shell and Raku basics and in a hurry:
> raku -e 'for slurp() ~~ m:g / "#article\{" (<-[,]>+) \, \s+
"title=\{" (<-[}]>+) \} / -> $/ { put "$0: $1\n" }' < derm.bib
This produces precisely the output you specified:
garg2017patch: Patch testing in patients with suspected cosmetic dermatitis: A retrospective study
hauso2008neuroendocrine: Neuroendocrine tumor epidemiology
siperstein1997laparoscopic: Laparoscopic thermal ablation of hepatic neuroendocrine tumor metastases
Same single statement, but in a script
Skipping shell escapes and adding:
Whitespace.
Comments.
► use tio.run to run the code below
for slurp() # "slurp" (read all of) stdin and then
~~ m :global # match it "globally" (all matches) against
/ '#article{' (<-[,]>+) ',' \s+ # a "nextgen regex" that uses (`(...)`) to
'title={' (<-[}]>+) '}' / # capture the article id and title and then
-> $/ { put "$0: $1\n" } # for each article, print "article id: title".
Don't worry if the above still seems like pure gobbledygook. Later sections explain the above while also introducing code that's more general, clean, and readable.[2]
Four statements instead of one
my \input = slurp;
my \pattern = rule { '#article{' ( <-[,]>+ ) ','
'title={' ( <-[}]>+ ) }
my \articles = input .match: pattern, :global;
for articles -> $/ { put "$0: $1\n" }
my declares a lexical variable. Raku supports sigils at the start of variable names. But it also allows devs to "slash them out" as I have done.
my \pattern ...
my \pattern = rule { '#article{' ( <-[,]>+ ) ','
'title={' ( <-[}]>+ ) }
I've switched the pattern syntax from / ... / in the original one-liner to rule { ... }. I did this to:
Eliminate the risk of pathological backtracking
Classic regexes risk pathological backtracking. That's fine if you can just kill a program that's gone wild, but click the link to read how bad it can get! 🤪 We don't need backtracking to match the .bib format.
Communicate that the pattern is a rule
If you write a good deal of pattern matching code, you'll frequently want to use rule { ... }. A rule eliminates any risk of the classic regex problem just described (pathological backtracking), and has another superpower. I'll cover both aspects below, after first introducing the adverbs corresponding to those superpowers.
Raku regexes/rules can be (often are) used with "adverbs". These are convenient shortcuts that modify how patterns are applied.
I've already used an adverb in the earlier versions of this code. The "global" adverb (specified using :global or its shorthand alias :g) directs the matching engine to consume all of the input, generating a list of as many matches as it contains, instead of returning just the first match.
While there are shorthand aliases for adverbs, some are used so repeatedly that it's a lot tidier to bundle them up into distinct rule declarators. That's why I've used rule. It bundles up two adverbs appropriate for matching many data formats like .bib files:
:ratchet (alias :r)
:sigspace (alias :s)
Ratcheting (:r / :ratchet) tells the compiler that when an "atom" (a sub-pattern in a rule that is treated as one unit) has matched, there can be no going back on that. If an atom further on in the pattern in the same rule fails, then the whole rule immediately fails.
This eliminates any risk of the "pathological backtracking" discussed earlier.
Significant space handling (:s / :sigspace) tells the compiler that an atom followed by literal spacing that is in the pattern indicates that a "token" boundary pattern, aka ws should be appended to the atom.
Thus this adverb deals with tokenizing. Did you spot that I'd dropped the \s+ from the pattern compared to the original one in the one-liner? That's because :sigspace, which use of rule implies, takes care of that automatically:
say 'x#y x # y' ~~ m:g:s /x\#y/; # (「x#y」) <-- only one match
say 'x#y x # y' ~~ m:g /x \# y/; # (「x#y」) <-- only one match
say 'x#y x # y' ~~ m:g:s /x \# y/; # (「x#y」 「x # y」) <-- two matches
You might wonder why I've reverted to using / ... / to show these two examples. Turns out that while you can use rule { ... } with the .match method (described in the next section), you can't use rule with m. No problem; I just used :s instead to get the desired effect. (I didn't bother to use :r for ratcheting because it makes no difference for this pattern/input.)
To round out this dive into the difference between classic regexes (which can also be written regex { ... }) and rule rules, let me mention the other main option: token. The token declarator implies the :ratchet adverb, but not the :sigspace one. So it also eliminates the pathological backtracking risk of a regex (or / ... /) but, just like a regex, and unlike a rule, a token ignores whitespace used by a dev in writing out the rule's pattern.
my \articles = input .match: pattern, :global
This line uses the method form (.match) of the m routine used in the one-liner solution.
