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| author | Yann Herklotz <git@yannherklotz.com> | 2021-01-20 14:53:34 +0000 |
|---|---|---|
| committer | Yann Herklotz <git@yannherklotz.com> | 2021-01-20 14:53:34 +0000 |
| commit | 8588ebb4621d85b7ccc738622339b3aa53486c31 (patch) | |
| tree | 89e78e3ec67f884f7062aebb81b68aa54cf5fc1c /docs/proof/Statemonad.html | |
| parent | 34afd2f6ea0fc55cca1c674ab9b2f181be878291 (diff) | |
| download | vericert-8588ebb4621d85b7ccc738622339b3aa53486c31.tar.gz vericert-8588ebb4621d85b7ccc738622339b3aa53486c31.zip | |
Delete documents folder and move to separate repository
Diffstat (limited to 'docs/proof/Statemonad.html')
| -rw-r--r-- | docs/proof/Statemonad.html | 83 |
1 files changed, 0 insertions, 83 deletions
diff --git a/docs/proof/Statemonad.html b/docs/proof/Statemonad.html deleted file mode 100644 index b78049c..0000000 --- a/docs/proof/Statemonad.html +++ /dev/null @@ -1,83 +0,0 @@ -<?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> |