html export trial

2021-07-19 18:33:17 +01:00 · 2021-07-19 18:33:17 +01:00 · b930e449e3
commit b930e449e3
parent 5e06eeb654
6 changed files with 561 additions and 88 deletions
--- a/.markdown-preview.html
+++ b/.markdown-preview.html
@ -0,0 +1,41 @@
+<!DOCTYPE html>
+<html>
+  <head>
+    <meta charset="utf-8">
+    <meta name="viewport" content="width=device-width, initial-scale=1, minimal-ui">
+    <title>Markdown preview</title>
+    <link rel="stylesheet" type="text/css" href="https://thomasf.github.io/solarized-css/solarized-dark.min.css">
+    <script src="http://code.jquery.com/jquery-1.12.4.min.js"></script>
+    
+    <script>
+     (function($, undefined) {
+         var socket = new WebSocket("ws://localhost:7379");
+         socket.onopen = function() {
+             console.log("Connection established.");
+	     socket.send("MDPM-Register-UUID: 95ef6ea9-905f-406e-ab19-bc8a950fbadb");
+         };
+         socket.onclose = function(event) {
+             if (event.wasClean) {
+                 console.log('Connection closed gracefully.');
+             } else {
+                 console.log('Connection terminated.');
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+             console.log('Code: ' + event.code + ' reason: ' + event.reason);
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+         socket.onmessage = function(event) {
+             $("#markdown-body").html($(event.data).find("#content").html()).trigger('mdContentChange');
+             var scroll = $(document).height() * ($(event.data).find("#position-percentage").html() / 100);
+             $("html, body").animate({ scrollTop: scroll }, 600);
+         };
+         socket.onerror = function(error) {
+             console.log("Error: " + error.message);
+         };
+     })(jQuery);
+    </script>
+  </head>
+  <body>
+    <article id="markdown-body" class="markdown-body">
+      <p>Markdown preview</p>
+    </article>
+  </body>
+</html>
--- a/.projectile
+++ b/.projectile
--- a/HoTTGame.agda-lib
+++ b/HoTTGame.agda-lib
@ -0,0 +1,4 @@
+name: HoTTGameLib
+include: .
+depend: cubical-0.3
+flags: --cubical --no-import-sorts
--- a/Plan.html
+++ b/Plan.html
@ -0,0 +1,377 @@
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+<!-- 2021-07-19 Mon 18:31 -->
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+</head>
+<body>
+<div id="content">
+<div id="table-of-contents">
+<h2>Table of Contents</h2>
+<div id="text-table-of-contents">
+<ul>
+<li><a href="#orgcb7a42f">Planning The HoTT Game</a>
+<ul>
+<li><a href="#org86f8abf">Aims of the HoTT Game</a></li>
+<li><a href="#org891bd67">Barriers</a></li>
+<li><a href="#org865979d">Format</a></li>
+<li><a href="#org7cb3a5d">Content</a></li>
+<li><a href="#org313668c">Debriefs</a></li>
+</ul>
+</li>
+</ul>
+</div>
+</div>
+
+<div id="outline-container-orgcb7a42f" class="outline-2">
+<h2 id="orgcb7a42f">Planning The HoTT Game</h2>
+<div class="outline-text-2" id="text-orgcb7a42f">
+</div>
+<div id="outline-container-org86f8abf" class="outline-3">
+<h3 id="org86f8abf">Aims of the HoTT Game</h3>
+<div class="outline-text-3" id="text-org86f8abf">
+<ul class="org-ul">
+<li>To get mathematicians with no experience in proof verification interested in HoTT and able to use Agda for HoTT</li>
+<li>[?] Work towards showing an interesting result in HoTT</li>
+<li>Try to balance hiding cubical implementations whilst exploiting their advantages</li>
+</ul>
+</div>
+</div>
+
+<div id="outline-container-org891bd67" class="outline-3">
+<h3 id="org891bd67">Barriers</h3>
+<div class="outline-text-3" id="text-org891bd67">
+<ul class="org-ul">
+<li>HOLD Installation of emacs</li>
+<li>TODO Usage of emacs</li>
+<li>TODO General type theoretic foundations</li>
+<li>TODO Cubical type theory</li>
+</ul>
+</div>
+</div>
+
+<div id="outline-container-org865979d" class="outline-3">
+<h3 id="org865979d">Format</h3>
+<div class="outline-text-3" id="text-org865979d">
+<ul class="org-ul">
+<li>[?] Everything done in .agda files</li>
+<li>Partially written code with spaces for participants to fill in + answer files</li>
+<li>Levels set out with mini-bosses like in Nat Num Game, but with an overall boss</li>
+<li>[?] Side quests</li>
+<li>References to Harper lectures and HoTT book</li>
+</ul>
+</div>
+</div>
+
+<div id="outline-container-org7cb3a5d" class="outline-3">
+<h3 id="org7cb3a5d">Content</h3>
+<div class="outline-text-3" id="text-org7cb3a5d">
+<ul class="org-ul">
+<li>emacs usage</li>
+<li>agda usage
+<ul class="org-ul">
+<li>basic commands (all covered in <a href="https://agda.readthedocs.io/en/v2.6.0.1/getting-started/quick-guide.html">https://agda.readthedocs.io/en/v2.6.0.1/getting-started/quick-guide.html</a>)</li>
+<li>recommend doom emacs</li>
+<li>implicit/explicit arguments</li>
+<li>holes and inferred types</li>
+<li><code>_+_</code> vs <code>plus__</code></li>
+</ul></li>
+<li>type theory basics
+<ul class="org-ul">
+<li>meta (judgemental/definitional) equality vs internal (propositional) equality
+<ul class="org-ul">
+<li>function extensionality</li>
+</ul></li>
+<li>type formation
+<ul class="org-ul">
+<li>inductive types
+<ul class="org-ul">
+<li>(side Q) positive and negative constructions of Pi/Sigma types</li>
+<li><code>data</code> and <code>record</code></li>
+</ul></li>
+</ul></li>
+<li>universes</li>
+<li>recursors / pattern matching</li>
+<li>(side Q) some natural number exercises as early evidence of being able to &rsquo;do maths&rsquo;?</li>
+<li>different notions of equivalence
+<ol class="org-ol">
+<li>fibers contractable</li>
+<li>quasi-inverse</li>
+<li>zig-zag</li>
+</ol></li>
+<li>(side Q) types are infinity groupoids</li>
+<li>extra paths (univalence, fun ext, HITs)</li>
+</ul></li>
+<li>HoTT
+<ul class="org-ul">
+<li>basics
+<ol class="org-ol">
+<li>meta interval, identity type vs path type
+<ul class="org-ul">
+<li>mention identity type for compatability with other sources, but just use path type</li>
+</ul></li>
+<li>path type on other types</li>
+<li>dependent path type PathP vs path over</li>
+<li>univalence</li>
+<li>the (non)-issue of J in (Cu)TT</li>
+<li>isContr, isProp, isSet</li>
+<li>drawing pictures</li>
+</ol></li>
+<li>Structures, using univalence to transport
+<ol class="org-ol">
+<li>transporting results between isomorphic structures</li>
+</ol></li>
+<li>HITs, examples
+<ol class="org-ol">
+<li>the constructed interval</li>
+<li>booleans and covers</li>
+<li>S<sup>n</sup></li>
+<li>S<sup>1</sup> with 2 cw structures equiv</li>
+</ol></li>
+<li>Homotopy n-types
+<ol class="org-ol">
+<li>homotopy levels being closed under type constructions, in particular Set and ETT inside HoTT
+<ul class="org-ul">
+<li>in particular sigma types</li>
+</ul></li>
+</ol></li>
+</ul></li>
+</ul>
+</div>
+</div>
+
+<div id="outline-container-org313668c" class="outline-3">
+<h3 id="org313668c">Debriefs</h3>
+<div class="outline-text-3" id="text-org313668c">
+<ul class="org-ul">
+<li>2021 July 15; Homotopy n-types
+<ul class="org-ul">
+<li>watched (Harper) lecture 15 on Sets being closed under type formations -&gt;- motivates showing in Agda Sets closed under Sigma.</li>
+<li>Harper does product case, claiming sigma case follows analogously,</li>
+<li>attempt proof in Cubical Agda but highly non-obvious how to use that fibers are Sets.</li>
+<li>difficulty is that PathP not in one fiber, but PathOver is, AND PathOver &lt;-&gt; PathP NON-obvious</li>
+<li>Easy to generalize situation to n-types being closed under Sigma (7.1.8 in HoTT book), we showed this assuming PathPIsoPath</li>
+</ul></li>
+</ul>
+</div>
+</div>
+</div>
+</div>
+<div id="postamble" class="status">
+<p class="author">Author: JLH KL</p>
+<p class="date">Created: 2021-07-19 Mon 18:31</p>
+</div>
+</body>
+</html>
--- a/Plan.md
+++ b/Plan.md
@ -1,72 +1,119 @@
-# 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
+# Table of Contents

