Drezil/emanote
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity
5e48571fda
emanote/static_gen/Haskell/Lenses.html

1801 lines
59 KiB
HTML
Raw Normal View History

addded static site
2022-08-24 14:52:32 +00:00
<!DOCTYPE html>
<html lang='en'>
<head>
<meta charset='UTF-8' />
<meta name='viewport' content='width=device-width, initial-scale=1' />
<title>
Lenses – Home
</title>
<meta property='og:description' content='Die Idee dahinter ist, dass man Zugriffsabstraktionen über Daten verknüpfen kann. Als einfachen Datenstruktur kann man einen Record mit der entsprechenden Syntax nehmen.' />
<meta property='og:site_name' content='Home' />
<meta property='og:image' content />
<meta property='og:type' content='website' />
<meta property='og:title' content='Lenses' />
<base href='/' />
<link href='favicon.svg' rel='icon' />
<script>
window.MathJax = {
startup: {
ready: () => {
MathJax.startup.defaultReady();
}
}
};
</script>
<script async id='MathJax-script' src='https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js'></script>
<!-- mermaid.js --><script src='https://cdn.jsdelivr.net/npm/mermaid/dist/mermaid.min.js'></script>
<script>
mermaid.initialize({startOnLoad:false});
mermaid.init(undefined,document.querySelectorAll(".mermaid"));
</script>
<!-- highlight.js -->
<link rel='stylesheet' href='https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.6.0/styles/hybrid.min.css' />
<script src='https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.6.0/highlight.min.js'></script>
<!-- Include languages that Emanote itself uses -->
<script src='https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.6.0/languages/haskell.min.js'></script>
<script src='https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.6.0/languages/nix.min.js'></script>
<script>hljs.highlightAll();</script>
<link href='tailwind.css?instanceId=faa07eb7-0f7a-4cb2-8347-d9aa01265a0e' rel='stylesheet' type='text/css' />
<!-- Heist error element -->
<style>
strong.error {
color: lightcoral;
font-size: 90%;
font-family: monospace;
}
</style>
<!-- What goes in this file will appear on near the end of <head>--><link rel='preload' href='_emanote-static/fonts/Maven_Pro/MavenPro-VariableFont_wght.ttf' as='font' type='font/ttf' crossorigin />
<style>
@font-face {
font-family: 'MavenPro';
/* FIXME: This ought to be: ${ema:emanoteStaticLayerUrl}/fonts/Maven_Pro/MavenPro-VariableFont_wght.ttf */
src: url(_emanote-static/fonts/Maven_Pro/MavenPro-VariableFont_wght.ttf) format("truetype");
font-display: swap;
}
body {
font-family: 'MavenPro', sans-serif;
/* font-variation-settings: 'wght'300; */
}
a.mavenLinkBold {
font-variation-settings: 'wght'500;
}
strong {
font-variation-settings: 'wght'500;
}
h1,
h2,
h3,
h4,
h5,
h6,
header,
.header-font {
font-family: 'MavenPro', sans-serif;
}
</style>
<link rel='stylesheet' href='_emanote-static/inverted-tree.css' />
<link rel='stylesheet' href='https://files.stork-search.net/releases/v1.5.0/flat.css' />
<!-- Custom Stork-search styling for Emanote -->
<style>
#stork-search-container {
z-index: 1000;
background-color: rgb(15 23 42/.8);
}
.stork-overflow-hidden-important {
overflow: hidden !important;
}
</style>
<script src='https://files.stork-search.net/releases/v1.5.0/stork.js'></script>
<script data-emanote-base-url='/'>
window.emanote = {};
window.emanote.stork = {
searchShown: false,
toggleSearch: function () {
document.getElementById('stork-search-container').classList.toggle('hidden');
window.emanote.stork.searchShown = document.body.classList.toggle('stork-overflow-hidden-important');
if (window.emanote.stork.searchShown) {
document.getElementById('stork-search-input').focus();
}
},
clearSearch: function () {
document.getElementById('stork-search-container').classList.add('hidden');
document.body.classList.remove('stork-overflow-hidden-important');
window.emanote.stork.searchShown = false;
},
init: function () {
const indexName = 'emanote-search'; // used to match input[data-stork] attribute value
const baseUrl = document.currentScript.getAttribute('data-emanote-base-url') || '/';
const indexUrl = baseUrl + '-/stork.st';
if (document.readyState !== 'complete') {
window.addEventListener('load', function () {
stork.register(indexName, indexUrl);
});
document.addEventListener('keydown', event => {
if (window.emanote.stork.searchShown && event.key === 'Escape') {
window.emanote.stork.clearSearch();
event.preventDefault();
} else if ((event.key == 'k' || event.key == 'K') && (event.ctrlKey || event.metaKey)) {
window.emanote.stork.toggleSearch();
event.preventDefault();
}
});
} else {
// Override existing on Ema's hot-reload
stork.register(indexName, indexUrl, { forceOverwrite: true });
}
}
};
window.emanote.stork.init();
</script>
</head>
<!-- DoNotFormat -->
<!-- DoNotFormat -->
<body class='bg-gray-400 overflow-y-scroll'>
<div class='container mx-auto'>
<nav id='breadcrumbs' class='w-full text-gray-700 md:hidden'>
<div class='flex justify-left'>
<div class='w-full px-2 py-2 bg-gray-50'>
<ul class='flex flex-wrap text-lg'>
<li class='inline-flex items-center'>
<img style='width: 1rem;' src='favicon.svg' />
</li>
<li class='inline-flex items-center'>
<a class='px-1 font-bold' href=''>
