diff options
| author | Yann Herklotz <git@yannherklotz.com> | 2020-11-26 01:00:41 +0000 |
|---|---|---|
| committer | Yann Herklotz <git@yannherklotz.com> | 2020-11-26 01:00:41 +0000 |
| commit | fa4b252945a870100305c159d20e264be18973ce (patch) | |
| tree | 435cbd07a2af45f3f08dc8ac892fa48044047eeb /docs/proof/Show.html | |
| parent | 29bee524cccfe08c680f655b1969a4c421e0a969 (diff) | |
| download | vericert-fa4b252945a870100305c159d20e264be18973ce.tar.gz vericert-fa4b252945a870100305c159d20e264be18973ce.zip | |
Add proof documentation
Diffstat (limited to 'docs/proof/Show.html')
| -rw-r--r-- | docs/proof/Show.html | 90 |
1 files changed, 90 insertions, 0 deletions
diff --git a/docs/proof/Show.html b/docs/proof/Show.html new file mode 100644 index 0000000..926ab3c --- /dev/null +++ b/docs/proof/Show.html @@ -0,0 +1,90 @@ +<?xml version="1.0" encoding="utf-8" ?> +<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> +<html xmlns="http://www.w3.org/1999/xhtml" class="alectryon-standalone" xml:lang="en" lang="en"> +<head> +<meta http-equiv="Content-Type" content="text/html; charset=utf-8" /> +<meta name="generator" content="Docutils 0.16: http://docutils.sourceforge.net/" /> +<title>Show.v</title> +<link rel="stylesheet" href="alectryon.css" type="text/css" /> +<link rel="stylesheet" href="docutils_basic.css" type="text/css" /> +<link rel="stylesheet" href="tango_subtle.css" type="text/css" /> +<link rel="stylesheet" href="tango_subtle.min.css" type="text/css" /> +<script type="text/javascript" src="alectryon.js"></script> +<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/IBM-type/0.5.4/css/ibm-type.min.css" integrity="sha512-sky5cf9Ts6FY1kstGOBHSybfKqdHR41M0Ldb0BjNiv3ifltoQIsg0zIaQ+wwdwgQ0w9vKFW7Js50lxH9vqNSSw==" crossorigin="anonymous" /> +<link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/firacode/5.2.0/fira_code.min.css" integrity="sha512-MbysAYimH1hH2xYzkkMHB6MqxBqfP0megxsCLknbYqHVwXTCg9IqHbk+ZP/vnhO8UEW6PaXAkKe2vQ+SWACxxA==" crossorigin="anonymous" /> +</head> +<body> +<div class="alectryon-root alectryon-floating"><div class="document"> + + +<pre class="alectryon-io"><!-- Generator: Alectryon v1.0 --><span class="coq-wsp"><span class="highlight"><span class="c">(* </span> +<span class="c"> * Vericert: Verified high-level synthesis.</span> +<span class="c"> * Copyright (C) 2019-2020 Yann Herklotz <yann@yannherklotz.com></span> +<span class="c"> *</span> +<span class="c"> * This program is free software: you can redistribute it and/or modify</span> +<span class="c"> * it under the terms of the GNU General Public License as published by</span> +<span class="c"> * the Free Software Foundation, either version 3 of the License, or</span> +<span class="c"> * (at your option) any later version.</span> +<span class="c"> *</span> +<span class="c"> * This program is distributed in the hope that it will be useful,</span> +<span class="c"> * but WITHOUT ANY WARRANTY; without even the implied warranty of</span> +<span class="c"> * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the</span> +<span class="c"> * GNU General Public License for more details.</span> +<span class="c"> *</span> +<span class="c"> * You should have received a copy of the GNU General Public License</span> +<span class="c"> * along with this program. If not, see <https://www.gnu.org/licenses/>.</span> +<span class="c"> *)</span> + +</span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">From</span> Coq <span class="kn">Require Import</span> + Strings.String + Bool.Bool + Arith.Arith + ZArith.ZArith.</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"><span class="highlight"> +</span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Local Open Scope</span> string.</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"><span class="highlight"> +</span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Class</span> <span class="nf">Show</span> <span class="nv">A</span> : <span class="kt">Type</span> := + { + show : A -> string + }.</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"><span class="highlight"> +</span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Instance</span> <span class="nf">showBool</span> : <span class="kn">Show</span> bool := + { + show := <span class="kr">fun</span> <span class="nv">b</span>:bool => <span class="kr">if</span> b <span class="kr">then</span> <span class="s2">"true"</span> <span class="kr">else</span> <span class="s2">"false"</span> + }.</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"><span class="highlight"> +</span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Fixpoint</span> <span class="nf">string_of_nat_aux</span> (<span class="nv">time</span> <span class="nv">n</span> : nat) (<span class="nv">acc</span> : string) : string := + <span class="kr">let</span> <span class="nv">d</span> := <span class="kr">match</span> n mod <span class="mi">10</span> <span class="kr">with</span> + | <span class="mi">0</span> => <span class="s2">"0"</span> | <span class="mi">1</span> => <span class="s2">"1"</span> | <span class="mi">2</span> => <span class="s2">"2"</span> | <span class="mi">3</span> => <span class="s2">"3"</span> | <span class="mi">4</span> => <span class="s2">"4"</span> | <span class="mi">5</span> => <span class="s2">"5"</span> + | <span class="mi">6</span> => <span class="s2">"6"</span> | <span class="mi">7</span> => <span class="s2">"7"</span> | <span class="mi">8</span> => <span class="s2">"8"</span> | _ => <span class="s2">"9"</span> + <span class="kr">end</span> <span class="kr">in</span> + <span class="kr">let</span> <span class="nv">acc'</span> := d ++ acc <span class="kr">in</span> + <span class="kr">match</span> <span class="kp">time</span> <span class="kr">with</span> + | <span class="mi">0</span> => acc' + | S time' => + <span class="kr">match</span> n / <span class="mi">10</span> <span class="kr">with</span> + | <span class="mi">0</span> => acc' + | n' => string_of_nat_aux time' n' acc' + <span class="kr">end</span> + <span class="kr">end</span>.</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"><span class="highlight"> +</span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Definition</span> <span class="nf">string_of_nat</span> (<span class="nv">n</span> : nat) : string := + string_of_nat_aux n n <span class="s2">""</span>.</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"><span class="highlight"> +</span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Instance</span> <span class="nf">showNat</span> : <span class="kn">Show</span> nat := + { + show := string_of_nat + }.</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"><span class="highlight"> +</span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Instance</span> <span class="nf">showZ</span> : <span class="kn">Show</span> Z := + { + show a := show (Z.to_nat a) + }.</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"><span class="highlight"> +</span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Instance</span> <span class="nf">showPositive</span> : <span class="kn">Show</span> positive := + { + show a := show (Zpos a) + }.</span></span></span></pre> +</div> +</div></body> +</html> |