Does working on your project, or running it, require a Dyalog license?

You'll need to get at least a free copy of Dyalog to use the compiler. They have a number of different free options. If you intend to use the compiler, it is available for use by all under an AGPL license. However, the generated code also uses Co-dfns code and is likewise under an AGPL license. If that license is unsuitable for you, then you'll need to arrange for an alternative license through Dyalog. Normally this will only be required for people interested in using Co-dfns commercially in their closed source projects.

The Co-dfns work is run like an Open Company however. You are welcome to submit contributions (see the README for more information) as pull requests and can onboard yourself at your leisure. I'm working to encourage more people to support the funding of Open Work on Co-dfns, but that's a long, slow process.

So, yes, generally speaking the compiler is designed to be used in conjunction with the host of additional tool support you get from Dyalog APL (the interpreter). However, Dyalog makes it as easy as possible to get a copy of the interpreter.

If I understand correctly, you can use the free, non-commercial-use Dyalog to run the AGPL Co-dfns compiler to produce programs. And also, the Co-dfns output is not independent of the compiler itself, meaning that the output must also be AGPL.

I'm speculating, but I suspect that anyone using Co-dfns output will be running it on a private bank of GPUs over a large private data-set, so I suppose the AGPL won't ever matter for them, in practice.

If that works for them, more power to them! They'll still likely need a commercial Co-dfns license if they are doing that, not because of the produced code, but because of the programming environment in which they do the development, unless they want to slice Co-dfns out of its "host" environment.

You are right, however, that you can use the free, non-commercial Dyalog to run the AGPL Co-dfns. Co-dfns is both a commercial and a research enterprise, and so it is important to me that the ideas in the compiler are manifest openly to the public, hence the open-source nature of the project. However, it also needs to fund that research somehow (have you ever tried to get a grant to write APL? Hahahaha!), and so commercial uses need to be managed in a reasonable way, namely, something mutually equitable.

Some interested parties are working to use Co-dfns in public facing services, and not just private data sets. One group is very slow moving, but we're exploring the possibility of a rewrite of the cryptographic stack.

The AGPL is not a "non-commercial" license. Freedom zero guarantees you can use it for any purpose. AGPL only becomes relevant when distributing.