Home
</a>
<svg fill='currentColor' viewBox='0 0 20 20' class='w-auto h-5 text-gray-400'>
<path fill-rule='evenodd' d='M7.293 14.707a1 1 0 010-1.414L10.586 10 7.293 6.707a1 1 0 011.414-1.414l4 4a1 1 0 010 1.414l-4 4a1 1 0 01-1.414 0z' clip-rule='evenodd'></path>
</svg>
</li>
<li class='inline-flex items-center'>
<a class='px-1 font-bold' href='Haskell'>
Haskell
</a>
<svg fill='currentColor' viewBox='0 0 20 20' class='w-auto h-5 text-gray-400'>
<path fill-rule='evenodd' d='M7.293 14.707a1 1 0 010-1.414L10.586 10 7.293 6.707a1 1 0 011.414-1.414l4 4a1 1 0 010 1.414l-4 4a1 1 0 01-1.414 0z' clip-rule='evenodd'></path>
</svg>
</li>
</ul>
</div>
<button class='inline px-2 py-1 bg-gray-50 outline-none cursor-pointer focus:outline-none' title='Search (Ctrl+K)' type='button' onclick='window.emanote.stork.toggleSearch()'>
<svg xmlns='http://www.w3.org/2000/svg' style='width: 1rem;' class='hover:text-red-700' f
fill='none' viewBox='0 0 24 24' stroke='currentColor' stroke-width='2'>
<path stroke-linecap='round' stroke-linejoin='round' d='M21 21l-6-6m2-5a7 7 0 11-14 0 7 7 0 0114 0z'></path>
</svg>
</button>
<button class='inline px-2 py-1 text-white bg-red-600 outline-none cursor-pointer focus:outline-none' title='Toggle sidebar' type='button' onclick="toggleHidden('sidebar')">
<svg xmlns='http://www.w3.org/2000/svg' class='w-4' fill='none' viewBox='0 0 24 24' stroke='currentColor'>
<path stroke-linecap='round' stroke-linejoin='round' stroke-width='2' d='M4 6h16M4 12h16M4 18h16'></path>
</svg>
</button>
<script>
function toggleHidden(elemId) {
document.getElementById(elemId).classList.toggle("hidden");
}
</script>
</div>
</nav>
<div id='container' class='flex flex-nowrap flex-col md:flex-row bg-gray-50 md:mt-8 md:shadow-2xl md:mb-8'>
<!-- Sidebar column -->
<nav id='sidebar' class='flex-shrink hidden leading-relaxed md:block md:sticky md:top-0 md:h-full md:w-48 xl:w-64'>
<div class='px-2 py-2 text-gray-800'>
<div id='indexing-links' class='flex flex-row float-right p-2 space-x-2 text-gray-500'>
<a href='-/tags' title='View tags'>
<svg style='width: 1rem;' class='hover:text-red-700' fill='none' stroke='currentColor' viewBox='0 0 24 24' xmlns='http://www.w3.org/2000/svg'>
<path stroke-linecap='round' stroke-linejoin='round' stroke-width='2' d='M7 7h.01M7 3h5c.512 0 1.024.195 1.414.586l7 7a2 2 0 010 2.828l-7 7a2 2 0 01-2.828 0l-7-7A1.994 1.994 0 013 12V7a4 4 0 014-4z'>
</path>
</svg>
</a>
<a href='-/all' title='Expand full tree'>
<svg style='width: 1rem;' class='hover:text-red-700' fill='none' stroke='currentColor' viewBox='0 0 24 24' xmlns='http://www.w3.org/2000/svg'>
<path stroke-linecap='round' stroke-linejoin='round' stroke-width='2' d='M4 8V4m0 0h4M4 4l5 5m11-1V4m0 0h-4m4 0l-5 5M4 16v4m0 0h4m-4 0l5-5m11 5l-5-5m5 5v-4m0 4h-4'>
</path>
</svg>
</a>
<a title='Search (Ctrl+K)' class='cursor-pointer' onclick='window.emanote.stork.toggleSearch()'>
<svg xmlns='http://www.w3.org/2000/svg' style='width: 1rem;' class='hover:text-red-700' f
fill='none' viewBox='0 0 24 24' stroke='currentColor' stroke-width='2'>
<path stroke-linecap='round' stroke-linejoin='round' d='M21 21l-6-6m2-5a7 7 0 11-14 0 7 7 0 0114 0z'></path>
</svg>
</a>
</div>
<div id='site-logo' class='pl-2'>
<div class='flex items-center my-2 space-x-2 justify-left'>
<a href='' title='Go to Home'>
<!-- The style width attribute here is to prevent huge
icon from displaying at those rare occasions when Tailwind
hasn't kicked in immediately on page load
-->
<img style='width: 1rem;' class='transition transform hover:scale-110 hover:opacity-80' src='favicon.svg' />
</a>
<a class='font-bold truncate' title='Go to Home' href=''>
Home
</a>
</div>
</div>
<!-- Variable bindings for this tree-->
<!-- Rendering of this tree -->
<div class='pl-2'>
<!-- Node's rootLabel-->
<div class='flex items-center my-2 space-x-2 justify-left'>
<svg xmlns='http://www.w3.org/2000/svg' class='w-4 h-4 flex-shrink-0 inline text-gray-700' viewBox='0 0 20 20' fill='currentColor'>
<path fill-rule='evenodd' d='M2 6a2 2 0 012-2h4l2 2h4a2 2 0 012 2v1H8a3 3 0 00-3 3v1.5a1.5 1.5 0 01-3 0V6z' clip-rule='evenodd'></path>
<path d='M6 12a2 2 0 012-2h8a2 2 0 012 2v2a2 2 0 01-2 2H2h2a2 2 0 002-2v-2z'></path>
</svg>
<a class='font-bold hover:underline truncate' title='About' href='About'>
About
</a>
</div>
<!-- Node's children forest, displayed only on active trees
TODO: Use <details> to toggle visibility?
-->
<!-- Variable bindings for this tree-->
<!-- Rendering of this tree -->
<div class='pl-2'>
<!-- Node's rootLabel-->
<div class='flex items-center my-2 space-x-2 justify-left'>
<svg class='w-4 h-4 flex-shrink-0 inline' fill='none' stroke='currentColor' viewBox='0 0 24 24' xmlns='http://www.w3.org/2000/svg'>
<path stroke-linecap='round' stroke-linejoin='round' stroke-width='2' d='M7 21h10a2 2 0 002-2V9.414a1 1 0 00-.293-.707l-5.414-5.414A1 1 0 0012.586 3H7a2 2 0 00-2 2v14a2 2 0 002 2z'>
</path>
</svg>
<a class='hover:underline truncate' title='Highlights of my experiences in the programming world' href='About/Experience'>
Highlights of my experiences in the programming world
</a>
</div>
<!-- Node's children forest, displayed only on active trees
TODO: Use <details> to toggle visibility?
