html export trial
This commit is contained in:
jlh
parent
5e06eeb654
commit
b930e449e3
41
.markdown-preview.html
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41
.markdown-preview.html
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<!DOCTYPE html>
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<html>
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<head>
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<meta charset="utf-8">
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<meta name="viewport" content="width=device-width, initial-scale=1, minimal-ui">
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<title>Markdown preview</title>
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<link rel="stylesheet" type="text/css" href="https://thomasf.github.io/solarized-css/solarized-dark.min.css">
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<script src="http://code.jquery.com/jquery-1.12.4.min.js"></script>
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<script>
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(function($, undefined) {
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var socket = new WebSocket("ws://localhost:7379");
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socket.onopen = function() {
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console.log("Connection established.");
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socket.send("MDPM-Register-UUID: 95ef6ea9-905f-406e-ab19-bc8a950fbadb");
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};
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socket.onclose = function(event) {
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if (event.wasClean) {
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console.log('Connection closed gracefully.');
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} else {
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console.log('Connection terminated.');
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}
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console.log('Code: ' + event.code + ' reason: ' + event.reason);
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};
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socket.onmessage = function(event) {
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$("#markdown-body").html($(event.data).find("#content").html()).trigger('mdContentChange');
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var scroll = $(document).height() * ($(event.data).find("#position-percentage").html() / 100);
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$("html, body").animate({ scrollTop: scroll }, 600);
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};
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socket.onerror = function(error) {
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console.log("Error: " + error.message);
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};
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})(jQuery);
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</script>
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</head>
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<body>
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<article id="markdown-body" class="markdown-body">
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<p>Markdown preview</p>
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</article>
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</body>
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</html>
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0
.projectile
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0
.projectile
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4
HoTTGame.agda-lib
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4
HoTTGame.agda-lib
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name: HoTTGameLib
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include: .
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depend: cubical-0.3
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flags: --cubical --no-import-sorts
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377
Plan.html
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377
Plan.html
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<?xml version="1.0" encoding="utf-8"?>
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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
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"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
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<head>
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<!-- 2021-07-19 Mon 18:31 -->
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<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
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<meta name="viewport" content="width=device-width, initial-scale=1" />
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<title>‎</title>
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<meta name="author" content="JLH KL" />
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<meta name="generator" content="Org Mode" />
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<style type="text/css">
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<!--/*--><![CDATA[/*><!--*/
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.title { text-align: center;
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margin-bottom: .2em; }
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.subtitle { text-align: center;
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font-size: medium;
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font-weight: bold;
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margin-top:0; }
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.todo { font-family: monospace; color: red; }
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.done { font-family: monospace; color: green; }
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.priority { font-family: monospace; color: orange; }
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.tag { background-color: #eee; font-family: monospace;
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padding: 2px; font-size: 80%; font-weight: normal; }
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.timestamp { color: #bebebe; }
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.timestamp-kwd { color: #5f9ea0; }
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.org-right { margin-left: auto; margin-right: 0px; text-align: right; }
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.org-left { margin-left: 0px; margin-right: auto; text-align: left; }
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.org-center { margin-left: auto; margin-right: auto; text-align: center; }
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.underline { text-decoration: underline; }
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#postamble p, #preamble p { font-size: 90%; margin: .2em; }
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p.verse { margin-left: 3%; }
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pre {
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border: 1px solid #ccc;
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box-shadow: 3px 3px 3px #eee;
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padding: 8pt;
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font-family: monospace;
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overflow: auto;
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margin: 1.2em;
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}
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pre.src {
