Using thinnings in this maximal way, they kind of serve as a “free variable analysis”. Consider the set form of thinnings described about (set[int], int). The missing piece in a free variable analysis is kind of the current scope you’re in, the latter half of the pair. Also it is a bit odd, but sensible to run a free variable analysis on de bruijn indices, you need to shift the analysis results as you pass binders. I do not think it is a good idea to consider these thinnings as merely an analysis though, since they are part of what it even is to be a well scoped term.
https://doi.org/10.1016/j.celrep.2025.116717
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