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Based on #1760
Currently the
Regionalityaxis has three levels:global,regionalandlocal. This PR generalizes it to natural numbers0, 1, 2, ...where0means global,1means the top level, and so on. For example:zis0,yis2.xwould be1, but it will be rejected because we force top-level to be global.Moreover,
Regionalityis indexed as follows:The essential idea is that, by indexing, we can avoid talking about
Regionality = 6when we are only in 5 layers of nested regions. This is essential for some morphisms to have adjoints.Note that the index starts at
1instead of0- this is also essential for some morphisms to have adjoints. Intuitively, some adjunctions lose meanings if there is only "global" and no local to talk about.