germax26/TheHoTTGame
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

into md

Browse Source
This commit is contained in:
jlh 2021-07-19 10:42:45 +01:00
parent bd73afd040
commit f32dde49e0
1 changed files with 27 additions and 28 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

55
Plan.org → Plan.md
View File

@ -1,33 +1,33 @@
#+TITLE: Planning The HoTT Game # Planning The HoTT Game
* Aims of 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 - 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 - [?] Work towards showing an interesting result in HoTT
** Try to balance hiding cubical implementations whilst exploiting their advantages - Try to balance hiding cubical implementations whilst exploiting their advantages
* Barriers ## Barriers
** HOLD Installation of emacs - HOLD Installation of emacs
** TODO Usage of emacs - TODO Usage of emacs
** TODO General type theoretic foundations - TODO General type theoretic foundations
** TODO Cubical type theory - TODO Cubical type theory
* Format ## Format
** [?] Everything done in .agda files - [?] Everything done in .agda files
** Partially written code with spaces for participants to fill in + answer 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 - Levels set out with mini-bosses like in Nat Num Game, but with an overall boss
** [?] Side quests - [?] Side quests
** References to Harper lectures and HoTT book - References to Harper lectures and HoTT book
* Content # Content
#+DESCRIPTION: listing topics we have pursued, NO ordering <!-- listing topics we have pursued, NO ordering -->
+ emacs usage - emacs usage
- `data` and `record` - `data` and `record`
- basic commands (all covered in https://agda.readthedocs.io/en/v2.6.0.1/getting-started/quick-guide.html) - 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. - recommend doom emacs? -> basic doom usage and command differences with nude agda.
- implicit/explicit arguments - implicit/explicit arguments
- holes and inferred types - holes and inferred types
- `_+_` and `plus__` - `_+_` and `plus__`
+ type theory basics - type theory basics
- meta (judgemental/definitional) equality vs internal (propositional) equality - meta (judgemental/definitional) equality vs internal (propositional) equality
- constructing types in universes - constructing types in universes
- universes - universes
@ -39,7 +39,7 @@
c) zig-zag c) zig-zag
- types are infinity groupoids - types are infinity groupoids
- positive and negative constructions of Pi/Sigma types - positive and negative constructions of Pi/Sigma types
+ HoTT - HoTT
- basics - basics
a) meta interval, identity type vs path type a) meta interval, identity type vs path type
b) path type on other types 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 a) homotopy levels being closed under type constructions, in particular Set and ETT inside HoTT
* in particular sigma types * in particular sigma types
* Debriefs ## Debriefs
- 2021 July 15; Homotopy n-types - 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. - 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, - 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. - 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 - 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 - Easy to generalize situation to n-types being closed under Sigma (7.1.8 in HoTT book), we showed this assuming PathPIsoPath
-