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Plan.md
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# Table of Contents # Table of Contents
1. [Aims of the HoTT Game](#org45da28b) - [Planning The HoTT Game](#org3bb90ed)
1. [To get mathematicians with no experience in proof verification interested in HoTT and able to use Agda for HoTT](#org6c86aa4) - [Aims of the HoTT Game](#orga8d795d)
2. [Work towards showing an interesting result in HoTT](#org5c370bf) - [Barriers](#org122a1d0)
3. [Try to balance hiding cubical implementations whilst exploiting their advantages](#org2cc236e) - [Format](#org3ea389f)
2. [Barriers](#org483c28e) - [Content](#org70d2231)
1. [Installation of emacs](#orgfaee064) - [Debriefs](#org37fbeb9)
2. [Usage of emacs](#org4ec8663)
3. [General type theoretic foundations](#orgd6212c3)
4. [Cubical type theory](#orgdb053bf)
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# Aims of the HoTT Game <a id="org3bb90ed"></a>
# Planning The HoTT Game
<a id="org6c86aa4"></a> <a id="orga8d795d"></a>
## To get mathematicians with no experience in proof verification interested in HoTT and able to use Agda for HoTT ## 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
<a id="org5c370bf"></a> <a id="org122a1d0"></a>
## [?] Work towards showing an interesting result in HoTT ## Barriers
- HOLD Installation of emacs
- TODO Usage of emacs
- TODO General type theoretic foundations
- TODO Cubical type theory
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## Try to balance hiding cubical implementations whilst exploiting their advantages ## Format
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# Barriers
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## HOLD Installation of emacs
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## TODO Usage of emacs
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## TODO General type theoretic foundations
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## TODO Cubical type theory
\## 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
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- [?] Side quests - [?] Side quests
- References to Harper lectures and HoTT book - References to Harper lectures and HoTT book
<!&#x2013; listing topics we have pursued, NO ordering &#x2013;>
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## Content
- emacs usage - emacs usage
- agda usage - agda usage
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- recommend doom emacs - recommend doom emacs
- implicit/explicit arguments - implicit/explicit arguments
- holes and inferred types - holes and inferred types
- \`\_+\_\` and \`plus\_\_\` - `_+_` vs `plus__`
- type theory basics - type theory basics
- meta (judgemental/definitional) equality vs internal (propositional) equality - meta (judgemental/definitional) equality vs internal (propositional) equality
- function extensionality - function extensionality
- type formation - type formation
- inductive types - inductive types
- (side Q) positive and negative constructions of Pi/Sigma types - (side Q) positive and negative constructions of Pi/Sigma types
- \`data\` and \`record\` - `data` and `record`
- universes - universes
- recursors / pattern matching - recursors / pattern matching
- (side Q) some natural number exercises as early evidence of being able to &rsquo;do maths&rsquo;? - (side Q) some natural number exercises as early evidence of being able to &rsquo;do maths&rsquo;?
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1. homotopy levels being closed under type constructions, in particular Set and ETT inside HoTT 1. homotopy levels being closed under type constructions, in particular Set and ETT inside HoTT
- in particular sigma types - in particular sigma types
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## 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,

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Plan.org
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** Content ** Content
# listing topics we have pursued, NO ordering # listing topics we have pursued, NO ordering
- emacs usage - emacs usage
- agda usage - agda usage
- 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 - recommend doom emacs
- implicit/explicit arguments - implicit/explicit arguments
- holes and inferred types - holes and inferred types
- src_elisp{(_+_)} and src_elisp{(plus__)} - =_+_= vs ~plus__~
- type theory basics - type theory basics
- meta (judgemental/definitional) equality vs internal (propositional) equality - meta (judgemental/definitional) equality vs internal (propositional) equality
- function extensionality - function extensionality
- type formation - type formation
- inductive types - inductive types
- (side Q) positive and negative constructions of Pi/Sigma types - (side Q) positive and negative constructions of Pi/Sigma types
- `data` and `record` - ~data~ and ~record~
- universes - universes
- recursors / pattern matching - recursors / pattern matching
- (side Q) some natural number exercises as early evidence of being able to 'do maths'? - (side Q) some natural number exercises as early evidence of being able to 'do maths'?