-->
</div>
<!-- Variable bindings for this tree-->
<!-- Rendering of this tree -->
<div class='pl-2'>
<!-- Node's rootLabel-->
<div class='flex items-center my-2 space-x-2 justify-left'>
<svg class='w-4 h-4 flex-shrink-0 inline' fill='none' stroke='currentColor' viewBox='0 0 24 24' xmlns='http://www.w3.org/2000/svg'>
<path stroke-linecap='round' stroke-linejoin='round' stroke-width='2' d='M7 21h10a2 2 0 002-2V9.414a1 1 0 00-.293-.707l-5.414-5.414A1 1 0 0012.586 3H7a2 2 0 00-2 2v14a2 2 0 002 2z'>
</path>
</svg>
<a class='hover:underline truncate' title='Stefan Dresselhaus' href='About/CV'>
Stefan Dresselhaus
</a>
</div>
<!-- Node's children forest, displayed only on active trees
TODO: Use <details> to toggle visibility?
-->
</div>
<!-- Variable bindings for this tree-->
<!-- Rendering of this tree -->
<div class='pl-2'>
<!-- Node's rootLabel-->
<div class='flex items-center my-2 space-x-2 justify-left'>
<svg class='w-4 h-4 flex-shrink-0 inline' fill='none' stroke='currentColor' viewBox='0 0 24 24' xmlns='http://www.w3.org/2000/svg'>
<path stroke-linecap='round' stroke-linejoin='round' stroke-width='2' d='M7 21h10a2 2 0 002-2V9.414a1 1 0 00-.293-.707l-5.414-5.414A1 1 0 0012.586 3H7a2 2 0 00-2 2v14a2 2 0 002 2z'>
</path>
</svg>
<a class='hover:underline truncate' title='Studium generale / University-Life' href='About/Extracurricular'>
Studium generale / University-Life
</a>
</div>
<!-- Node's children forest, displayed only on active trees
TODO: Use <details> to toggle visibility?
-->
</div>
<!-- Variable bindings for this tree-->
<!-- Rendering of this tree -->
<div class='pl-2'>
<!-- Node's rootLabel-->
<div class='flex items-center my-2 space-x-2 justify-left'>
<svg class='w-4 h-4 flex-shrink-0 inline' fill='none' stroke='currentColor' viewBox='0 0 24 24' xmlns='http://www.w3.org/2000/svg'>
<path stroke-linecap='round' stroke-linejoin='round' stroke-width='2' d='M7 21h10a2 2 0 002-2V9.414a1 1 0 00-.293-.707l-5.414-5.414A1 1 0 0012.586 3H7a2 2 0 00-2 2v14a2 2 0 002 2z'>
</path>
</svg>
<a class='hover:underline truncate' title='Work-Experience' href='About/Work'>
Work-Experience
</a>
</div>
<!-- Node's children forest, displayed only on active trees
TODO: Use <details> to toggle visibility?
-->
</div>
</div>
<!-- Variable bindings for this tree-->
<!-- Rendering of this tree -->
<div class='pl-2'>
<!-- Node's rootLabel-->
<div class='flex items-center my-2 space-x-2 justify-left'>
<svg xmlns='http://www.w3.org/2000/svg' class='w-4 h-4 flex-shrink-0 inline text-gray-700' viewBox='0 0 20 20' fill='currentColor'>
<path fill-rule='evenodd' d='M2 6a2 2 0 012-2h4l2 2h4a2 2 0 012 2v1H8a3 3 0 00-3 3v1.5a1.5 1.5 0 01-3 0V6z' clip-rule='evenodd'></path>
<path d='M6 12a2 2 0 012-2h8a2 2 0 012 2v2a2 2 0 01-2 2H2h2a2 2 0 002-2v-2z'></path>
</svg>
<a class='font-bold hover:underline truncate' title='Android' href='Android'>
Android
</a>
</div>
<!-- Node's children forest, displayed only on active trees
TODO: Use <details> to toggle visibility?
-->
<!-- Variable bindings for this tree-->
<!-- Rendering of this tree -->
<div class='pl-2'>
<!-- Node's rootLabel-->
<div class='flex items-center my-2 space-x-2 justify-left'>
<svg class='w-4 h-4 flex-shrink-0 inline' fill='none' stroke='currentColor' viewBox='0 0 24 24' xmlns='http://www.w3.org/2000/svg'>
<path stroke-linecap='round' stroke-linejoin='round' stroke-width='2' d='M7 21h10a2 2 0 002-2V9.414a1 1 0 00-.293-.707l-5.414-5.414A1 1 0 0012.586 3H7a2 2 0 00-2 2v14a2 2 0 002 2z'>
</path>
</svg>
<a class='hover:underline truncate' title='Einrichtung Android-Smartphones' href='Android/Einrichtung'>
Einrichtung Android-Smartphones
</a>
</div>
<!-- Node's children forest, displayed only on active trees
TODO: Use <details> to toggle visibility?
-->
</div>
</div>
<!-- Variable bindings for this tree-->
<!-- Rendering of this tree -->
<div class='pl-2'>
<!-- Node's rootLabel-->
<div class='flex items-center my-2 space-x-2 justify-left'>
<svg xmlns='http://www.w3.org/2000/svg' class='w-4 h-4 flex-shrink-0 inline text-gray-700' viewBox='0 0 20 20' fill='currentColor'>
<path fill-rule='evenodd' d='M2 6a2 2 0 012-2h4l2 2h4a2 2 0 012 2v1H8a3 3 0 00-3 3v1.5a1.5 1.5 0 01-3 0V6z' clip-rule='evenodd'></path>
<path d='M6 12a2 2 0 012-2h8a2 2 0 012 2v2a2 2 0 01-2 2H2h2a2 2 0 002-2v-2z'></path>
</svg>
<a class='font-bold hover:underline truncate' title='Haskell' href='Haskell'>
Haskell
</a>
</div>
<!-- Node's children forest, displayed only on active trees
TODO: Use <details> to toggle visibility?
