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redtt mathematical library

This is the home of the redtt mathematical library.

Style and conventions

We have no absolute rules, but try to adhere to the following:

  • Generally use lowercase
  • Keep line lengths reasonably short (< 90 characters)
  • Write multi-word semantic units with hyphen (is-contr, weak-connection)
  • Write subordinate semantic units with slash (plus/assoc, symm/unit)
  • Reserve is- and has- for h-propositions (is-contr, has-hlevel)

Library structure

  • prelude/ contains definitions that are expected to be needed in all redtt developments.

  • data/ contains the bare definitions of datatypes, and whatever functions can be defined without needing other constructions and lemmas.

  • basics/ contains basic theorems of cubical type theory, which might not be needed everywhere.

  • paths/ contains theorems about the higher dimensional structure of types in cubical type theory, such as characterizations of loop spaces, etc.

  • cool/ contains cool constructions and theorems which aren't needed by anything; many new developments will first start in cool/, and become their own folders as become more complex and mature.