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position: relative;
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overflow: auto;
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padding-top: 1.2em;
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}
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pre.src:before {
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display: none;
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position: absolute;
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background-color: white;
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top: -10px;
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right: 10px;
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padding: 3px;
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border: 1px solid black;
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}
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pre.src:hover:before { display: inline; margin-top: 14px;}
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/* Languages per Org manual */
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pre.src-asymptote:before { content: 'Asymptote'; }
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pre.src-awk:before { content: 'Awk'; }
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pre.src-C:before { content: 'C'; }
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/* pre.src-C++ doesn't work in CSS */
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pre.src-clojure:before { content: 'Clojure'; }
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pre.src-css:before { content: 'CSS'; }
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pre.src-D:before { content: 'D'; }
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pre.src-ditaa:before { content: 'ditaa'; }
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pre.src-dot:before { content: 'Graphviz'; }
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pre.src-calc:before { content: 'Emacs Calc'; }
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pre.src-emacs-lisp:before { content: 'Emacs Lisp'; }
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pre.src-fortran:before { content: 'Fortran'; }
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pre.src-gnuplot:before { content: 'gnuplot'; }
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pre.src-haskell:before { content: 'Haskell'; }
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pre.src-hledger:before { content: 'hledger'; }
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pre.src-java:before { content: 'Java'; }
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pre.src-js:before { content: 'Javascript'; }
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pre.src-latex:before { content: 'LaTeX'; }
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pre.src-ledger:before { content: 'Ledger'; }
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pre.src-lisp:before { content: 'Lisp'; }
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pre.src-lilypond:before { content: 'Lilypond'; }
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pre.src-lua:before { content: 'Lua'; }
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pre.src-matlab:before { content: 'MATLAB'; }
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pre.src-mscgen:before { content: 'Mscgen'; }
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pre.src-ocaml:before { content: 'Objective Caml'; }
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pre.src-octave:before { content: 'Octave'; }
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pre.src-org:before { content: 'Org mode'; }
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pre.src-oz:before { content: 'OZ'; }
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pre.src-plantuml:before { content: 'Plantuml'; }
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pre.src-processing:before { content: 'Processing.js'; }
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pre.src-python:before { content: 'Python'; }
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pre.src-R:before { content: 'R'; }
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pre.src-ruby:before { content: 'Ruby'; }
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pre.src-sass:before { content: 'Sass'; }
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pre.src-scheme:before { content: 'Scheme'; }
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pre.src-screen:before { content: 'Gnu Screen'; }
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pre.src-sed:before { content: 'Sed'; }
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pre.src-sh:before { content: 'shell'; }
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pre.src-sql:before { content: 'SQL'; }
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pre.src-sqlite:before { content: 'SQLite'; }
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/* additional languages in org.el's org-babel-load-languages alist */
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pre.src-forth:before { content: 'Forth'; }
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pre.src-io:before { content: 'IO'; }
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pre.src-J:before { content: 'J'; }
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pre.src-makefile:before { content: 'Makefile'; }
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pre.src-maxima:before { content: 'Maxima'; }
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pre.src-perl:before { content: 'Perl'; }
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pre.src-picolisp:before { content: 'Pico Lisp'; }
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pre.src-scala:before { content: 'Scala'; }
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pre.src-shell:before { content: 'Shell Script'; }
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pre.src-ebnf2ps:before { content: 'ebfn2ps'; }
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/* additional language identifiers per "defun org-babel-execute"
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in ob-*.el */
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pre.src-cpp:before { content: 'C++'; }
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pre.src-abc:before { content: 'ABC'; }
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pre.src-coq:before { content: 'Coq'; }
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pre.src-groovy:before { content: 'Groovy'; }
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/* additional language identifiers from org-babel-shell-names in
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ob-shell.el: ob-shell is the only babel language using a lambda to put
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the execution function name together. */
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pre.src-bash:before { content: 'bash'; }
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pre.src-csh:before { content: 'csh'; }
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pre.src-ash:before { content: 'ash'; }
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pre.src-dash:before { content: 'dash'; }
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pre.src-ksh:before { content: 'ksh'; }
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pre.src-mksh:before { content: 'mksh'; }
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pre.src-posh:before { content: 'posh'; }
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/* Additional Emacs modes also supported by the LaTeX listings package */
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pre.src-ada:before { content: 'Ada'; }
