60 lines
2.1 KiB
Org Mode
60 lines
2.1 KiB
Org Mode
#+TITLE: 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
|
|
|
|
* 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
|
|
|
|
* Content
|
|
#+DESCRIPTION: 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
|
|
- meta (judgemental/definitional) equality vs internal (propositional) equality
|
|
- constructing types in universes
|
|
- universes
|
|
- recursors / pattern matching
|
|
- side quest: some natural number exercises as early evidence of being able to 'do maths'?
|
|
- different notions of equivalence
|
|
a) fibers contractable
|
|
b) quasi-inverse
|
|
c) zig-zag
|
|
- types are infinity groupoids
|
|
- positive and negative constructions of Pi/Sigma types
|
|
+ HoTT
|
|
- basics
|
|
a) meta interval, identity type vs path type
|
|
b) path type on other types
|
|
c) dependent path type PathP vs path over
|
|
d) univalence
|
|
e) the (non)-issue of J in (Cu)TT
|
|
f) isContr, isProp, isSet
|
|
- Structures, univalence and transport
|
|
a) transporting results between isomorphic structures
|
|
- HITs, examples
|
|
a) the constructed interval
|
|
b) booleans and covers
|
|
c) S^n
|
|
d)
|
|
- Homotopy n-types
|
|
a) homotopy levels being closed under type constructions, in particular Set and ETT inside HoTT
|
|
* in particular sigma types
|