-->
<!-- Variable bindings for this tree-->
<!-- Rendering of this tree -->
<div class='pl-2'>
<!-- Node's rootLabel-->
<div class='flex items-center my-2 space-x-2 justify-left'>
<svg xmlns='http://www.w3.org/2000/svg' class='w-4 h-4 flex-shrink-0 inline text-gray-700' viewBox='0 0 20 20' fill='currentColor'>
<path fill-rule='evenodd' d='M2 6a2 2 0 012-2h4l2 2h4a2 2 0 012 2v1H8a3 3 0 00-3 3v1.5a1.5 1.5 0 01-3 0V6z' clip-rule='evenodd'></path>
<path d='M6 12a2 2 0 012-2h8a2 2 0 012 2v2a2 2 0 01-2 2H2h2a2 2 0 002-2v-2z'></path>
</svg>
<a class='font-bold hover:underline truncate' title='Code-Snippets' href='Haskell/Code%20Snippets'>
Code-Snippets
</a>
</div>
<!-- Node's children forest, displayed only on active trees
TODO: Use <details> to toggle visibility?
-->
<!-- Variable bindings for this tree-->
<!-- Rendering of this tree -->
<div class='pl-2'>
<!-- Node's rootLabel-->
<div class='flex items-center my-2 space-x-2 justify-left'>
<svg class='w-4 h-4 flex-shrink-0 inline' fill='none' stroke='currentColor' viewBox='0 0 24 24' xmlns='http://www.w3.org/2000/svg'>
<path stroke-linecap='round' stroke-linejoin='round' stroke-width='2' d='M7 21h10a2 2 0 002-2V9.414a1 1 0 00-.293-.707l-5.414-5.414A1 1 0 0012.586 3H7a2 2 0 00-2 2v14a2 2 0 002 2z'>
</path>
</svg>
<a class='hover:underline truncate' title='*-Morpisms' href='Haskell/Code%20Snippets/Morphisms'>
*-Morpisms
</a>
</div>
<!-- Node's children forest, displayed only on active trees
TODO: Use <details> to toggle visibility?
-->
</div>
<!-- Variable bindings for this tree-->
<!-- Rendering of this tree -->
<div class='pl-2'>
<!-- Node's rootLabel-->
<div class='flex items-center my-2 space-x-2 justify-left'>
<svg class='w-4 h-4 flex-shrink-0 inline' fill='none' stroke='currentColor' viewBox='0 0 24 24' xmlns='http://www.w3.org/2000/svg'>
<path stroke-linecap='round' stroke-linejoin='round' stroke-width='2' d='M7 21h10a2 2 0 002-2V9.414a1 1 0 00-.293-.707l-5.414-5.414A1 1 0 0012.586 3H7a2 2 0 00-2 2v14a2 2 0 002 2z'>
</path>
</svg>
<a class='hover:underline truncate' title='Monoid? Da war doch was…' href='Haskell/Code%20Snippets/Monoid'>
Monoid? Da war doch was…
</a>
</div>
<!-- Node's children forest, displayed only on active trees
TODO: Use <details> to toggle visibility?
-->
</div>
</div>
<!-- Variable bindings for this tree-->
<!-- Rendering of this tree -->
<div class='pl-2'>
<!-- Node's rootLabel-->
<div class='flex items-center my-2 space-x-2 justify-left'>
<svg class='w-4 h-4 flex-shrink-0 inline' fill='none' stroke='currentColor' viewBox='0 0 24 24' xmlns='http://www.w3.org/2000/svg'>
<path stroke-linecap='round' stroke-linejoin='round' stroke-width='2' d='M7 21h10a2 2 0 002-2V9.414a1 1 0 00-.293-.707l-5.414-5.414A1 1 0 0012.586 3H7a2 2 0 00-2 2v14a2 2 0 002 2z'>
</path>
</svg>
<a class='hover:underline truncate' title='Fortgeschrittene funktionale Programmierung in Haskell' href='Haskell/FFPiH'>
Fortgeschrittene funktionale Programmierung in Haskell
</a>
</div>
<!-- Node's children forest, displayed only on active trees
TODO: Use <details> to toggle visibility?
-->
</div>
<!-- Variable bindings for this tree-->
<!-- Rendering of this tree -->
<div class='pl-2'>
<!-- Node's rootLabel-->
<div class='flex items-center my-2 space-x-2 justify-left'>
<svg class='w-4 h-4 flex-shrink-0 inline' fill='none' stroke='currentColor' viewBox='0 0 24 24' xmlns='http://www.w3.org/2000/svg'>
<path stroke-linecap='round' stroke-linejoin='round' stroke-width='2' d='M9 12h6m-6 4h6m2 5H7a2 2 0 01-2-2V5a2 2 0 012-2h5.586a1 1 0 01.707.293l5.414 5.414a1 1 0 01.293.707V19a2 2 0 01-2 2z'>
</path>
</svg>
<a class='font-bold text-red-600 hover:underline truncate' title='Lenses' href='Haskell/Lenses'>
Lenses
</a>
</div>
<!-- Node's children forest, displayed only on active trees
TODO: Use <details> to toggle visibility?
-->
</div>
<!-- Variable bindings for this tree-->
<!-- Rendering of this tree -->
<div class='pl-2'>
<!-- Node's rootLabel-->
<div class='flex items-center my-2 space-x-2 justify-left'>
<svg class='w-4 h-4 flex-shrink-0 inline' fill='none' stroke='currentColor' viewBox='0 0 24 24' xmlns='http://www.w3.org/2000/svg'>
<path stroke-linecap='round' stroke-linejoin='round' stroke-width='2' d='M7 21h10a2 2 0 002-2V9.414a1 1 0 00-.293-.707l-5.414-5.414A1 1 0 0012.586 3H7a2 2 0 00-2 2v14a2 2 0 002 2z'>
</path>
</svg>
<a class='hover:underline truncate' title='Talks und Posts zu Haskell' href='Haskell/Advantages'>
Talks und Posts zu Haskell
</a>
</div>
<!-- Node's children forest, displayed only on active trees
TODO: Use <details> to toggle visibility?
