Arriving at opetopes for higher quasiquotation

This is another journal entry of my progress toward an extensible quasiquotation syntax. It wanders a bit, but I think it has a happy ending. :)

My last post was about “higher quasiquotation.” Since then, I’ve taken to calling that subject hypersnippets, since the characteristic feature is that it’s a repeated iteration of the concept of “the snippet of code between this boundary and this boundary.” Degree-N hypersnippets are made up of all the code in between a degree-(N-1) hypersnippet shape and zero or more nonoverlapping degree-(N-1) hypersnippet shapes appearing inside it. A degree-1 hypersnippet is like a text selection, and degree-0 hypersnippet is a text stream. Quotation is a certain kind of DSL where the syntax is hypersnippet-shaped, but there are potentially other uses for these shapes.

(Spoilers: Yesterday I finally convinced myself hypersnippet shapes were precisely the opetopes, and hypersnippet-shaped data is data that’s composable using the operations of an opetopic ω-category. So hypersnippets in my original sense are an ω-category generated by some free 1-cells corresponding to characters that can appear in a text stream. (Update 6-3-2018: Michael Arntzenius points out that these generators on their own would just generate strings. I was also sloppy about specifying the generator cells’ sources and targets here. Looks like I need one generator of each opetopic shape to be the holes, with each one’s sources and target being lower-dimensional holes; as well as one generator corresponding to each text character, each of which is a 2-cell with no sources, targeting the unique 1-cell hole.) Nevertheless, I’m still going to refer to these as “hypersnippets” in this post, and I think it’s valuable to refer to them by their intended usage domain in case they morph into a slightly different concept, even if the concept now seems to have stabilized into something that corresponds with opetopes.)

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Pursuing higher quasiquotation

Lately I’ve been trying to iron out the details of a generalization of quasiquotation which I call “higher quasiquotation.” The basic idea is that just as a quasiquotation is a region in one parenthesis-delimited region (marked by quasiquote) and a set of other parenthesis-delimited regions (marked by unquote​), we can go on to talk about regions between quasiquoted regions, regions between those regions, and so on.

If you think of values with holes as being functions, then the notion that this is a “higher-order” quasiquotation is clear: Each quasiquotation determines a value of type (c SExpr -> SExpr), the next higher degree of quasiquotation determines a value of type (c (c SExpr -> SExpr) -> (c SExpr -> SExpr)),  and so on, where c is some collection like c a = Map String a. But these functions aren’t the whole story; the quasiquotations should be able to be pulled apart like other data structures, not just filled in to create s-expressions.

I haven’t managed to write a full macroexpander for higher quasiquotation yet. I’ve written this post to share my status as it is.

Design and due diligence of the Cene language

Cene is a language I’ve built over the last couple of years. I’ve talked about Staccato and Tenerezza here, and that code has turned into Cene.

What sets Cene apart: Extensibility support

Cene’s design revolves around the primary idea that future generations will have better ideas for programming languages than we do, so most of what sets it apart is its support for custom languages, which mainly has to do with the design of its macroexpander.

Cene’s macroexpansion phase incrementally writes definitions (of macros, functions, etc.) to monotonic state resources using deterministic concurrency. These state resources are expressive enough that user-defined macros can use them to achieve combinations of open-world and closed-world extensibility, which is what I consider to be Cene’s primary feature.

RKN, Constant Time Steps, and Other Adventures

It’s been a couple of years since I posted here! Somehow 2014 turned into an opportunity for me to practice forms of expression other than programming, but that’s not what I’m here to talk about. I still spent lots of time on language design throughout 2014, and I’ve been zooming along in the new year.

Ethics for language design

I still dream big enough in my language design that ethics is an important consideration, but I’ve mellowed down when it comes to long-term ethics, and I’ve riled up a little about short-term ethics. :) Whatever happens, I think we’ll eventually build systems for better communication throughput between people, reducing the kind of violent pressure releases I was afraid of. After all, whatever organizations have better communication methods will probably become more intelligent as organizations, and they’ll outcompete the others. We just have to worry about how brutal that competition will be. So I figure we should foster egalitarianism in ways that cultivate competitive markets. Does that make me a left-libertarian? I don’t even know.

