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Homotopy type theory is a flavor of type theory – specifically of intensional (Martin-Löf-) dependent type theory – which takes seriously the natural interpretation of identity types as formalizing path space objects in homotopy theory. (from nLab)
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Higher Observational Type Theory: variables becoming free in reduction rules
This question is based on the talks given by Mike Shulman on higher observational type theory (part 1, part 2, part 3).
In trying to understand the reduction rules of the calculus, I tried to work th …