You can get to it from the "Type operations" link in the table of contents. Of course, you might've been drawn to the "Templates" page instead.

And unfortunately, that documentation describes Anarki's stable branch. Making documentation of similar quality for Anarki's master branch might be quite a bit more work. So even if you were familiar with tagged types already, the knowledge that template instances were a tagged type on Anarki master might be hard to discover.

I'm trying to follow, but I think you and I must have different understandings of the expression problem. That article lists several known solutions to the expression problem. The solution Anarki uses is `defextend`.

What do you mean by "sharing too much"?

I don't think that aspect of the expression problem is solvable in a language design. Instead, it's an ongoing conversation in the community. Sometimes the intent of one feature and the intent of another feature interact, leading people to do a nonzero amount of work to figure out the intent of the two features put together. That work is an essential part of what the community is trying to accomplish together, so it's a cost that can't be eliminated. The intent has to be reflected in the code somewhere, so there will be a nonzero amount of code that serves feature-coordinating purposes.

I haven't read any more than a few papers on it, and maybe only one of those in depth (which I'll mention below). Mostly I'm going by forum threads, wiki articles, and the design choices certain languages make (like Inform's multimethods and Haskell's type classes).

As far as I understand the history, Philip Wadler's work basically defined the strict parameters of the expression problem and explored solutions for it. Separate compilation and the avoidance of dynamic casts were big deals for Wadler for some reason.

That work was focused on Java, where it's easy to define new classes that implement existing interfaces but impossible to implement new interfaces on existing classes.

The solution I'm most familiar with for Java-style languages is the use of object algebras, as described in Oliveira and Cook's "Extensibility for the Masses: Practical Extensibility with Object Algebras" (https://www.cs.utexas.edu/~wcook/Drafts/2012/ecoop2012.pdf). In this approach, when you extend the system with a new type, you define a new interface with a generic type parameter and a factory method for building that type, and you have that interface inherit all the existing factory methods. So you don't have to solve the unsolvable task of implementing a new interface for an existing class, because you're representing your types as type parameters and methods, not simply as classes.

So I think the main subject of research was how best to represent an extensible program's types and functions in a language like Java where the most obvious choices weren't expressive enough. I think it's more of a "how do we allow extensions to be made at all" problem than a "how do we make all the extensions maintainable" problem.

If we do, then I don't know if it matters if we run unit-test.arc tests -- it's just one Arc library, presumably of several.

It's a little different than other libraries because it's what we use for Anarki unit tests.

As I referred in README.md, the implementation of this arc's continuations is based on https://github.com/nukata/little-scheme-in-java. If you are planning to port this arc to JavaScript, I suggest reading https://github.com/nukata/little-scheme-in-typescript which implements the continuations in the same way in TypeScript.

And in the latter, the display function https://github.com/nukata/little-scheme-in-typescript/blob/v...

  c('display', 1, x => {
      write(stringify(fst(x), false));
      return new Promise(resolve => {
          runOnNextLoop(() => resolve(None));
      });
  },

  case ContOp.ApplyFun: // exp2 is a function.
      [exp, env] = applyFunction(exp2, args, k, env);
      if (exp instanceof Promise)
          exp = await exp;
      break;

Right now I have a lot to say about the math analogy in particular. (The rest of the discussion has been great too.)

Mathematics has a lot in common with even the messy parts of programming.

Mathematics involves a lot of computation, and not necessarily of the digital computer kind or the arithmetic kind. If a human reader has to look up a definition of a word they don't know, then they're practically having to perform a manual lambda calculus substitution step. A lot of popular concepts in math are subject to transitive closure, which gives them indirect consequences hidden away on non-obvious reasoning paths. A lot of topics in math have to do with metareasoning and higher-order reasoning. Altogether, the kind of effort it takes for a human reader to understand a mathematical claim can involve a lot of the same things that on a computer we'd consider program execution.

As much as people might not like to admit it, mathematical theorems don't always take the form of the precise "don't lie" abstractions shader is describing. When a proof has a flaw in it, people still make use of the theorem, either by conjecturing that it's true anyway for some as-yet-undiscovered reason, or by explaining why the flaws in the proof don't matter in this context. In domains where it makes sense to change the mathematical foundations (e.g. deciding to use a different logic or a different set theory), a lot of the bread-and-butter theorems and concepts of mathematics can end up having flaws in them, but instead of coining new names for all those theorems and concepts, it's easier to use the same names and merely describe all the little patches that are necessary for them to work. So I think mathematics makes use of its share of abstraction-breaking techniques, techniques a software engineer might simulate with some combination of dynamic scope, side effects, preprocessing passes, code-walking, aspect-oriented weaving, dependency injection, or something like that. (This is mostly visible to people who are trying to make the math precise enough that a computer can verify or assist with it.)