Pragmatics for language design

At this point I think of a programming language as something that has niche value. “Programming” is a rather nebulous term itself, and “language” describes the skill you use rather than the reward you get. As user interfaces go, programming languages are optimized for tasks where the user will have a) a long time to prepare their input, b) a higher tolerance for complexity than for redundancy, and c) a rather strong commitment to their chosen code once it’s deployed out of their reach. Well-designed UIs avoid such high complexity and commitment burdens, so my expectation as a programming language designer is to put myself out of a hobby.

Between complexity and commitment, commitment is the more essential problem. Much of the complexity in programming can be traced back to commitment thresholds: Either the bit is set, or it’s clear, never in between. Furthermore I think it’s plausible to trace this back to the mind-body threshold: Human minds are so disconnected from each other that we insist on personal identity, and this insistence lends a sense of absolute discreteness to so many of the concepts we form. (Although I’m attributing this to humans, this might be more specifically a Western trend. My perspective is too myopic to tell.)

On the other hand, not all complex artifacts are deployed with a high commitment cost. Sometimes people deploy complex artifacts because they can’t help it, leaving behind fingerprints and memories. We might want to take advantage of this, focusing on programming languages that help us interpret found artifacts in a useful way.

If I’m on the right track here, then programs would do best to be shaped like some kind of fingerprint, and encapsulation boundaries in programming would do best to behave like the encapsulation boundaries of people. That way we’re not introducing unnecessary concepts. Well, people are vaguely like modules: Not only is a program module encapsulated in a way vaguely similar to a person, but orderless sets of interacting modules are vaguely similar to orderless sets of interacting people. When modules interact, their interaction membrane, if we took a fingerprint of it, would be their import/export type signature. Maybe a type signature is a fingerprint for person-to-person interaction too.

Based on this train of thought, we might like to find a language with only type signatures. If we took a typed functional language with implicits or type classes, removed everything but the type signatures, and tried to program with it anyway, we would accomplish some form of logic programming. Maybe logic programming languages are on to something.

Below the cut, I’ll list some of the language projects I’ve worked on over the past year or two. The above philosophical premises will be relevant for a few of them, but I won’t refrain from discussing tangential features and challenges I’m excited about. If you’d like to avoid most of the technical meat-fluff and get back to the philosophical fluff-meat, I recommend skipping to the section titled “Era Tenerezza” and reading from there. :)

An extensible type system for meaning-preserving modularity

I’m gradually figuring out a foundation for a general-purpose programming language, and I think I just laid a great cornerstone,  which seems to solve the expression problem for dependent type theory. My pseudocode is in this long GitHub Gist, which comes with a long revision history showing my progress over the last 12 days.

I haven’t yet looked for a proof of strong normalization, consistency, and whatnot (and I don’t even intend for my theory to be expressive enough to support induction!), but the final insight has turned out to be very straightforward: If we can extend an extensible type and reimplement its interface (and re-prove its invariant) so that the new implementation/proof is observationally equal to the original as far as the original cases are concerned, then our extension may as well have been part of the type all along.

I’m using the observational equality infrastructure described by Altenkirch and McBride in “Observational Equality, Now!” and the way I think of the expression problem pretty much lines up with the requirements listed in Zenger and Odersky’s “Independently Extensible Solutions to the Expression Problem.”

Reactive Knowledge Networking

On December 20, just in time for the Mayan apocalypse, I thought of an approach to computer programming that unites my meaning-preserving modularity, some of David Barbour‘s RDP vision, and my own philosophical worldview.

I’m calling it Reactive Knowledge Networking. It takes the philosophical idea that a person does nothing with the world except observation and action, and it uses that idea to facilitate people’s communication with each other, with minimal (if any) computer configuration bureaucracy along the way. Its network structure is very similar to RDP, and it uses meaning-preserving modularity to encode the partial knowledge a person has observed.

Introducing Cairntaker, a garbage collector

I’ve been using JavaScript for a while now, and I’m finally getting fed up with it in ways that I just can’t deal with. Or can I? Now that I’m fed up with its memory model, I’ve built a garbage collector. In JS.

I call it Cairntaker. It’s for programmers who want well-tended heaps.