-## Barriers
- HOLD Installation of emacs
- TODO Usage of emacs
- TODO General type theoretic foundations
- TODO Cubical type theory
+1.  [Aims of the HoTT Game](#org45da28b)
+    1.  [To get mathematicians with no experience in proof verification interested in HoTT and able to use Agda for HoTT](#org6c86aa4)
+    2.  [Work towards showing an interesting result in HoTT](#org5c370bf)
+    3.  [Try to balance hiding cubical implementations whilst exploiting their advantages](#org2cc236e)
+2.  [Barriers](#org483c28e)
+    1.  [Installation of emacs](#orgfaee064)
+    2.  [Usage of emacs](#org4ec8663)
+    3.  [General type theoretic foundations](#orgd6212c3)
+    4.  [Cubical type theory](#orgdb053bf)
+
+
+<a id="org45da28b"></a>
+
+# Aims of the HoTT Game
+
+
+<a id="org6c86aa4"></a>
+
+## To get mathematicians with no experience in proof verification interested in HoTT and able to use Agda for HoTT
+
+
+<a id="org5c370bf"></a>
+
+## [?] Work towards showing an interesting result in HoTT
+
+
+<a id="org2cc236e"></a>
+
+## Try to balance hiding cubical implementations whilst exploiting their advantages
+
+
+<a id="org483c28e"></a>
+
+# Barriers
+
+
+<a id="orgfaee064"></a>
+
+## HOLD Installation of emacs
+
+
+<a id="org4ec8663"></a>
+
+## TODO Usage of emacs
+
+
+<a id="orgd6212c3"></a>
+
+## TODO General type theoretic foundations
+
+
+<a id="orgdb053bf"></a>
+
+## TODO Cubical type theory
+
+\## Format

