diff --git a/Plan.org b/Plan.md similarity index 57% rename from Plan.org rename to Plan.md index d28bb8b..8ab1763 100644 --- a/Plan.org +++ b/Plan.md @@ -1,33 +1,33 @@ -#+TITLE: Planning The HoTT Game +# Planning The HoTT Game -* Aims of the HoTT Game -** To get mathematicians with no experience in proof verification interested in HoTT and able to use Agda for HoTT -** [?] Work towards showing an interesting result in HoTT -** Try to balance hiding cubical implementations whilst exploiting their advantages +## Aims of the HoTT Game +- To get mathematicians with no experience in proof verification interested in HoTT and able to use Agda for HoTT +- [?] Work towards showing an interesting result in HoTT +- Try to balance hiding cubical implementations whilst exploiting their advantages -* Barriers -** HOLD Installation of emacs -** TODO Usage of emacs -** TODO General type theoretic foundations -** TODO Cubical type theory +## Barriers +- HOLD Installation of emacs +- TODO Usage of emacs +- TODO General type theoretic foundations +- TODO Cubical type theory -* Format -** [?] Everything done in .agda files -** Partially written code with spaces for participants to fill in + answer files -** Levels set out with mini-bosses like in Nat Num Game, but with an overall boss -** [?] Side quests -** References to Harper lectures and HoTT book +## Format +- [?] Everything done in .agda files +- Partially written code with spaces for participants to fill in + answer files +- Levels set out with mini-bosses like in Nat Num Game, but with an overall boss +- [?] Side quests +- References to Harper lectures and HoTT book -* Content -#+DESCRIPTION: listing topics we have pursued, NO ordering -+ emacs usage +# Content + +- emacs usage - `data` and `record` - basic commands (all covered in https://agda.readthedocs.io/en/v2.6.0.1/getting-started/quick-guide.html) - recommend doom emacs? -> basic doom usage and command differences with nude agda. - implicit/explicit arguments - holes and inferred types - `_+_` and `plus__` -+ type theory basics +- type theory basics - meta (judgemental/definitional) equality vs internal (propositional) equality - constructing types in universes - universes @@ -39,7 +39,7 @@ c) zig-zag - types are infinity groupoids - positive and negative constructions of Pi/Sigma types -+ HoTT +- HoTT - basics a) meta interval, identity type vs path type b) path type on other types @@ -58,11 +58,10 @@ a) homotopy levels being closed under type constructions, in particular Set and ETT inside HoTT * in particular sigma types -* Debriefs +## Debriefs - 2021 July 15; Homotopy n-types - + watched (Harper) lecture 15 on Sets being closed under type formations ->- motivates showing in Agda Sets closed under Sigma. - + Harper does product case, claiming sigma case follows analogously, - + attempt proof in Cubical Agda but highly non-obvious how to use that fibers are Sets. - + difficulty is that PathP not in one fiber, but PathOver is, AND PathOver <-> PathP NON-obvious - + Easy to generalize situation to n-types being closed under Sigma (7.1.8 in HoTT book), we showed this assuming PathPIsoPath -- + - watched (Harper) lecture 15 on Sets being closed under type formations ->- motivates showing in Agda Sets closed under Sigma. + - Harper does product case, claiming sigma case follows analogously, + - attempt proof in Cubical Agda but highly non-obvious how to use that fibers are Sets. + - difficulty is that PathP not in one fiber, but PathOver is, AND PathOver <-> PathP NON-obvious + - Easy to generalize situation to n-types being closed under Sigma (7.1.8 in HoTT book), we showed this assuming PathPIsoPath