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pre.src-asm:before { content: 'Assembler'; }
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pre.src-caml:before { content: 'Caml'; }
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pre.src-delphi:before { content: 'Delphi'; }
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pre.src-html:before { content: 'HTML'; }
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pre.src-idl:before { content: 'IDL'; }
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pre.src-mercury:before { content: 'Mercury'; }
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pre.src-metapost:before { content: 'MetaPost'; }
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pre.src-modula-2:before { content: 'Modula-2'; }
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pre.src-pascal:before { content: 'Pascal'; }
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pre.src-ps:before { content: 'PostScript'; }
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pre.src-prolog:before { content: 'Prolog'; }
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pre.src-simula:before { content: 'Simula'; }
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pre.src-tcl:before { content: 'tcl'; }
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pre.src-tex:before { content: 'TeX'; }
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pre.src-plain-tex:before { content: 'Plain TeX'; }
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pre.src-verilog:before { content: 'Verilog'; }
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pre.src-vhdl:before { content: 'VHDL'; }
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pre.src-xml:before { content: 'XML'; }
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pre.src-nxml:before { content: 'XML'; }
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/* add a generic configuration mode; LaTeX export needs an additional
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(add-to-list 'org-latex-listings-langs '(conf " ")) in .emacs */
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pre.src-conf:before { content: 'Configuration File'; }
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table { border-collapse:collapse; }
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caption.t-above { caption-side: top; }
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caption.t-bottom { caption-side: bottom; }
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td, th { vertical-align:top; }
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th.org-right { text-align: center; }
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th.org-left { text-align: center; }
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th.org-center { text-align: center; }
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td.org-right { text-align: right; }
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td.org-left { text-align: left; }
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td.org-center { text-align: center; }
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dt { font-weight: bold; }
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.footpara { display: inline; }
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.footdef { margin-bottom: 1em; }
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.figure { padding: 1em; }
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.figure p { text-align: center; }
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.equation-container {
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display: table;
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text-align: center;
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width: 100%;
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}
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.equation {
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vertical-align: middle;
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}
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.equation-label {
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display: table-cell;
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text-align: right;
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vertical-align: middle;
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}
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.inlinetask {
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padding: 10px;
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border: 2px solid gray;
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margin: 10px;
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background: #ffffcc;
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}
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#org-div-home-and-up
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{ text-align: right; font-size: 70%; white-space: nowrap; }
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textarea { overflow-x: auto; }
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.linenr { font-size: smaller }
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.code-highlighted { background-color: #ffff00; }
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.org-info-js_info-navigation { border-style: none; }
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#org-info-js_console-label
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{ font-size: 10px; font-weight: bold; white-space: nowrap; }
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.org-info-js_search-highlight
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{ background-color: #ffff00; color: #000000; font-weight: bold; }
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.org-svg { width: 90%; }
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/*]]>*/-->
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</style>
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<script type="text/javascript">
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// @license magnet:?xt=urn:btih:e95b018ef3580986a04669f1b5879592219e2a7a&dn=public-domain.txt Public Domain
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<!--/*--><![CDATA[/*><!--*/
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function CodeHighlightOn(elem, id)
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{
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var target = document.getElementById(id);
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if(null != target) {
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elem.classList.add("code-highlighted");
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target.classList.add("code-highlighted");
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}
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}
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function CodeHighlightOff(elem, id)
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{
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var target = document.getElementById(id);
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if(null != target) {
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elem.classList.remove("code-highlighted");
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target.classList.remove("code-highlighted");
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}
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}
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/*]]>*///-->
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// @license-end
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</script>
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</head>
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<body>
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<div id="content">
