AFAIK using dependent records-as-modules in a simpler MLTT-based type systems is tricky, because singleton types (aka. 'manifest fields') usually depend on equality reflection. Has anyone applied cubical type theory to the problem of first class module systems?
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YES, looking into this draft I am excited! This looks really nice and useful, and I am so glad you are working on this stuff! 👏🤩
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Can you see any connections with the 'phase distinction' and multi-stage programming or two-level/multi-level type theory? That's where I was hoping to find solutions (in my ignorant way). Still need to get my head around your 'synthetic phase distinction'. 😅
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Those seem to be handy for typed macros, monomorphisation, and inlining at least - just seemed (on the surface) to be similar to how you might want to distinguish between different phases of runtime and compile time.