-## 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
-<!-- listing topics we have pursued, NO ordering -->
+<!&#x2013; listing topics we have pursued, NO ordering &#x2013;>
+
 -   emacs usage
 -   agda usage
-  - 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.
+    -   basic commands (all covered in <https://agda.readthedocs.io/en/v2.6.0.1/getting-started/quick-guide.html>)
+    -   recommend doom emacs
    -   implicit/explicit arguments
    -   holes and inferred types
-  - `_+_` and `plus__`
+    -   \`\_+\_\` and \`plus\_\_\`
 -   type theory basics
    -   meta (judgemental/definitional) equality vs internal (propositional) equality
        -   function extensionality
    -   type formation
-  - universes
-  - recursors / pattern matching
-  - (side Q) 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
-  - (side Q) types are infinity groupoids
        -   inductive types
            -   (side Q) positive and negative constructions of Pi/Sigma types
-    - `data` and `record`
+            -   \`data\` and \`record\`
+    -   universes
+    -   recursors / pattern matching
+    -   (side Q) some natural number exercises as early evidence of being able to &rsquo;do maths&rsquo;?
+    -   different notions of equivalence
+        1.  fibers contractable
+        2.  quasi-inverse
+        3.  zig-zag
+    -   (side Q) types are infinity groupoids
+    -   extra paths (univalence, fun ext, HITs)
 -   HoTT
    -   basics
-    a) meta interval, identity type vs path type
+        1.  meta interval, identity type vs path type
            -   mention identity type for compatability with other sources, but just use 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
-    g) drawing pictures
-  - Structures, univalence and transport
-    a) transporting results between isomorphic structures
+        2.  path type on other types
+        3.  dependent path type PathP vs path over
+        4.  univalence
+        5.  the (non)-issue of J in (Cu)TT
+        6.  isContr, isProp, isSet
+        7.  drawing pictures
+    -   Structures, using univalence to transport
+        1.  transporting results between isomorphic structures
    -   HITs, examples
-    a) the constructed interval
-    b) booleans and covers
-    c) S^n
-    d)
+        1.  the constructed interval
+        2.  booleans and covers
+        3.  S<sup>n</sup>
+        4.  S<sup>1</sup> with 2 cw structures equiv
    -   Homotopy n-types
-    a) homotopy levels being closed under type constructions, in particular Set and ETT inside HoTT
-       * in particular sigma types
+        1.  homotopy levels being closed under type constructions, in particular Set and ETT inside HoTT
+            -   in particular sigma types

-# 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
+
--- a/Plan.org
+++ b/Plan.org
@ -1,32 +1,36 @@
-# Planning The HoTT Game
+#+OPTIONS: num:nil
+#+AUTHOR: JLH
+#+AUTHOR: KL

-## 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
+* Planning The HoTT Game

-## Barriers
- HOLD Installation of emacs
- TODO Usage of emacs
- TODO General type theoretic foundations
- TODO Cubical type theory
+** 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

-## 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
+** Barriers
+  - HOLD Installation of emacs
+  - TODO Usage of emacs
+  - TODO General type theoretic foundations
+  - TODO Cubical type theory

-# Content
-<!-- listing topics we have pursued, NO ordering -->
+** 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
+# listing topics we have pursued, NO ordering
 - emacs usage
 - agda usage
  - 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
  - implicit/explicit arguments
  - holes and inferred types
-  - `_+_` and `plus__`
+  - src_elisp{(_+_)} and src_elisp{(plus__)}
 - type theory basics
  - meta (judgemental/definitional) equality vs internal (propositional) equality
    - function extensionality
@ -64,7 +68,7 @@
    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,