The result of a match when :global is used is a list of Match objects rather than just one. In this case we'll get three, corresponding to the three articles in the input file.
for articles -> $/ { put "$0: $1\n" }
This for statement successively binds a Match object corresponding to each of the three articles in your sample file to the symbol $/ inside the code block ({ ... }).
Per Raku doc on $/, "$/ is the match variable, so it usually contains objects of type Match.". It also provides some other conveniences; we take advantage of one of these conveniences related to numbered captures:
The pattern that was matched earlier contained two pairs of parentheses;
The overall Match object ($/) provides access to these two Positional captures via Positional subscripting (postfix []), so within the for's block, $/[0] and $/[1] provide access to the two Positional captures for each article;
Raku aliases $0 to $/[0] (and so on) for convenience, so most devs use the shorter syntax.
Interlude
This would be a good time to take a break. Maybe just a cuppa, or return here another day.
The last part of this answer builds up and thoroughly explains a grammar-based approach. Reading it may provide further insight into the solutions above and will show how to extend Raku's parsing to more complex scenarios.
But first...
A "boring" practical approach
I want to parse this with Raku. Can anyone help?
Raku may make writing parsers less tedious than with other tools. But less tedious is still tedious. And Raku parsing is currently slow.
In most cases, the practical answer when you want to parse well known formats and/or really big files is to find and use an existing parser. This might mean not using Raku at all, or using an existing Raku module, or using an existing non-Raku parser in Raku.
A suggested starting point is to search for the file format on modules.raku.org or raku.land. Look for a publicly shared parsing module already specifically packaged for Raku for the given file format. Then do some simple testing to see if you have a good solution.
At the time of writing there are no matches for 'bib'.
Even if you don't know C, there's almost certainly a 'bib' parsing C library already available that you can use. And it's likely to be the fastest solution. It's typically surprisingly easy to use an external library in your own Raku code, even if it's written in another programming language.
Using C libs is done using a feature called NativeCall. The doc I just linked may well be too much or too little, but please feel free to visit the freenode IRC channel #raku and ask for help. (Or post an SO question.) We're friendly folk. :)
If a C lib isn't right for a particular use case, then you can probably still use packages written in some other language such as Perl, Python, Ruby, Lua, etc. via their respective Inline::* language adapters.
The steps are:
Install a package (that's written in Perl, Python or whatever);
Make sure it runs on your system using a compiler of the language it's written for;
Install the appropriate Inline language adapter that lets Raku run packages in that other language;
Use the "foreign" package as if it were a Raku package containing exported Raku functions, classes, objects, values, etc.
(At least, that's the theory. Again, if you need help, please pop on the IRC channel or post an SO question.)
The Perl adapter is the most mature so I'll use that as an example. Let's say you use Perl's Text::BibTex packages and now wish to use Raku with that package. First, setup it up as it's supposed to be per its README. Then, in Raku, write something like:
use Text::BibTeX::BibFormat:from<Perl5>;
...
#blocks = $entry.format;
Explanation of these two lines:
The first line is how you tell Raku that you wish to load a Perl module.
(It won't work unless Inline::Perl5 is already installed and working. But it should be if you're using a popular Raku bundle. And if not, you should at least have the module installer zef so you can run zef install Inline::Perl5.)
The last line is just a mechanical Raku translation of the #blocks = $entry->format; line from the SYNOPSIS of the Perl package Text::BibTeX::BibFormat.
A Raku grammar / parser
OK. Enough "boring" practical advice. Let's now try have some fun creating a grammar based Raku parser good enough for the example from your question.
► use glot.io to run the code below
unit grammar bib;
rule TOP { <article>* }
rule article { '#article{' $<id>=<-[,]>+ ','
<kv-pairs>
'}'
}
rule kv-pairs { <kv-pair>* % ',' }
rule kv-pair { $<key>=\w* '={' ~ '}' $<value>=<-[}]>* }
With this grammar in place, we can now write something like:
die "Use CommaIDE?" unless bib .parsefile: 'derm.bib';
for $<article> -> $/ { put "$<id>: $<kv-pairs><kv-pair>[0]<value>\n" }
to generate exactly the same output as the previous solutions.
When a match or parse fails, by default Raku just returns Nil, which is, well, rather terse feedback.
