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#+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
<!-- listing topics we have pursued, NO ordering -->
- 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