> You can definitely not provide any guarantee for arbitrary DSLs implemented in your system, but claim you do.
No, I never claimed so. It's a responsibility of a DSL developer, although it is very easy, because of the small size of any practical DSL implementation.
> I can't find any code here that would suggest you're interfacing with a theorem prover
I did not publish yet a large chunk of work which contains a statically typed version of the host language with an ACL2-like inference engine. It's still quite experimental, but I did many mechanical proofs manually in the past (mostly in the hardware-related DSLs).
> much less the incredibly amount of machinery that must be involved in taking two correctness proofs and producing a correctness proof for their combination.
I still cannot understand your point. Why exactly a combination of DSLs is going to introduce any additional complexity?
I demonstrated in my examples that mixing the DSLs is exactly the same thing as using them. There is a dataflow dependency between various semantic realms, but it is really hard to break any constraints by merely feeding valid data in and getting a valid data out.
So, yes, no existing language workbench enforce language soundness, it's up to the designer to ensure the correctness. But, can you name a single general purpose language with an enforced soundness, CompCert aside?
> get inter-leaved in unexpected ways
Mind providing any examples of this? I cannot think of any interesting case, due to the very nature of this approach, there is no difference between using the languages in a "normal" way and targetting them in code generation.
> guarantee that the writer of DSL2 worked hard to achieve
What does this guarantee worth if it can be broken by merely using this language?
I see that you're more on a bondage&discipline side of the PL research. In this case we have to agree to disagree, my decades of Lisp experience are forcing me to lean the other way. I'm all for the formal proofs and I'm doing them a lot when it is really necessary (e.g., in hardware, where the cost of error is huge and verification capabilities are limited), but besides that, having a hacking and permissive language allows experimentation, while b&d languages inhibit innovative designs.
I only built a b&d, non-Turing-complete (total functional), strictly typed version of my language workbench after years of experimenting on a dynamic, unrestricted codebase.
So, my claims are:
1) It's dead simple to implement eDSLs using metaprogramming, if you've got the right tools (features for dealing with ASTs and their transforms; examples: Nanopass framwork, Racket in general)
2) If you have a hierarchy of ready-made DSLs, then with the above approach you can easily mix arbitrarily selected properties of all of your existing languages into a new DSL.
3) PEG and GLR are great. The others are inferior. All hail the lexerless parsing!
And, btw., my framework is not any different from the other metaprogramming-based language workbenches. You can achieve this ease of development and robustness with any other framework.