There are several nice debugging options to figure out what's going on with a regex or grammar, but the best option by far is to use CommaIDE's Grammar-Live-View.
If you haven't already installed and used Comma, you're missing one of the best parts of using Raku. The features built in to the free version of Comma ("Community Edition") include outstanding grammar development / tracing / debugging tools.
Explanation of the 'bib' grammar
unit grammar bib;
The unit declarator is used at the start of a source file to tell Raku that the rest of the file declares a named package of code of a particular type.
The grammar keyword specifies a grammar. A grammar is like a class, but contains named "rules" -- not just named methods, but also named regexs, tokens, and rules. A grammar also inherits a bunch of general purpose rules from a base grammar.
rule TOP {
Unless you specify otherwise, parsing methods (.parse and .parsefile) that are called on a grammar start by calling the grammar's rule named TOP (declared with a rule, token, regex, or method declarator).
As a, er, rule of thumb, if you don't know if you should be using a rule, regex, token, or method for some bit of parsing, use a token. (Unlike regex patterns, tokens don't risk pathological backtracking.)
But I've used a rule. Like token patterns, rules also avoid the pathological backtracking risk. But, in addition rules interpret some whitespace in the pattern to be significant, in a natural manner. (See this SO answer for precise details.)
rules are typically appropriate towards the top of the parse tree. (Tokens are typically appropriate towards the leaves.)
rule TOP { <article>* }
The space at the end of the rule (between the * and pattern closing }) means the grammar will match any amount of whitespace at the end of the input.
<article> invokes another named rule in this grammar.
Because it looks like one should allow for any number of articles per bib file, I added a * (zero or more quantifier) at the end of <article>*.
rule article { '#article{' $<id>=<-[,]>+ ','
<kv-pairs>
'}'
}
If you compare this article pattern with the ones I wrote for the earlier Raku rules based solutions, you'll see various changes:
Rule in original one-liner
Rule in this grammar
Kept pattern as simple as possible.
Introduced <kv-pairs> and closing }
No attempt to echo layout of your input.
Visually echoes your input.
<[...]> is the Raku syntax for a character class, like[...] in traditional regex syntax. It's more powerful, but for now all you need to know is that the - in <-[,]> indicates negation, i.e. the same as the ^ in the [^,] syntax of ye olde regex. So <-[,]>+ attempts a match of one or more characters, none of which are ,.
$<id>=<-[,]>+ tells Raku to attempt to match the quantified "atom" on the right of the = (i.e. the <-[,]>+ bit) and store the results at the key <id> within the current match object. The latter will be hung from a branch of the parse tree; we'll get to precisely where later.
rule kv-pairs { <kv-pair>* % ',' }
This pattern illustrates one of several convenient Raku regex features. It declares you want to match zero or more kv-pairs separated by commas.
(In more detail, the % regex infix operator requires that matches of the quantified atom on its left are separated by the atom on its right.)
rule kv-pair { $<key>=\w* '={' ~ '}' $<value>=<-[}]>* }
The new bit here is '={' ~ '}'. This is another convenient regex feature. The regex Tilde operator parses a delimited structure (in this case one with a ={ opener and } closer) with the bit between the delimiters matching the quantified regex atom on the right of the closer. This confers several benefits but the main one is that error messages can be clearer.
I could have used the ~ approach in the /.../ regex in the one-liner, and vice-versa. But I wanted this grammar solution to continue the progression toward illustrating "better practice" idioms.
Constructing / deconstructing the parse tree
for $<article> { put "$<id>: $<kv-pairs><kv-pair>[0]<value>\n" }`
$<article>, $<id> etc. refer to named match objects that are stored somewhere in the "parse tree". But how did they get there? And exactly where is "there"?
Returning to the top of the grammar:
rule TOP {
If a .parse is successful, a single 'TOP' level match object is returned. (After a parse is complete the variable $/ is also bound to that top match object.) During parsing a tree will have been formed by hanging other match objects off this top match object, and then others hung off those, and so on.
Addition of match objects to a parse tree is done by adding either a single generated match object, or a list of them, to either a Positional (numbered) or Associative (named) capture of a "parent" match object. This process is explained below.
rule TOP { <article>* }
<article> invokes a match of the rule named article. An invocation of the rule <article> has two effects:
Raku tries to match the rule.
If it matches, Raku captures that match by generating a corresponding match object and adding it to the parse tree under the key <article> of the parent match object. (In this case the parent is the top match object.)
