Progress: Quasiquotation; Cene; co-opetopes?

About two months ago, in my ongoing project to make a quasiquote operation that allows users to define their own variants of unquote as macros, I hit a snag. I took some time away from the problem for a couple of months, but lately I’ve come back to pick up where I left off, and the extensible quasiquote now has a complete implementation. (Here’s the relevant Git commit.) It doesn’t do anything out of the box that other quasiquote implementations don’t do, but it uses hypersnippets to do it, and as planned, it allows users to define their own alternatives to unquote.

To get past the snag I hit, I thought I would need to implement several “selective” operations on hypertees. It turns out I only needed one: hypertee-zip-selective. This operation makes it possible to zip two hypertees while selectively skipping some of the holes of each one. This makes it easy to store data in some hypertee holes while still treating others as actual holes, which is useful for representing hypersnippet-shaped data besides hypertees themselves.

So, now I have a working implementation of a quasiquotation operator with user-definable unquote. I should really write a better post at some point describing how this technique works. In order to get to something that’s simple and stable enough to write useful guide materials for, I’m planning to focus next on cleaning up some of the mess I’ve made trying to implement it over the past couple of years.

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Status

Status update: A new library, Lathe Ordinals

I pulled out my ordinal code from Lathe Morphisms into its own library, Lathe Ordinals. It’s like a lot of ordinal number libraries out there already. This Maple documentation is a pretty thorough, if terse, description of the kind of thing I’m implementing for Racket.

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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.

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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.

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The storytelling worlds of Mega Man and Red Ash

So the Kickstarter for Red Ash is live! I have mixed feelings about it, and to explain, I’m going to have to explain my take on Mighty No. 9 and the Mega Man franchise first.

If you don’t know any of those things, well, they’re all projects that were (for the most part) led by Keiji Inafune, and they’re all about robots. I started being a Mega Man fan at a young age, and it’s funny how seriously I’ve come to take it.

With the 2011 cancellation of Mega Man Legends 3 and some further cancellations that followed, the Mega Man franchise entered a dry spell that’s still ongoing. Keiji Inafune left Capcom, started up Comcept, and eventually unveiled the Mighty No. 9 Kickstarter to great success in 2013. To most people, Mighty No. 9 is a “spiritual successor” of the Mega Man franchise. Likewise, to most people, Red Ash is now a revival of Mega Man Legends 3 in particular.

If I want some simple nostalgic enjoyment like Yooka-Laylee, I’ll buy it off the (virtual) shelf; I don’t need to back it. I back a project when I want it to exist when it otherwise couldn’t, or if I consider it to have positive cultural impact.

Mighty No. 9: Telling stories about responsibility

The Mighty No. 9 Kickstarter was meaningful to me because it was a new launching point for Keiji Inafune to build story worlds.

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