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<div id="table-of-contents">
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<h2>Table of Contents</h2>
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<div id="text-table-of-contents">
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<ul>
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<li><a href="#orgcb7a42f">Planning The HoTT Game</a>
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<ul>
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<li><a href="#org86f8abf">Aims of the HoTT Game</a></li>
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<li><a href="#org891bd67">Barriers</a></li>
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<li><a href="#org865979d">Format</a></li>
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<li><a href="#org7cb3a5d">Content</a></li>
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<li><a href="#org313668c">Debriefs</a></li>
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</ul>
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</li>
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</ul>
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</div>
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</div>
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<div id="outline-container-orgcb7a42f" class="outline-2">
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<h2 id="orgcb7a42f">Planning The HoTT Game</h2>
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<div class="outline-text-2" id="text-orgcb7a42f">
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</div>
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<div id="outline-container-org86f8abf" class="outline-3">
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<h3 id="org86f8abf">Aims of the HoTT Game</h3>
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<div class="outline-text-3" id="text-org86f8abf">
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<ul class="org-ul">
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<li>To get mathematicians with no experience in proof verification interested in HoTT and able to use Agda for HoTT</li>
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<li>[?] Work towards showing an interesting result in HoTT</li>
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<li>Try to balance hiding cubical implementations whilst exploiting their advantages</li>
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</ul>
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</div>
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</div>
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<div id="outline-container-org891bd67" class="outline-3">
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<h3 id="org891bd67">Barriers</h3>
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<div class="outline-text-3" id="text-org891bd67">
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<ul class="org-ul">
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<li>HOLD Installation of emacs</li>
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||||||
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<li>TODO Usage of emacs</li>
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||||||
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<li>TODO General type theoretic foundations</li>
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||||||
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<li>TODO Cubical type theory</li>
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||||||
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</ul>
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||||||
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</div>
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||||||
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</div>
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||||||
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<div id="outline-container-org865979d" class="outline-3">
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<h3 id="org865979d">Format</h3>
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||||||
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<div class="outline-text-3" id="text-org865979d">
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||||||
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<ul class="org-ul">
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||||||
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<li>[?] Everything done in .agda files</li>
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||||||
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<li>Partially written code with spaces for participants to fill in + answer files</li>
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||||||
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<li>Levels set out with mini-bosses like in Nat Num Game, but with an overall boss</li>
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||||||
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<li>[?] Side quests</li>
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||||||
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<li>References to Harper lectures and HoTT book</li>
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||||||
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</ul>
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||||||
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</div>
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</div>
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||||||
|
<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 ’do maths’?</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 ->- 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 <-> 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>
|
||||||
181
Plan.md
181
Plan.md
@ -1,72 +1,119 @@
|
|||||||
# Planning The HoTT Game
|
|
||||||
|
|
||||||
## Aims of the HoTT Game
|
# Table of Contents
|
||||||
- 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
|
1. [Aims of the HoTT Game](#org45da28b)
|
||||||
- HOLD Installation of emacs
|
1. [To get mathematicians with no experience in proof verification interested in HoTT and able to use Agda for HoTT](#org6c86aa4)
|
||||||
- TODO Usage of emacs
|
2. [Work towards showing an interesting result in HoTT](#org5c370bf)
|
||||||
- TODO General type theoretic foundations
|
3. [Try to balance hiding cubical implementations whilst exploiting their advantages](#org2cc236e)
|
||||||
- TODO Cubical type theory
|
2. [Barriers](#org483c28e)
|
||||||
|
1. [Installation of emacs](#orgfaee064)
|
||||||
|
2. [Usage of emacs](#org4ec8663)
|
||||||
|
3. [General type theoretic foundations](#orgd6212c3)
|
||||||
|
4. [Cubical type theory](#orgdb053bf)
|
||||||
|
|
||||||
## 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
|
<a id="org45da28b"></a>
|
||||||
<!-- listing topics we have pursued, NO ordering -->
|
|
||||||
- emacs usage
|
# Aims of the HoTT Game
|
||||||
- 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.
|
<a id="org6c86aa4"></a>
|
||||||
- implicit/explicit arguments
|
|
||||||
- holes and inferred types
|
## To get mathematicians with no experience in proof verification interested in HoTT and able to use Agda for HoTT
|
||||||
- `_+_` and `plus__`
|
|
||||||
- type theory basics
|
|
||||||
- meta (judgemental/definitional) equality vs internal (propositional) equality
|
<a id="org5c370bf"></a>
|
||||||
- function extensionality
|
|
||||||
- type formation
|
## [?] Work towards showing an interesting result in HoTT
|
||||||
- universes
|
|
||||||
- recursors / pattern matching
|
|
||||||
- (side Q) some natural number exercises as early evidence of being able to 'do maths'?