If the successfully matched pattern had been specified as just <article>, rather than as <article>*, then only one match would have been attempted, and only one value, a single match object, would have been generated and added under the key <article>.
But the pattern was <article>*, not merely <article>. So Raku attempts to match the article rule as many times as it can. If it matches at all, then a list of one or more match objects is stored as the value of the <article> key. (See my answer to "How do I access the captures within a match?" for a more detailed explanation.)
$<article> is short for $/<article>. It refers to the value stored under the <article> key of the current match object (which is stored in $/). In this case that value is a list of 3 match objects corresponding to the 3 articles in the input.
rule article { '#article{' $<id>=<-[,]>+ ','
Just as the top match object has several match objects hung off of it (the three captures of article matches that are stored under the top match object's <article> key), so too do each of those three article match objects have their own "child" match objects hanging off of them.
To see how that works, let's consider just the first of the three article match objects, the one corresponding to the text that starts "#article{garg2017patch,...". The article rule matches this article. As it's doing that matching, the $<id>=<-[,]>+ part tells Raku to store the match object corresponding to the id part of the article ("garg2017patch") under that article match object's <id> key.
Hopefully this is enough (quite possibly way too much!) and I can at last exhaustively (exhaustingly?) explain the last line of code, which, once again, was:
for $<article> -> $/ { put "$<id>: $<kv-pairs><kv-pair>[0]<value>\n" }`
At the level of the for, the variable $/ refers to the top of the parse tree generated by the parse that just completed. Thus $<article>, which is shorthand for $/<article>, refers to the list of three article match objects.
The for then iterates over that list, binding $/ within the lexical scope of the -> $/ { ... } block to each of those 3 article match objects in turn.
The $<id> bit is shorthand for $/<id>, which inside the block refers to the <id> key within the article match object that $/ has been bound to. In other words, $<id> inside the block is equivalent to $<article><id> outside the block.
The $<kv-pairs><kv-pair>[0]<value> follows the same scheme, albeit with more levels and a positional child (the [0]) in the midst of all the key (named/ associative) children.
(Note that there was no need for the article pattern to include a $<kv-pairs>=<kv-pairs> because Raku just presumes a pattern of the form <foo> should store its results under the key <foo>. If you wish to disable that, write a pattern with a non-alpha character as the first symbol. For example, use <.foo> if you want to have exactly the same matching effect as <foo> but just not store the matched input in the parse tree.)
Phew!
When the automatically generated parse tree isn't what you want
As if all the above were not enough, I need to mention one more thing.
The parse tree strongly reflects the tree structure of the grammar's rules calling one another from the top rule down to leaf rules. But the resulting structure is sometimes inconvenient.
Often one still wants a tree, but a simpler one, or perhaps some non-tree data structure.
The primary mechanism for generating exactly what you want from a parse, when the automatic results aren't suitable, is make. (This can be used in code blocks inside rules or factored out into Action classes that are separate from grammars.)
In turn, the primary use case for make is to generate a sparse tree of nodes hanging off the parse tree, such as an AST.
Footnotes
[1] Basic Raku is good for exploratory programming, spikes, one-offs, PoCs and other scenarios where the emphasis is on quickly producing working code that can be refactored later if need be.
[2] Raku's regexes/rules scale up to arbitrary parsing, as introduced in the latter half of this answer. This contrasts with past generations of regex which could not.[3]
[3] That said, ZA̡͊͠͝LGΌ ISͮ̂҉̯͈͕̹̘̱ TO͇̹̺ͅƝ̴ȳ̳ TH̘Ë͖́̉ ͠P̯͍̭O̚​N̐Y̡ remains a great and relevant read. Not because Raku rules can't parse (X)HTML. In principle they can. But for a task as monumental as correctly handling full arbitrary in-the-wild XHTML I would strongly recommend you use an existing parser written expressly for that purpose. And this applies generally for existing formats; it's best not to reinvent the wheel. But the good news with Raku rules is that if you need to write a full parser, not just a bunch of regexes, you can do so, and it need not involve going insane!

Which templating languages output HTML *as a tree of nodes*?

HTML is a tree of nodes, before all. It's not just a text.
However, most templating engines handle their input and output as it was just a text; they don't care what happens around their tags, their {$foo}'s and <% bar() %>'s; also they don't care about what are they outputting. Sometimes they happen to produce a correct html, but that's just a coincidence; they didn't aim for that, all they wanted is to replace some funny marks in the text stream with their evaluation.