-->
</div>
<!-- Variable bindings for this tree-->
<!-- Rendering of this tree -->
<div class='pl-2'>
<!-- Node's rootLabel-->
<div class='flex items-center my-2 space-x-2 justify-left'>
<svg class='w-4 h-4 flex-shrink-0 inline' fill='none' stroke='currentColor' viewBox='0 0 24 24' xmlns='http://www.w3.org/2000/svg'>
<path stroke-linecap='round' stroke-linejoin='round' stroke-width='2' d='M7 21h10a2 2 0 002-2V9.414a1 1 0 00-.293-.707l-5.414-5.414A1 1 0 0012.586 3H7a2 2 0 00-2 2v14a2 2 0 002 2z'>
</path>
</svg>
<a class='hover:underline truncate' title='Webapp-Development in Haskell' href='Haskell/Webapp_Development'>
Webapp-Development in Haskell
</a>
</div>
<!-- Node's children forest, displayed only on active trees
TODO: Use <details> to toggle visibility?
-->
</div>
</div>
<!-- Variable bindings for this tree-->
<!-- Rendering of this tree -->
<div class='pl-2'>
<!-- Node's rootLabel-->
<div class='flex items-center my-2 space-x-2 justify-left'>
<svg class='w-4 h-4 flex-shrink-0 inline' fill='none' stroke='currentColor' viewBox='0 0 24 24' xmlns='http://www.w3.org/2000/svg'>
<path stroke-linecap='round' stroke-linejoin='round' stroke-width='2' d='M7 21h10a2 2 0 002-2V9.414a1 1 0 00-.293-.707l-5.414-5.414A1 1 0 0012.586 3H7a2 2 0 00-2 2v14a2 2 0 002 2z'>
</path>
</svg>
<a class='hover:underline truncate' title='Logik für Dummies' href='Logik'>
Logik für Dummies
</a>
</div>
<!-- Node's children forest, displayed only on active trees
TODO: Use <details> to toggle visibility?
-->
</div>
<!-- Variable bindings for this tree-->
<!-- Rendering of this tree -->
<div class='pl-2'>
<!-- Node's rootLabel-->
<div class='flex items-center my-2 space-x-2 justify-left'>
<svg xmlns='http://www.w3.org/2000/svg' class='w-4 h-4 flex-shrink-0 inline text-gray-700' viewBox='0 0 20 20' fill='currentColor'>
<path fill-rule='evenodd' d='M2 6a2 2 0 012-2h4l2 2h4a2 2 0 012 2v1H8a3 3 0 00-3 3v1.5a1.5 1.5 0 01-3 0V6z' clip-rule='evenodd'></path>
<path d='M6 12a2 2 0 012-2h8a2 2 0 012 2v2a2 2 0 01-2 2H2h2a2 2 0 002-2v-2z'></path>
</svg>
<a class='font-bold hover:underline truncate' title='Uni' href='Uni'>
Uni
</a>
</div>
<!-- Node's children forest, displayed only on active trees
TODO: Use <details> to toggle visibility?
-->
<!-- Variable bindings for this tree-->
<!-- Rendering of this tree -->
<div class='pl-2'>
<!-- Node's rootLabel-->
<div class='flex items-center my-2 space-x-2 justify-left'>
<svg class='w-4 h-4 flex-shrink-0 inline' fill='none' stroke='currentColor' viewBox='0 0 24 24' xmlns='http://www.w3.org/2000/svg'>
<path stroke-linecap='round' stroke-linejoin='round' stroke-width='2' d='M7 21h10a2 2 0 002-2V9.414a1 1 0 00-.293-.707l-5.414-5.414A1 1 0 0012.586 3H7a2 2 0 00-2 2v14a2 2 0 002 2z'>
</path>
</svg>
<a class='hover:underline truncate' title='Wie lerne ich richtig an der Uni?' href='Uni/Lernerfolg_an_der_Uni'>
Wie lerne ich richtig an der Uni?
</a>
</div>
<!-- Node's children forest, displayed only on active trees
TODO: Use <details> to toggle visibility?
-->
</div>
</div>
<!-- Variable bindings for this tree-->
<!-- Rendering of this tree -->
<div class='pl-2'>
<!-- Node's rootLabel-->
<div class='flex items-center my-2 space-x-2 justify-left'>
<svg xmlns='http://www.w3.org/2000/svg' class='w-4 h-4 flex-shrink-0 inline text-gray-700' viewBox='0 0 20 20' fill='currentColor'>
<path fill-rule='evenodd' d='M2 6a2 2 0 012-2h4l2 2h4a2 2 0 012 2v1H8a3 3 0 00-3 3v1.5a1.5 1.5 0 01-3 0V6z' clip-rule='evenodd'></path>
<path d='M6 12a2 2 0 012-2h8a2 2 0 012 2v2a2 2 0 01-2 2H2h2a2 2 0 002-2v-2z'></path>
</svg>
<a class='font-bold hover:underline truncate' title='Unix' href='Unix'>
Unix
</a>
</div>
<!-- Node's children forest, displayed only on active trees
TODO: Use <details> to toggle visibility?
-->
<!-- Variable bindings for this tree-->
<!-- Rendering of this tree -->
<div class='pl-2'>
<!-- Node's rootLabel-->
<div class='flex items-center my-2 space-x-2 justify-left'>
<svg class='w-4 h-4 flex-shrink-0 inline' fill='none' stroke='currentColor' viewBox='0 0 24 24' xmlns='http://www.w3.org/2000/svg'>
<path stroke-linecap='round' stroke-linejoin='round' stroke-width='2' d='M7 21h10a2 2 0 002-2V9.414a1 1 0 00-.293-.707l-5.414-5.414A1 1 0 0012.586 3H7a2 2 0 00-2 2v14a2 2 0 002 2z'>
</path>
</svg>
<a class='hover:underline truncate' title='SSH-Filter' href='Unix/SSH-Filter'>
SSH-Filter
</a>
</div>
<!-- Node's children forest, displayed only on active trees
TODO: Use <details> to toggle visibility?
