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Not that it helps you much now, but the best documentation for tagged types (including the `rep` operation) is probably this:

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 suppose a more ideal form of the documentation would describe on the "Templates" page that template instances were a tagged type with a certain representation. It could describe the direct implications of that, but it would also have a link to the "Type operations" page for more background.


2 points by krapp 126 days ago | link

>I suppose a more ideal form of the documentation would describe on the "Templates" page that template instances were a tagged type with a certain representation. It could describe the direct implications of that, but it would also have a link to the "Type operations" page for more background.

That would have been tremendously helpful, can we do that? Who actually maintains the documentation, can it be updated?


1 point by akkartik 127 days ago | link

Perhaps we should maintain the docs only in plain-text and only within the repo, just because of the operational overheads of managing multiple branches. At least that way they won't seem to lie to a newcomer. I'm curious to hear what others think.


2 points by krapp 126 days ago | link

There is already a wiki that isn't getting much use[0].



"But in general, having incompatible types easily share functions without sharing too much is an open problem: A language can easily add a method to many types, or add a new type to many methods. But we don't yet know how to achieve both sides."

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"?

Is Anarki's `defextend` technique already encouraging a bloated codebase, or is there some other technique you're thinking of that would do that?


2 points by akkartik 127 days ago | link

Yeah, I suppose you could say the problem is 'solved'. I think of it as a trade-off with costs. We don't know how to achieve zero cost.

For example, I absolutely agree with you that 2 lines per method to extend every table method to some new type constitutes a solution for us. But if we had a thousand such types and a thousand such methods, it may seem like less of a solution. But then `defextend` would be the victim rather than cause of bloat.


3 points by rocketnia 126 days ago | link

Ah, you're imagining us having to write and maintain 1000×1000 individual `defextend` forms someday? Yeah, that does seem like a problem that would not feel solved once we got to it. :-p

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.

Regardless, I'm optimistic that although the amount of code will be nonzero, it'll still have a manageable size. To the extent we have any kind of consistency around these feature interaction decisions, those consistent principles can develop into abstractions. The only way we'll have 1000×1000 individual intersections to maintain is if we as a community culture are already maintaining 1,000,000 compelling and distinct justifications for them. :)


1 point by akkartik 126 days ago | link

Indeed. I'm curious: does my interpretation of the expression problem miss what the papers tend to focus on?


2 points by rocketnia 125 days ago | link

Well... That's a good question.

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" ( 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.

But then, I've really barely scratched the surface of the research, so I could easily be missing stuff like that.


"to find out about it"

Sorry, to find out about which part?


2 points by rocketnia 127 days ago | link

Ah, I think I understand: The fact that you can call `rep` on a template instance.


Once that last one is passing (or maybe even before it's passing), should the top-level tests.arc run these tests too? That way this can be caught not only by Travis CI, but also by people running tests.arc according to the readme.


2 points by zck 135 days ago | link

Good question. I guess it's a question of if we have enough Anarki tests to minimze breaking changes.

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.

Running it as part of Anarki's unit tests would prevent breakage, and is a simple solution to get a lot more tests added to the language. Anyone want to write a bunch of tests for Anarki itself?


3 points by akkartik 135 days ago | link

Anarki isn't really intended to avoid or minimize breaking changes. The unit tests verify only that everything is internally consistent. That boundary around 'internal' should include unit-test.arc, I think.


1 point by chomu 101 days ago | link

ok boomer


It's great to see you again! Sometimes I've wondered about the status of Semi-Arc. Looks like you've been working on a number of other Lisp implementations in the meantime! Pretty exciting. Thanks for sharing this update with us.

As someone who ported Rainbow line by line to JavaScript, I have to say, the size of the codebase can be quite daunting. A smaller implementation sounds a lot easier to work on.


5 points by suzuki 140 days ago | link

It is my pleasure.

As I referred in, the implementation of this arc's continuations is based on If you are planning to port this arc to JavaScript, I suggest reading which implements the continuations in the same way in TypeScript.

And in the latter, the display function

  c('display', 1, x => {
      write(stringify(fst(x), false));
      return new Promise(resolve => {
          runOnNextLoop(() => resolve(None));
is applied asynchronously, in a sense, as follows:

  case ContOp.ApplyFun: // exp2 is a function.
      [exp, env] = applyFunction(exp2, args, k, env);
      if (exp instanceof Promise)
          exp = await exp;
This means the web page is still interactive during the evaluation effectively. Here is an example: Click the "Load" button twice and you will see two "yin-yang puzzle" threads run on the page. Click the "Stop at Writing" button twice to stop them.


I like this whole discussion, akkartik and shader. You've both made a lot of excellent points, and I found myself nodding along to one comment only to nod along to the next as well.

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?

Is that the right perception for software? Well... is it the right perception for mathematics? I think the perception doesn't matter that much one way or the other. Everyday software can have leakless abstractions of the same kind everyday mathematics is known for, and many of math's abstractions are actually riddled with holes in ways software engineers might find familiar.


