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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/Statemonad.html | |
| parent | 29bee524cccfe08c680f655b1969a4c421e0a969 (diff) | |
| download | vericert-fa4b252945a870100305c159d20e264be18973ce.tar.gz vericert-fa4b252945a870100305c159d20e264be18973ce.zip | |
Add proof documentation
Diffstat (limited to 'docs/proof/Statemonad.html')
| -rw-r--r-- | docs/proof/Statemonad.html | 83 |
1 files changed, 83 insertions, 0 deletions
diff --git a/docs/proof/Statemonad.html b/docs/proof/Statemonad.html new file mode 100644 index 0000000..b78049c --- /dev/null +++ b/docs/proof/Statemonad.html @@ -0,0 +1,83 @@ +<?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>Statemonad.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-sentence"><span class="coq-input"><span class="highlight"><span class="kn">From</span> compcert <span class="kn">Require</span> Errors.</span></span><span class="coq-wsp"> +</span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">From</span> vericert <span class="kn">Require Import</span> Monad.</span></span><span class="coq-wsp"> +</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> 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">State</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">Parameter</span> <span class="nv">st</span> : <span class="kt">Type</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">Parameter</span> <span class="nv">st_prop</span> : st -> st -> <span class="kt">Prop</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">Axiom</span> <span class="nv">st_refl</span> : <span class="kr">forall</span> <span class="nv">s</span>, st_prop s s.</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">Axiom</span> <span class="nv">st_trans</span> : <span class="kr">forall</span> <span class="nv">s1</span> <span class="nv">s2</span> <span class="nv">s3</span>, st_prop s1 s2 -> st_prop s2 s3 -> st_prop s1 s3.</span></span><span class="coq-wsp"> +</span></span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">End</span> <span class="nf">State</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">Statemonad</span>(S : State) <: Monad.</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">Inductive</span> <span class="nf">res</span> (<span class="nv">A</span>: <span class="kt">Type</span>) (<span class="nv">s</span>: S.st): <span class="kt">Type</span> := + | Error : Errors.errmsg -> res A s + | OK : A -> <span class="kr">forall</span> (<span class="nv">s'</span> : S.st), S.st_prop s s' -> res A s.</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">Arguments</span> OK [A s].</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> Error [A s].</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">Definition</span> <span class="nf">mon</span> (<span class="nv">A</span>: <span class="kt">Type</span>) : <span class="kt">Type</span> := <span class="kr">forall</span> (<span class="nv">s</span>: S.st), res A s.</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">Definition</span> <span class="nf">ret</span> {<span class="nv">A</span>: <span class="kt">Type</span>} (<span class="nv">x</span>: A) : mon A := + <span class="kr">fun</span> (<span class="nv">s</span> : S.st) => OK x s (S.st_refl s).</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">Definition</span> <span class="nf">bind</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 class="kr">fun</span> (<span class="nv">s</span> : S.st) => + <span class="kr">match</span> f s <span class="kr">with</span> + | Error msg => Error msg + | OK a s' i => + <span class="kr">match</span> g a s' <span class="kr">with</span> + | Error msg => Error msg + | OK b s'' i' => OK b s'' (S.st_trans s s' s'' i i') + <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-wsp"> </span><span class="coq-sentence"><span class="coq-input"><span class="highlight"><span class="kn">Definition</span> <span class="nf">bind2</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 := + bind f (<span class="kr">fun</span> <span class="nv">xy</span> => g (fst xy) (snd xy)).</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">Definition</span> <span class="nf">handle_error</span> {<span class="nv">A</span>: <span class="kt">Type</span>} (<span class="nv">f</span> <span class="nv">g</span>: mon A) : mon A := + <span class="kr">fun</span> (<span class="nv">s</span> : S.st) => + <span class="kr">match</span> f s <span class="kr">with</span> + | OK a s' i => OK a s' i + | Error _ => g s + <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">Definition</span> <span class="nf">error</span> {<span class="nv">A</span>: <span class="kt">Type</span>} (<span class="nv">err</span>: Errors.errmsg) : mon A := <span class="kr">fun</span> (<span class="nv">s</span>: S.st) => Error err.</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">Definition</span> <span class="nf">get</span> : mon S.st := <span class="kr">fun</span> <span class="nv">s</span> => OK s s (S.st_refl s).</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">Definition</span> <span class="nf">set</span> (<span class="nv">s</span>: S.st) (<span class="nv">i</span>: <span class="kr">forall</span> <span class="nv">s'</span>, S.st_prop s' s) : mon unit := + <span class="kr">fun</span> <span class="nv">s'</span> => OK tt s (i s').</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">Definition</span> <span class="nf">run_mon</span> {<span class="nv">A</span>: <span class="kt">Type</span>} (<span class="nv">s</span>: S.st) (<span class="nv">m</span>: mon A): Errors.res A := + <span class="kr">match</span> m s <span class="kr">with</span> + | OK a s' i => Errors.OK a + | Error err => Errors.Error err + <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">Statemonad</span>.</span></span></span></pre> +</div> +</div></body> +</html> |