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exercise2home.html
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<!DOCTYPE html>
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="content-type" content="text/html;charset=utf-8" />
<link rel="stylesheet" href="jscoq/node_modules/bootstrap/dist/css/bootstrap.min.css" />
<title>Machine-Checked Mathematics</title>
<link rel="stylesheet" href="local.css" />
<script src='https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-MML-AM_CHTML'
async></script>
<script src="Blob.js" type="text/javascript"></script>
<script src="FileSaver.js" type="text/javascript"></script>
</head>
<body>
<div id="ide-wrapper" class="toggled">
<div id="code-wrapper">
<div id="document">
<p>
Use ALT-(up-arrow) and ALT-(down-arrow) to process this document inside your browser, line-by-line.
Use ALT-(right-arrow) to go to the cursor.
You can
<span class="save-button" onClick="save_coq_snippets()">save your edits</span>
inside your browser and
<span class="save-button" onClick="load_coq_snippets()">load them back</span>.
<!-- (edits are also saved when you close the window) -->
Finally, you can
<span class="save-button" onClick="download_coq_snippets()">download</span>
your working copy of the file, e.g., for sending it to teachers.
<hl />
</p>
<div><textarea id='coq-ta-1'>
(* ignore these directives *)
From mathcomp Require Import mini_ssreflect.
Set Implicit Arguments.
Unset Strict Implicit.
Unset Printing Implicit Defensive.
Add Printing Coercion is_true.
Notation "x '= true'" := (is_true x) (x at level 100, at level 0, only printing).
Remove Printing If bool.
</textarea></div>
<div><p>
<h3>
Exercise 1:
</h3>
<p>
<ul class="doclist">
<li> Write a recursive function taking a natural number to a boolean
value. That value is true iff the number if even
</li>
</ul>
</div>
<div><textarea id='coq-ta-2'>
Fixpoint even (n : nat) : bool := (* fill me *)
Eval lazy in even 3. (* = false *)
Eval lazy in even 6. (* = true *)
</textarea></div>
<div><p>
<h3>
Exercise 2:
</h3>
<p>
<ul class="doclist">
<li> State and prove the following boolean formulas:
<tt>b1 && (~~ b2 || b3) = (b1 && ~~ b2) || (b1 && b3)</tt>
</li>
</ul>
</div>
<div><textarea id='coq-ta-3'>
Lemma exercise2 (* fill me *)
</textarea></div>
<div><p>
<h3>
Exercise 3 :
</h3>
Prove Peirce's law using only the rewrite command.
<p>
<ul class="doclist">
<li> Hint: use Search to find relevant lemmas about <tt>==></tt> and <tt>~~</tt>
</li>
<li> Hint: use the lemma that says <tt>(a || b) && a = a</tt>
</li>
</ul>
</div>
<div><textarea id='coq-ta-4'>
Search _ (_ ==> _) in MC.Bool. (* All the lemmas you need are in MC.Bool *)
Lemma Peirce p q : ((p ==> q) ==> p) ==> p.
</textarea></div>
<div><p>
When you are done, click the Download link at the top of the page
and send us your homework by email: [email protected] </div>
<div><textarea id='coq-ta-5'>
</textarea></div>
<script type="text/javascript">
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tprev.setAttribute('onclick', 'prev_slide();');
tnext.setAttribute('id', 'next');
tnext.setAttribute('onclick', 'next_slide();');
toolbar.prepend(tools);
tools.appendChild(tprev);
tools.appendChild(tnext);
slides = document.getElementsByClassName('slide');
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</script>
</div> <!-- /#document -->
</div> <!-- /#code-wrapper -->
</div> <!-- /#ide-wrapper -->
<script src="./jscoq/ui-js/jscoq-loader.js" type="text/javascript"></script>
<script type="text/javascript">
var coq;
loadJsCoq('./jscoq/')
.then(loadJs("./jscoq/node_modules/codemirror/addon/runmode/runmode"))
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{ base_path: './jscoq/',
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</body>
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