"And a self-closed tag lets you know there's no body, which is also a plus."

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

    <p>First paragraph
    <p>Second paragraph
Is treated basically like this:

    <p>First paragraph
    </p><p>Second paragraph
If instead you write:

    <p />First paragraph
    <p />Second paragraph
Then... Well, I should try to be precise....

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:

    <p>First paragraph
    </p><p>Second paragraph
But when you process it as XML, you get structure like this:

    <p></p>First paragraph
    <p></p>Second paragraph
So if you're trying to write a polyglot HTML/XML document, self-closing <p /> tags still probably aren't a great option. Closing the paragraphs explicitly, like so, makes it clearer how the structure will end up:

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

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...

In the very early days of XML and XHTML, when people were trying to make their HTML pages as XML-like as possible, many browsers would interpret something like <br/> as an element with the tag name "br/". That's why people got into the habit of putting in a space like <br />. That way those browsers would instead interpret the / as an attribute named "/", which was mostly harmless. Nowadays, the space is pretty much vestigial and you can just write <br/> if you want to.


3 points by zck 160 days ago | link

Yeah, when I dug more into the spec, I found out that <p> tags can't be self-closed. Only void and foreign elements can be self-closed (

The closing </p> can be omitted if the next tag is one of 25 different tags (, see "tag omission").

What I ended up coding was that the (para) call will always add a closing tag. This is more consistent with the spec -- as far as I can tell, the closing tag is never required to be omitted.


Incredible! Minimalism in language design taken to a maximalist extreme! ^_~ This is what it's all about. And the documentation/tutorial material looks like the cornerstone of the success here.


3 points by rocketnia 344 days ago | link | parent | on: Pg just released a new Lisp: Bel

From the perspective of my time on Arc Forum, it's great to see Bel. For most purposes Bel is pretty similar to Arc, but the Bel guide goes into pretty extensive detail about how Bel is intended to work, and that's information that was pretty sparse for Arc implementers and maintainers.

The fact that Bel contains a full description of reading, printing, and even arithmetic and thread arbitrarion means when someone tries to implement Bel in a non-Racket language, they'll have a good idea of how much work they're getting themselves into. They won't get lost in Racket documentation trying to understand how Bel works, and they won't find themselves questioning whether they need to implement every single obscure Racket feature just because a Bel program might use it.

I think some of the specific design choices in Bel are a bit wacky, like using mutable lists to represent numbers, functions, and continuations. Frankly I hope people won't invest their time trying to implement it all with perfect precision. Still, the goalposts are far clearer than trying to implement Arc.


I'm seeing a few pairs of design choices in Bel that seem to be in opposition, which might be a sign that one of the two is a bug. I suppose I don't know how many of these will turn out to be actual bugs, how many will turn out to be by design, and how many will turn out to be spurious products of my own misunderstanding.

1. Why do missing arguments to prims like `join` and `car` default to nil? In contrast, why do almost none of the functions defined in bel.bel have arguments that default to nil? It seems like the explanation for one of these would apply just as easily to the other, so I'm curious where the difference comes from.

2. Dynamic binding in Bel is a little surprising: "Dynamic bindings take precendence over lexical bindings, which take precedence over global ones." Does that mean we can set up dynamic bindings that interfere with the local lexical bindings of a function we call, like this?

  > inc.10
  > (dyn n 4 inc.10)
If Bel's functions expose their local bindings this way, then why do its macros go to the trouble to use gensyms (uvars) to avoid exposing theirs?

3. Exploring another consequence of dynamic binding: Considering the way Bel's macro calls are expanded at run time, can we can interfere with the local variables of macros' macroexpansion logic as well, like this?

  > (repeat 5 prn!hello)
  > (dyn init 'prn!4 (repeat 5 prn!hello))
If indeed we can do this, then why can't we do the same thing with Bel's special forms? Special forms' implementations are invoked at run time as well, but they're invoked using a plain function call in the interpreter rather than using `applyf`, so it looks like they have access to the dynamic scope of the interpreter host rather than that of the interpreted guest.

4. In the the printer, special care is taken for strings: "strings are lists and can thus share structure with other things we're printing." Shouldn't the printer pay the same kind of attention to numbers, since those are also lists?


4 points by rocketnia 344 days ago | link | parent | on: Pg just released a new Lisp: Bel

There's at least one implementation attempt starting up here:

Other name ideas:

- (isa bel)

- Rebel -- similar in theme to "Anarki," although there's already an unrelated Racket library called "Rebellion"

- Bombelli -- analogous to the spelling of "Anarki," and it can refer to a mathematician credited for putting complex numbers on solid ground

- Pachelbel -- would be a good name for an implementation written in D :-p


2 points by rocketnia 323 days ago | link

That one was Believe, written in C11. Here's the link again:

Looks like there's another project now, BelJS, written in JavaScript: