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Plan.md
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Plan.md
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# Table of Contents
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1. [Aims of the HoTT Game](#org45da28b)
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1. [To get mathematicians with no experience in proof verification interested in HoTT and able to use Agda for HoTT](#org6c86aa4)
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2. [Work towards showing an interesting result in HoTT](#org5c370bf)
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3. [Try to balance hiding cubical implementations whilst exploiting their advantages](#org2cc236e)
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2. [Barriers](#org483c28e)
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1. [Installation of emacs](#orgfaee064)
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2. [Usage of emacs](#org4ec8663)
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3. [General type theoretic foundations](#orgd6212c3)
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4. [Cubical type theory](#orgdb053bf)
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- [Planning The HoTT Game](#org3bb90ed)
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- [Aims of the HoTT Game](#orga8d795d)
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- [Barriers](#org122a1d0)
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- [Format](#org3ea389f)
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- [Content](#org70d2231)
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- [Debriefs](#org37fbeb9)
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<a id="org45da28b"></a>
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# Aims of the HoTT Game
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<a id="org3bb90ed"></a>
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# Planning The HoTT Game
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<a id="org6c86aa4"></a>
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<a id="orga8d795d"></a>
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## To get mathematicians with no experience in proof verification interested in HoTT and able to use Agda for HoTT
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## Aims of the HoTT Game
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- To get mathematicians with no experience in proof verification interested in HoTT and able to use Agda for HoTT
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- [?] Work towards showing an interesting result in HoTT
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- Try to balance hiding cubical implementations whilst exploiting their advantages
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<a id="org5c370bf"></a>
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<a id="org122a1d0"></a>
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## [?] Work towards showing an interesting result in HoTT
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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
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<a id="org2cc236e"></a>
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<a id="org3ea389f"></a>
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## Try to balance hiding cubical implementations whilst exploiting their advantages
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<a id="org483c28e"></a>
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# Barriers
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<a id="orgfaee064"></a>
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## HOLD Installation of emacs
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<a id="org4ec8663"></a>
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## TODO Usage of emacs
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<a id="orgd6212c3"></a>
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## TODO General type theoretic foundations
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<a id="orgdb053bf"></a>
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## TODO Cubical type theory
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\## Format
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## Format
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- [?] Everything done in .agda files
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- Partially written code with spaces for participants to fill in + answer files
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@ -64,7 +44,10 @@
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- [?] Side quests
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- References to Harper lectures and HoTT book
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<!– listing topics we have pursued, NO ordering –>
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<a id="org70d2231"></a>
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## Content
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- emacs usage
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- agda usage
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@ -72,14 +55,14 @@
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- recommend doom emacs
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- implicit/explicit arguments
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- holes and inferred types
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- \`\_+\_\` and \`plus\_\_\`
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- `_+_` vs `plus__`
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- type theory basics
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- meta (judgemental/definitional) equality vs internal (propositional) equality
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- function extensionality
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- type formation
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- inductive types
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- (side Q) positive and negative constructions of Pi/Sigma types
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- \`data\` and \`record\`
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- `data` and `record`
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- universes
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- recursors / pattern matching
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- (side Q) some natural number exercises as early evidence of being able to ’do maths’?
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@ -110,6 +93,11 @@
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1. homotopy levels being closed under type constructions, in particular Set and ETT inside HoTT
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- in particular sigma types
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<a id="org37fbeb9"></a>
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## Debriefs
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- 2021 July 15; Homotopy n-types
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- watched (Harper) lecture 15 on Sets being closed under type formations ->- motivates showing in Agda Sets closed under Sigma.
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- Harper does product case, claiming sigma case follows analogously,
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5
Plan.org
5
Plan.org
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** Content
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# listing topics we have pursued, NO ordering
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- emacs usage
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- agda usage
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- basic commands (all covered in https://agda.readthedocs.io/en/v2.6.0.1/getting-started/quick-guide.html)
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- recommend doom emacs
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- implicit/explicit arguments
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- holes and inferred types
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- src_elisp{(_+_)} and src_elisp{(plus__)}
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- =_+_= vs ~plus__~
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- type theory basics
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- meta (judgemental/definitional) equality vs internal (propositional) equality
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- function extensionality
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- type formation
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- inductive types
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- (side Q) positive and negative constructions of Pi/Sigma types
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- `data` and `record`
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- ~data~ and ~record~
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- universes
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- recursors / pattern matching
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- (side Q) some natural number exercises as early evidence of being able to 'do maths'?
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