|
<a id="org2cc236e"></a>
|
||||||
- different notions of equivalence
|
|
||||||
a) fibers contractable
|
## Try to balance hiding cubical implementations whilst exploiting their advantages
|
||||||
b) quasi-inverse
|
|
||||||
c) zig-zag
|
|
||||||
- (side Q) types are infinity groupoids
|
<a id="org483c28e"></a>
|
||||||
- inductive types
|
|
||||||
- (side Q) positive and negative constructions of Pi/Sigma types
|
# Barriers
|
||||||
- `data` and `record`
|
|
||||||
- HoTT
|
|
||||||
- basics
|
<a id="orgfaee064"></a>
|
||||||
a) meta interval, identity type vs path type
|
|
||||||
- mention identity type for compatability with other sources, but just use path type
|
## HOLD Installation of emacs
|
||||||
b) path type on other types
|
|
||||||
c) dependent path type PathP vs path over
|
|
||||||
d) univalence
|
<a id="org4ec8663"></a>
|
||||||
e) the (non)-issue of J in (Cu)TT
|
|
||||||
f) isContr, isProp, isSet
|
## TODO Usage of emacs
|
||||||
g) drawing pictures
|
|
||||||
- Structures, univalence and transport
|
|
||||||
a) transporting results between isomorphic structures
|
<a id="orgd6212c3"></a>
|
||||||
- HITs, examples
|
|
||||||
a) the constructed interval
|
## TODO General type theoretic foundations
|
||||||
b) booleans and covers
|
|
||||||
c) S^n
|
|
||||||
d)
|
<a id="orgdb053bf"></a>
|
||||||
- Homotopy n-types
|
|
||||||
a) homotopy levels being closed under type constructions, in particular Set and ETT inside HoTT
|
## TODO Cubical type theory
|
||||||
* in particular sigma types
|
|
||||||
|
\## 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
|
||||||
|
|
||||||
|
<!– 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
|
||||||
|
- implicit/explicit arguments
|
||||||
|
- holes and inferred types
|
||||||
|
- \`\_+\_\` and \`plus\_\_\`
|
||||||
|
- type theory basics
|
||||||
|
- meta (judgemental/definitional) equality vs internal (propositional) equality
|
||||||
|
- function extensionality
|
||||||
|
- type formation
|
||||||
|
- inductive types
|
||||||
|
- (side Q) positive and negative constructions of Pi/Sigma types
|
||||||
|
- \`data\` and \`record\`
|
||||||
|
- universes
|
||||||
|
- recursors / pattern matching
|
||||||
|
- (side Q) some natural number exercises as early evidence of being able to ’do maths’?
|
||||||
|
- 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
|
||||||
|
1. meta interval, identity type vs path type
|
||||||
|
- mention identity type for compatability with other sources, but just use path type
|
||||||
|
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
|
||||||
|
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
|
||||||
|
1. homotopy levels being closed under type constructions, in particular Set and ETT inside HoTT
|
||||||
|
- in particular sigma 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.
|
||||||
|
- 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
|
||||||
|
|
||||||
# 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
|
|
||||||
|
|||||||
46
Plan.org
46
Plan.org
@ -1,32 +1,36 @@
|
|||||||
# Planning The HoTT Game
|
#+OPTIONS: num:nil
|
||||||
|
#+AUTHOR: JLH
|
||||||
|
#+AUTHOR: KL
|
||||||
|
|
||||||
## Aims of the HoTT Game
|
* Planning 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
|
** Aims of the HoTT Game
|
||||||
- HOLD Installation of emacs
|
- To get mathematicians with no experience in proof verification interested in HoTT and able to use Agda for HoTT
|
||||||
- TODO Usage of emacs
|
- [?] Work towards showing an interesting result in HoTT
|
||||||
- TODO General type theoretic foundations
|
- Try to balance hiding cubical implementations whilst exploiting their advantages
|
||||||
- TODO Cubical type theory
|
|
||||||
|
|
||||||
## Format
|
** Barriers
|
||||||
- [?] Everything done in .agda files
|
- HOLD Installation of emacs
|
||||||
- Partially written code with spaces for participants to fill in + answer files
|
- TODO Usage of emacs
|
||||||
- Levels set out with mini-bosses like in Nat Num Game, but with an overall boss
|
- TODO General type theoretic foundations
|
||||||
- [?] Side quests
|
- TODO Cubical type theory
|
||||||
- References to Harper lectures and HoTT book
|
|
||||||
|
|
||||||
# Content
|
** Format
|
||||||
<!-- listing topics we have pursued, NO ordering -->
|
- [?] 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
|
- 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? -> basic doom usage and command differences with nude agda.
|
- recommend doom emacs
|
||||||
- implicit/explicit arguments
|
- implicit/explicit arguments
|
||||||
- holes and inferred types
|
- holes and inferred types
|
||||||
- `_+_` and `plus__`
|
- src_elisp{(_+_)} and src_elisp{(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
|
||||||
@ -64,7 +68,7 @@
|
|||||||
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,
|
||||||
|
|||||||
Loading…
Reference in New Issue
Block a user