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| 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/Monad.html | |
| parent | 29bee524cccfe08c680f655b1969a4c421e0a969 (diff) | |
| download | vericert-kvx-fa4b252945a870100305c159d20e264be18973ce.tar.gz vericert-kvx-fa4b252945a870100305c159d20e264be18973ce.zip | |
Add proof documentation
Diffstat (limited to 'docs/proof/Monad.html')
| -rw-r--r-- | docs/proof/Monad.html | 82 |
1 files changed, 82 insertions, 0 deletions
diff --git a/docs/proof/Monad.html b/docs/proof/Monad.html new file mode 100644 index 0000000..864f5b6 --- /dev/null +++ b/docs/proof/Monad.html @@ -0,0 +1,82 @@ +<?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>Monad.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" /> +<link rel="stylesheet" href="../docs/css/org.css" type="text/css" /> +</head> +<body> +<div id="left-bar"> +<header id="ymhg-header"> +<div class="logo"><a href="/vericert">Vericert</a></div> +<nav id="navbar"> +<span><a href="/vericert/documentation.html">Documentation</a></span> +<span><a href="/vericert/proof/toc.html">Proof</a></span> +</nav> +<p>Vericert is the first formally verified high-level synthesis tool.</p> +</header> +<div id="toc"></div> +</div> +<div class="alectryon-root alectryon-floating"><div class="document"> + + +<pre class="alectryon-io"><!-- Generator: Alectryon v1.0 --><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">From</span> Coq <span class="kn">Require Import</span> Lists.List.</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">Module Type</span> <span class="nf">Monad</span>.</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"><span class="highlight"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Parameter</span> <span class="nv">mon</span> : <span class="kt">Type</span> -> <span class="kt">Type</span>.</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"><span class="highlight"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Parameter</span> <span class="nv">ret</span> : <span class="kr">forall</span> (<span class="nv">A</span> : <span class="kt">Type</span>) (<span class="nv">x</span> : A), mon A.</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Arguments</span> ret [A].</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"><span class="highlight"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Parameter</span> <span class="nv">bind</span> : <span class="kr">forall</span> (<span class="nv">A</span> <span class="nv">B</span> : <span class="kt">Type</span>) (<span class="nv">f</span> : mon A) (<span class="nv">g</span> : A -> mon B), mon B.</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Arguments</span> bind [A B].</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"><span class="highlight"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Parameter</span> <span class="nv">bind2</span> : <span class="kr">forall</span> (<span class="nv">A</span> <span class="nv">B</span> <span class="nv">C</span>: <span class="kt">Type</span>) (<span class="nv">f</span>: mon (A * B)) (<span class="nv">g</span>: A -> B -> mon C), mon C.</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Arguments</span> bind2 [A B C].</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">End</span> <span class="nf">Monad</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">Module</span> <span class="nf">MonadExtra</span>(M : Monad).</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Import</span> M.</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"><span class="highlight"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Module</span> <span class="nf">MonadNotation</span>.</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"><span class="highlight"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Notation</span> <span class="s2">"'do' X <- A ; B"</span> := + (bind A (<span class="kr">fun</span> <span class="nv">X</span> => B)) + (<span class="kn">at level</span> <span class="mi">200</span>, X <span class="kn">ident</span>, A <span class="kn">at level</span> <span class="mi">100</span>, B <span class="kn">at level</span> <span class="mi">200</span>).</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Notation</span> <span class="s2">"'do' ( X , Y ) <- A ; B"</span> := + (bind2 A (<span class="kr">fun</span> <span class="nv">X</span> <span class="nv">Y</span> => B)) + (<span class="kn">at level</span> <span class="mi">200</span>, X <span class="kn">ident</span>, Y <span class="kn">ident</span>, A <span class="kn">at level</span> <span class="mi">100</span>, B <span class="kn">at level</span> <span class="mi">200</span>).</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"><span class="highlight"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">End</span> <span class="nf">MonadNotation</span>.</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Import</span> MonadNotation.</span></span><span class="coq-wsp"> +</span></span><span class="coq-wsp"><span class="highlight"> +</span></span><span class="coq-wsp"> </span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Fixpoint</span> <span class="nf">traverselist</span> {<span class="nv">A</span> <span class="nv">B</span>: <span class="kt">Type</span>} (<span class="nv">f</span>: A -> mon B) (<span class="nv">l</span>: list A) {<span class="nv">struct</span> <span class="nv">l</span>}: mon (list B) := + <span class="kr">match</span> l <span class="kr">with</span> + | nil => ret nil + | x::xs => + <span class="kp">do</span> r <- f x; + <span class="kp">do</span> rs <- traverselist f xs; + ret (r::rs) + <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-wsp"> </span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Fixpoint</span> <span class="nf">collectlist</span> {<span class="nv">A</span> : <span class="kt">Type</span>} (<span class="nv">f</span> : A -> mon unit) (<span class="nv">l</span> : list A) {<span class="nv">struct</span> <span class="nv">l</span>} : mon unit := + <span class="kr">match</span> l <span class="kr">with</span> + | nil => ret tt + | x::xs => <span class="kp">do</span> _ <- f x; collectlist f xs + <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">End</span> <span class="nf">MonadExtra</span>.</span></span></span></pre> +</div> +</div></body> +</html> |