-->
</div>
</div>
</div>
</nav>
<!-- Main body column -->
<div class='flex-1 w-full overflow-x-auto bg-white'>
<main class='px-4 py-4'>
<!-- DoNotFormat -->
<!-- DoNotFormat -->
<nav id='uptree' class='flipped tree' style='transform-origin: 50%;'>
<ul class='root'>
<li>
<ul>
<li>
<div class='text-gray-900 forest-link'>
<a href='Haskell/Advantages'>
Talks und Posts zu Haskell
</a>
</div>
<ul>
<li>
<div class='text-gray-900 forest-link'>
<a href='Haskell'>
Haskell
</a>
</div>
<ul>
<li>
<div class='text-gray-900 forest-link'>
<a href=''>
Home
</a>
</div>
</li>
</ul>
</li>
</ul>
</li>
<li>
<div class='text-gray-900 forest-link'>
<a href='Haskell/FFPiH'>
Fortgeschrittene funktionale Programmierung in Haskell
</a>
</div>
<ul>
<li>
<div class='text-gray-900 forest-link'>
<a href='About/CV'>
Stefan Dresselhaus
</a>
</div>
<ul>
<li>
<div class='text-gray-900 forest-link'>
<a href='About'>
About
</a>
</div>
</li>
</ul>
</li>
<li>
<div class='text-gray-900 forest-link'>
<a href='About/Extracurricular'>
Studium generale / University-Life
</a>
</div>
</li>
</ul>
</li>
</ul>
</li>
</ul>
</nav>
<h1 class='flex items-end justify-center mb-4 p-3 bg-red-100 text-5xl font-extrabold text-black rounded'>
<a class='z-40 tracking-tighter '>
Lenses
</a>
</h1>
<article class='overflow-auto'>
<!-- What goes in this file will appear on top of note body-->
<h2 id='wofür-brauchen-wir-das-überhaupt' class='inline-block mt-6 mb-4 text-4xl font-bold text-gray-700 border-b-2'>Wofür brauchen wir das überhaupt?</h2>
<p class='mb-3'>
Die Idee dahinter ist, dass man Zugriffsabstraktionen über Daten verknüpfen kann. Als einfachen Datenstruktur kann man einen Record mit der entsprechenden Syntax nehmen.
</p>
<h3 id='beispiel' class='mt-6 mb-2 text-3xl font-bold text-gray-700'>Beispiel</h3><div class='py-0.5 mb-3 text-sm'><pre><code class='haskell language-haskell numberLines'>data Person = P { name :: String
, addr :: Address
, salary :: Int }
data Address = A { road :: String
, city :: String
, postcode :: String }
-- autogeneriert unten anderem: addr :: Person -&gt; Address
setName :: String -&gt; Person -&gt; Person
setName n p = p { name = n } --record update notation
setPostcode :: String -&gt; Person -&gt; Person
setPostcode pc p
= p { addr = addr p { postcode = pc } }
-- update of a record inside a record</code></pre></div><h3 id='probleme' class='mt-6 mb-2 text-3xl font-bold text-gray-700'>Probleme</h3>
<p class='mb-3'>
Probleme mit diesem Code:
</p>
<ul class='my-3 ml-6 space-y-1 list-disc'>
<li>
für 1-Dimensionale Felder ist die record-syntax ok.
</li>
<li>
tiefere Ebenen nur umständlich zu erreichen
</li>
<li>
eigentlich wollen wir nur pe in p setzen, müssen aber über addr etc. gehen.
</li>
<li>
wir brauchen wissen über die “Zwischenstrukturen”, an denen wir nicht interessiert sind
</li>
</ul>
<h3 id='was-wir-gern-hätten' class='mt-6 mb-2 text-3xl font-bold text-gray-700'>Was wir gern hätten</h3><div class='py-0.5 mb-3 text-sm'><pre><code class='haskell language-haskell numberLines'>data Person = P { name :: String
, addr :: Address
, salary :: Int }
-- a lens for each field
lname :: Lens' Person String
laddr :: Lens' Person Adress
lsalary :: Lens' Person Int
-- getter/setter for them
view :: Lens' s a -&gt; s -&gt; a
set :: Lens' s a -&gt; a -&gt; s -&gt; s
-- lens-composition
composeL :: Lens' s1 s2 -&gt; Lens s2 a -&gt; Lens' s1 a</code></pre></div><h3 id='wie-uns-das-hilft' class='mt-6 mb-2 text-3xl font-bold text-gray-700'>Wie uns das hilft</h3>
<p class='mb-3'>
Mit diesen Dingen (wenn wir sie hätten) könnte man dann
</p>
<div class='py-0.5 mb-3 text-sm'><pre><code class='haskell language-haskell numberLines'>data Person = P { name :: String
, addr :: Address
, salary :: Int }
data Address = A { road :: String
, city :: String
, postcode :: String }
setPostcode :: String -&gt; Person -&gt; Person
setPostcode pc p
= set (laddr `composeL` lpostcode) pc p</code></pre></div>
<p class='mb-3'>
machen und wäre fertig.
</p>
<h2 id='trivialer-ansatz' class='inline-block mt-6 mb-4 text-4xl font-bold text-gray-700 border-b-2'>Trivialer Ansatz</h2><h3 id='gettersetter-als-lens-methoden' class='mt-6 mb-2 text-3xl font-bold text-gray-700'>Getter/Setter als Lens-Methoden</h3><div class='py-0.5 mb-3 text-sm'><pre><code class='haskell language-haskell numberLines'>data LensR s a = L { viewR :: s -&gt; a
, setR :: a -&gt; s -&gt; s }
composeL (L v1 u1) (L v2 u2)
= L (\s -&gt; v2 (v1 s))
(\a s -&gt; u1 (u2 a (v1 s)) s)</code></pre></div><h3 id='wieso-ist-das-schlecht' class='mt-6 mb-2 text-3xl font-bold text-gray-700'>Wieso ist das schlecht?</h3>
<ul class='my-3 ml-6 space-y-1 list-disc'>
<li>
extrem ineffizient
</li>
</ul>
<p class='mb-3'>
Auslesen traversiert die Datenstruktur, dann wird die Funktion angewendet und zum setzen wird die Datenstruktur erneut traversiert:
</p>
<div class='py-0.5 mb-3 text-sm'><pre><code class='haskell language-haskell numberLines'>over :: LensR s a -&gt; (a -&gt; a) -&gt; s -&gt; s
over ln f s = setR l (f (viewR l s)) s</code></pre></div>
<ul class='my-3 ml-6 space-y-1 list-disc'>
<li>
Lösung: modify-funktion hinzufügen
</li>
</ul>
<div class='py-0.5 mb-3 text-sm'><pre><code class='haskell language-haskell numberLines'>data LensR s a
= L { viewR :: s -&gt; a
, setR :: a -&gt; s -&gt; s
, mod :: (a-&gt;a) -&gt; s -&gt; s
, modM :: (a-&gt;Maybe a) -&gt; s -&gt; Maybe s
, modIO :: (a-&gt;IO a) -&gt; s -&gt; IO s }</code></pre></div>
<p class='mb-3'>
Neues Problem: Für jeden Spezialfall muss die Lens erweitert werden.
