Thanks! The reason it's hard to get is probably there's very little to get - this is just a syntax/notation tweak, I haven't built a proper language on top of it yet.
The main idea is pretty much just 'S-expressions have dots; what if that dotted part could be not just an atom but a full structured expression like a Lisp form'. (or a Prolog term, if you are familiar with Prolog).
This very small idea opens up a number of new possibilities in creating very compressed notation, I think. It's mostly useful for people interested in building Domain Specific Languages, where you want a minimum amount of friction from the underlying syntax, and no limit on the kinds of expressions that can be represented.
With a particular emphasis on something that can be embedded easily into raw text as a markup language, without needing to remap a lot of characters like in HTML, but that also allows the full syntactic power of an arbitrary programming or data-representation language (eg Lisp or Prolog) if required. Also something that can be used to represent very low-level concerns, like circular references and read-time macro insertion and other tricky syntax-level things that Lisps tend to use reader macros to do.
Again, this is purely at the syntax level. Translating an actual language to work smoothly on top of this syntax is a much bigger project. But this syntax stands midway between raw S-expressions and 'heavier' syntaxes that have a notion of 'typed expressions' which S-expressions don't natively provide.
Think of T-expressions as a proposal for a 'concrete syntax tree' format: ie, an unambiguous representation of an arbitrary Abstract Syntax Tree on top of the usual Lisp/S-expression components of pairs and symbols. Raw S-expressions don't quite provide enough tools to express all possible Abstract Syntax Trees (because the CDR of a dotted pair can't distinguish between a list and a typed expression). But T-expressions can.
And then `quasiquote` itself is a macro. It's an interesting macro to implement, and I just spent like two years trying to streamline the way I was implementing it for my languages 'cause I kept adding bells and whistles to it. :)
If you write a slightly different macro where the syntax for (unquote ___) is (/ . ___), then you could use it like this, which matches the syntax of your example exactly:
(t-expr (1 (/ car x) / cdr y))
I think the advantages of quasiquotation specifically shine when the quoted data is also program code in the same language (or like you just said, a DSL). In that specific case, I like that the code I'm writing looks the same regardless of whether it's under an unquote or not. There's a practical advantage in terms of being able to copy the code back and forth as necessary.
It sounds like you're looking at this as a data encoding? A lot of data encodings take pains not to be Turing-complete. Then again, for inexpressive languages like HTML, there are a lot of Turing-complete templating languages designed to dynamically generate them.
You can of course experiment with that in most Lisp dialects using a quasiquoted term where all the unquotes have functions in them:
And you could write a macro that puts in those lambdas automatically so it's not so verbose. Then your parser could use the Lisp's reader, wrap the result in (t-expr ...), and eval it in an appropriate namespace to yield your compiled program-syntax-with-functions-in-it. Then you could pass that syntax through an interpreter.
Is this all making sense? XD I started going through ideas a little fast, and maybe I missed your point a long time ago.