What is needed to use our own miden-lsp for this? Just integrating the decompiler?

You mentioned that it is inferring type signatures? Static analysis can obviously check signatures to a limited extent, but inferring signatures would be all but useless due to over-approximation of types. I suspect that it's just computing stack effects (i.e. the number of felts that must have been on the operand stack on entry to be able to even do abstract interpretation at all, and how many remain on exit, and in both cases the values can be constrained to u32 based on instruction context), which our LSP also does - but relying on stack effect analysis for type information leads to a lot of spurious diagnostics once you start doing type checking for real. You basically want to separate the two, and refuse to type check things without type signatures being annotated (and lint on missing signatures) - that way you avoid emitting false positive diagnostics.

Anyway, that doesn't really have any bearing on this PR per se - but I do want this functionality to be provided via our own tooling that we're already working on, rather than splitting our efforts. I'll spend some time today integrating the TOB decompiler (or leveraging the analysis we already have in midenc), and follow up with my findings.

@bitwalker I was too coarse in the description. The interesting part I meant to describe is that masm-decompiler does infer stack signatures: input felt count, output felt count, net stack effect, and public_inputs. That is not a rich type signature, but it is required so lifting can know how many stack values exist at procedure entry and how many return values to name.

masm-decompiler also has a posterior, separate best-effort type analysis over the lifted IR, which is indeed primitive, and not something used (or emitted) here at all. Further, we're not using the lsp implementation from masm-lsp at all — it just happens to be colocated in the same repo (to which it gives its name) as masm-analysis. This analysis is a basic abstract interpretation loop over the IR, made easy to implement because of its value-oriented SSA form. masm-lint is a small CLI on top of it.

I have plans for how we can move this code somewhere maintained, better discussed elsewhere.