Of course, math is not quite the same as software engineering. Unlike software, math is written primarily for humans to understand, and it only incidentally has computational aspects. This influences the kind of BS that's possible with math, both for better and for worse.

- For the worse: Once a mathematical argument goes on for a bit too long, humans rarely have the diligence to require that every single part of that reasoning makes sense; they're content to give leeway to some parts that they already feel they understand clearly. Some popular points of leeway end up serving as the foundations for a lot of mathematics, and we might call those the "syscalls" of math. Of course, every paradox of barbers and liars and time travel and infinity and whatnot reveals that humans are stubbornly hospitable to inconsistent ideas, and software engineering shows that humans' leeway leaves room for bugs on an extremely frequent basis.

- For the better: Since humans are in the loop when it comes to reading and sharing mathematical results, the kind of BS that confuses and dismays people has some trouble thriving. If the effort it takes to apply a mathematical concept is too full of hacks and spaghetti, people probably won't find it to be their favorite concept and won't share it with each other. (Of course, there seem to be some concepts which make a lot of sense once people get to know them, but still seem to require a rather circuitous route to learn about. In this way, people can end up being enthusiastic about parts of math that look, from the outside, to be full of nope.)

Considering all that mess, math nevertheless has a reputation for leakless abstractions, and that reputation is well deserved. "The study and development of leakless abstractions" would be a fitting definition of mathematics. The mess comes from the fact that humans are the ones discussing, developing, identifying examples of, and using the abstractions.

Likewise, even if software engineering deals with a big mess of leaky abstractions a lot of the time, the leakless ones are an important part of the design space. Unlike hardware, software code is a mathematically precise chunk of data, and the ways we transform it and compile it are easily a mathematical topic with lots of room for leakless abstractions. The reason (and perhaps the only essential reason) for the mess is that humans are the ones discussing, developing, making hardware for, and using the software.

While it's clear that math and software are two worlds with notable differences -- distinguished at least by the presence of computer hardware that gives a user meaningful value out of using software they don't know how to maintain -- I believe software could very well develop a popular perception as a world of Platonic forms, the same kind of perception math has. It's not that farfetched for people today to say, "obviously, as soon as you put an algorithm on a device and execute it, it's not the same algorithm." What if someday people say nothing we build or do can be a "true" algorithm because an algorithm is a Platonic concept that our world can only approximate?

A <p> tag does have a body. HTML like this:

  <body>
    <p>First paragraph
    <p>Second paragraph
  </body>

  <body>
    <p>First paragraph
    </p><p>Second paragraph
  </p></body>

  <body>
    <p />First paragraph
    <p />Second paragraph
  </body>

It looks like the HTML specification defines this as a "non-void-html-element-start-tag-with-trailing-solidus parse error." The spec says that in this case, "The parser behaves as if the U+002F (/) is not present," but also that "[browsers] may abort the parser at the first parse error that they encounter for which they do not wish to apply the rules described in this specification."

I don't know of any browsers that abort the parsing altogether, so it's still reliable to write the HTML that way.

However, the similarity to XML is actively misleading in this case. When you process that document as HTML, you still get structure like this:

  <body>
    <p>First paragraph
    </p><p>Second paragraph
  </p></body>

  <body>
    <p></p>First paragraph
    <p></p>Second paragraph
  </body>

  <body>
    <p>First paragraph</p>
    <p>Second paragraph</p>
  </body>

I think modern HTML does have a reliable common subset with XML. Modern HTML treats <br></br> and <p /> as parse errors, but it treats <br /> and <p></p> as valid. To write HTML/XML polyglot content, you just need to pay attention to whether you're dealing with a void element like "br" or a non-void element like "p".

Incidentally, why use an HTML/XML polyglot at all? There are at least a few situations where it can make sense:

- You're serving it as HTML, but (at least someday) you might want to use an XML-processing tool on it or serve it as XHTML.

- You're trying to serve it as XHTML, but you're worried you'll mess up your server configuration and serve it as HTML by mistake.

- You're confident you can serve it as XHTML today, but you have a backup plan to serve it as HTML if needed. In particular, you're afraid someday your XHTML will be invalid due to a bug in your code, a bug in a browser, an intentional spec violation in a browser (e.g. for security or user privacy), or a backwards-incompatible change in the spec. The XHTML spec dictates that an invalid page won't be displayed at all, so if you end up with invalid XHTML for any of those reasons, your site will be rather unusable until you can implement a fix. If that happens at a time you're not ready to drop everything and look at the bug in depth, then you can make a pretty quick switch to serving it as HTML, and most of the page will display again.

Because of the brittle handling of errors, XHTML still hasn't really gotten off the ground. So it seems like the primary value of the HTML/XML polyglot is to serve a document as HTML but use XML-processing tools on it behind the scenes.

---

A side note...

The closing </p> can be omitted if the next tag is one of 25 different tags (https://developer.mozilla.org/en-US/docs/Web/HTML/Element/p, see "tag omission").