There are a few templating engines which do treat their output as a set of nodes; XSLT and Haml come to mind. For some tasks, this has advantages: for example, you can automatically reformat (like, delete all empty text nodes; auto-indent; word-wrap). The result is guaranteed to be a correct xml/sgml unless you use a strict subset of operations that can break that. Also, such templating engine would automatically quote strings, differently in text nodes and in attributes, because it strictly knows whether you're writing an attribute or a text node.
Moreover, it can conditionally remove a node from output because it knows where it does begin and end, which is useful, and do other non-trivial node operations.
You might not like XSLT for its verbosiness or functionalness, but it's damn helps that your template is xmllint-able XML, and your output is a good sgml/xml.
So the question is: Which template engines do you know that treat their output as a set of correct nodes, not just an unstructured text?
I know XSLT, Haml and some obscure python-based one. Moar!
Which template engines do you know
that treat their output as a set of
correct nodes
Surprisingly ASP.NET does! You can change the HTML output of the page through a kind of DOM if you want: http://en.wikipedia.org/wiki/Asp.net#Rendering_technique
HTML combinator libraries, e.g.:
Wing Beats (F#)
SharpDOM (C#)
CityLizard (.NET, any language)
BlazeHtml (Haskell)
Ocsigen / Eliom (OCaml)
XML literals as a language feature can easily act as a "HTML template language"
VB.NET XML literals
Hasic (uses VB.NET XML literals)
Scala XML literals
Hamlet (uses Template Haskell)
though these are all embedded DSLs, dependent on their host language
There is a standard way of representing XML (or a subset of it such as XHTML) in Scheme known as SXML. This is one of the things that, in my opinion, make Scheme a good language for web development. It is possible to build up the contents of a document as a native Scheme list, and then render this to (correct) XHTML in one function call.
Here is an example that takes a simple text string, and wraps it as the contents of a one-paragraph HTML page. So the function as-page is acting as a template; its output is a Scheme list which can be easily translated to its equivalent HTML. Unbalanced or malformed tags are not possible with this approach.
(use-modules (sxml simple))
(define (as-page txt)
`(html
(head (title "A web page"))
(body (p ,txt))))
(as-page "It works!!!!!")
;; $2 = (html (head (title "A web page")) (body (p "It works!!!!")))
(sxml->xml (as-page "It works!!!!"))
;; $3 = <html><head><title>A web page</title></head><body><p>It works!!!!</p></body></html>
TAL (originally part of Zope but now implemented in a variety of languages) is XML-based. It's very logical and intention-revealing to work with - instead of shoving in a heap of text you're telling the template something like "set the href attribute of this link to http://google.com/ and set its text content to 'Search Google'. You don't have to manage which strings need to be escaped - generally if you intend something to be interpreted as markup, you put it in a template, and if you don't intend it to be interpreted as markup you feed it in as an attribute value or text content and TAL will escape it correctly.
Basically all templating engines which use XML as their file format (for defining templates). By using XML, they enforce that the file must be well-formed.
[EDIT] Examples are: Genshi (Python) or JSP 2.0 (Java).
With the Nagare web framework, the views are always a tree of XML nodes, directly built in Python.
The tree can then be manipulated in Python, transformed with XSL, serialized in HTML or XHTML ...
(the 'nagare.namespaces' package comes with the Nagare projet but can be used in any Python application)
Example:
>>> from nagare.namespaces import xhtml_base
>>> h = xhtml_base.Renderer() # The XHTML tree builder
>>>
>>> # Building the tree of nodes
>>> with h.html:
>>> with h.body:
>>> h << h.h1('Hello world')
>>> tree = h.root # The tree root element
>>>
>>> print tree.write_xmlstring() # Tree serialized in XML
<html><body><h1>Hello world</h1></body></html>
I maintain a list of push-style templating systems here:
http://perlmonks.org/?node_id=674273
And am in the process of evaluating various Perl templating systems for their separation index:
http://bit.ly/bXaYt7
But the tree-based one is written by me, HTML::Seamstress -
http://search.cpan.org/dist/HTML-Seamstress/
The term "push-style" comes from Terence Parr's Paper "Enforcing Strict Model-View
Separation in Template Engines" -
http://www.cs.usfca.edu/~parrt/papers/mvc.templates.pdf
Also, http://snapframework.com/docs/tutorials/heist from Haskell's snap seems to fit.
TAL is absolutely not push-style. It may be XML-based but it is pull-style (the most degenerate form of push-style).

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