</p>
<h3 id='something-in-common' class='mt-6 mb-2 text-3xl font-bold text-gray-700'>Something in common</h3>
<p class='mb-3'>
Man kann alle Monaden abstrahieren. Functor reicht schon:
</p>
<div class='py-0.5 mb-3 text-sm'><pre><code class='haskell language-haskell numberLines'>data LensR s a
= L { viewR :: s -&gt; a
, setR :: a -&gt; s -&gt; s
, mod :: (a-&gt;a) -&gt; s -&gt; s
, modF :: Functor f =&gt; (a-&gt;f a) -&gt; s -&gt; f s }</code></pre></div>
<p class='mb-3'>
Idee: Die 3 darüberliegenden durch modF ausdrücken.
</p>
<h3 id='typ-einer-lens' class='mt-6 mb-2 text-3xl font-bold text-gray-700'>Typ einer Lens</h3>
<p class='mb-3'>
Wenn man das berücksichtigt, dann hat einen Lens folgenden Typ:
</p>
<div class='py-0.5 mb-3 text-sm'><pre><code class='haskell language-haskell'>type Lens' s a = forall f. Functor f
=&gt; (a -&gt; f a) -&gt; s -&gt; f s</code></pre></div>
<p class='mb-3'>
Allerdings haben wir dann noch unseren getter/setter:
</p>
<div class='py-0.5 mb-3 text-sm'><pre><code class='haskell language-haskell'>data LensR s a = L { viewR :: s -&gt; a
, setR :: a -&gt; s -&gt; s }</code></pre></div>
<p class='mb-3'>
Stellt sich raus: Die sind isomorph! Auch wenn die von den Typen her komplett anders aussehen.
</p>
<h2 id='benutzen-einer-lens-als-setter' class='inline-block mt-6 mb-4 text-4xl font-bold text-gray-700 border-b-2'>Benutzen einer Lens als Setter</h2><div class='py-0.5 mb-3 text-sm'><pre><code class='haskell language-haskell numberLines'>set :: Lens' s a -&gt; (a -&gt; s -&gt; s)
set ln a s = --...umm...
--:t ln =&gt; (a -&gt; f a) -&gt; s -&gt; f s
-- =&gt; get s out of f s to return it</code></pre></div>
<p class='mb-3'>
Wir können für f einfach die “Identity”-Monade nehmen, die wir nachher wegcasten können.
</p>
<div class='py-0.5 mb-3 text-sm'><pre><code class='haskell language-haskell numberLines'>newtype Identity a = Identity a
-- Id :: a -&gt; Identity a
runIdentity :: Identity s -&gt; s
runIdentity (Identity x) = x
instance Functor Identity where
fmap f (Identity x) = Identity (f x)</code></pre></div>
<p class='mb-3'>
somit ist set einfach nur
</p>
<div class='py-0.5 mb-3 text-sm'><pre><code class='haskell language-haskell numberLines'>set :: Lens' s a -&gt; (a -&gt; s -&gt; s)
set ln x s
= runIdentity (ls set_fld s)
where
set_fld :: a -&gt; Identity a
set_fld _ = Identity x
-- a was the OLD value.
-- We throw that away and set the new value</code></pre></div>
<p class='mb-3'>
oder kürzer (für nerds wie den Autor der Lens-Lib)
</p>
<div class='py-0.5 mb-3 text-sm'><pre><code class='haskell language-haskell'>set :: Lens' s a -&gt; (a -&gt; s -&gt; s)
set ln x = runIdentity . ln (Identity . const x)</code></pre></div><h2 id='benutzen-einer-lens-als-modify' class='inline-block mt-6 mb-4 text-4xl font-bold text-gray-700 border-b-2'>Benutzen einer Lens als Modify</h2>
<p class='mb-3'>
Dasselbe wie Set, nur dass wir den Parameter nicht entsorgen, sondern in die mitgelieferte Funktion stopfen.
</p>
<div class='py-0.5 mb-3 text-sm'><pre><code class='haskell language-haskell'>over :: Lens' s a -&gt; (a -&gt; a) -&gt; s -&gt; s
over ln f = runIdentity . ln (Identity . f)</code></pre></div><h2 id='benutzen-einer-lens-als-getter' class='inline-block mt-6 mb-4 text-4xl font-bold text-gray-700 border-b-2'>Benutzen einer Lens als Getter</h2><div class='py-0.5 mb-3 text-sm'><pre><code class='haskell language-haskell numberLines'>view :: Lens' s a -&gt; (s -&gt; a)
view ln s = --...umm...
--:t ln =&gt; (a -&gt; f a) -&gt; s -&gt; f s
-- =&gt; get a out of the (f s) return-value
-- Wait, WHAT?</code></pre></div>
<p class='mb-3'>
Auch hier gibt es einen netten Funktor. Wir packen das “a” einfach in das “f” und werfen das “s” am Ende weg.
</p>
<div class='py-0.5 mb-3 text-sm'><pre><code class='haskell language-haskell numberLines'>newtype Const v a = Const v
getConst :: Const v a -&gt; v
getConst (Const x) = x
instance Functor (Const v) where
fmap f (Const x) = Const x
-- throw f away. Nothing changes our const!</code></pre></div>
<p class='mb-3'>
somit ergibt sich
</p>
<div class='py-0.5 mb-3 text-sm'><pre><code class='haskell language-haskell numberLines'>view :: Lens' s a -&gt; (s -&gt; a)
view ln s
= getConst (ln Const s)
-- Const :: s -&gt; Const a s</code></pre></div>
<p class='mb-3'>
oder nerdig
</p>
<div class='py-0.5 mb-3 text-sm'><pre><code class='haskell language-haskell'>view :: Lens' s a -&gt; (s -&gt; a)
view ln = getConst . ln Const</code></pre></div><h2 id='lenses-bauen' class='inline-block mt-6 mb-4 text-4xl font-bold text-gray-700 border-b-2'>Lenses bauen</h2>
<p class='mb-3'>
Nochmal kurz der Typ:
</p>
<div class='py-0.5 mb-3 text-sm'><pre><code class='haskell language-haskell'>type Lens' s a = forall f. Functor f
=&gt; (a -&gt; f a) -&gt; s -&gt; f s</code></pre></div>
<p class='mb-3'>
Für unser Personen-Beispiel vom Anfang:
</p>
<div class='py-0.5 mb-3 text-sm'><pre><code class='haskell language-haskell numberLines'>data Person = P { _name :: String, _salary :: Int }
name :: Lens' Person String
-- name :: Functor f =&gt; (String -&gt; f String)
-- -&gt; Person -&gt; f Person
name elt_fn (P n s)
= fmap (\n' -&gt; P n' s) (elt_fn n)
-- fmap :: Functor f =&gt; (a-&gt;b) -&gt; f a -&gt; f b - der Funktor, der alles verknüpft
-- \n' -&gt; .. :: String -&gt; Person - Funktion um das Element zu lokalisieren (WO wird ersetzt/gelesen/...)
-- elt_fn n :: f String - Funktion um das Element zu verändern (setzen, ändern, ...)</code></pre></div>
<p class='mb-3'>
Die Lambda-Funktion ersetzt einfach den Namen. Häufig sieht man auch
</p>
<div class='py-0.5 mb-3 text-sm'><pre><code class='haskell language-haskell'>name elt_fn (P n s)
= (\n' -&gt; P n' s) &lt;$&gt; (elt_fn n)
-- | Focus | |Function|</code></pre></div><h2 id='wie-funktioniert-das-intern' class='inline-block mt-6 mb-4 text-4xl font-bold text-gray-700 border-b-2'>Wie funktioniert das intern?</h2><div class='py-0.5 mb-3 text-sm'><pre><code class='haskell language-haskell numberLines'>view name (P {_name="Fred", _salary=100})
-- inline view-function
= getConst (name Const (P {_name="Fred", _salary=100})
-- inline name
= getConst (fmap (\n' -&gt; P n' 100) (Const "Fred"))
-- fmap f (Const x) = Const x - Definition von Const
= getConst (Const "Fred")
-- getConst (Const x) = x
= "Fred"</code></pre></div>
<p class='mb-3'>
Dieser Aufruf hat KEINE Runtime-Kosten, weil der Compiler direkt die Adresse des Feldes einsetzen kann. Der gesamte Boilerplate-Code wird vom Compiler wegoptimiert.
</p>
<p class='mb-3'>
Dies gilt für jeden Funktor mit newtype, da das nur ein Typalias ist.
</p>
<h2 id='composing-lenses-und-deren-benutzung' class='inline-block mt-6 mb-4 text-4xl font-bold text-gray-700 border-b-2'>Composing Lenses und deren Benutzung</h2>
<p class='mb-3'>
Wie sehen denn die Typen aus?
</p>
<p class='mb-3'>
Wir wollen ein
</p>
<blockquote class='py-0.5 px-4 mb-3 italic border-l-4 bg-gray-50 text-gray-600 border-gray-400 quote'>
<p class='mb-3'>
Lens’ s1 s2 -&gt; Lens’ s2 a -&gt; Lens’ s1 a
</p>
</blockquote>
<p class='mb-3'>
Wir haben 2 Lenses
</p>
<blockquote class='py-0.5 px-4 mb-3 italic border-l-4 bg-gray-50 text-gray-600 border-gray-400 quote'>
<p class='mb-3'>
ln1 :: (s2 -&gt; f s2) -&gt; (s1 -&gt; f s1) ln2 :: (a -&gt; f a) -&gt; (s2 -&gt; f s2)
</p>
</blockquote>
<p class='mb-3'>
wenn man scharf hinsieht, kann man die verbinden
</p>
<blockquote class='py-0.5 px-4 mb-3 italic border-l-4 bg-gray-50 text-gray-600 border-gray-400 quote'>
<p class='mb-3'>
ln1 . ln2 :: (a -&gt; f s) -&gt; (s1 -&gt; f s1)
</p>
</blockquote>
<p class='mb-3'>
und erhält eine Lens. Sogar die Gewünschte!<br />Somit ist Lens-Composition einfach nur Function-Composition (.).
</p>
<h2 id='automatisieren-mit-template-haskell' class='inline-block mt-6 mb-4 text-4xl font-bold text-gray-700 border-b-2'>Automatisieren mit Template-Haskell</h2>
<p class='mb-3'>
Der Code um die Lenses zu bauen ist für records immer Identisch:
</p>
<div class='py-0.5 mb-3 text-sm'><pre><code class='haskell language-haskell numberLines'>data Person = P { _name :: String, _salary :: Int }
name :: Lens' Person String
name elt_fn (P n s) = (\n' -&gt; P n' s) &lt;$&gt; (elt_fn n)</code></pre></div>
<p class='mb-3'>
Daher kann man einfach
</p>
<div class='py-0.5 mb-3 text-sm'><pre><code class='haskell language-haskell numberLines'>import Control.Lens.TH
data Person = P { _name :: String, _salary :: Int }
$(makeLenses ''Person)</code></pre></div>
<p class='mb-3'>
nehmen, was einem eine Lens für “name” und eine Lens für “salary” generiert.<br />Mit anderen Templates kann man auch weitere Dinge steuern (etwa wofür Lenses generiert werden, welches Prefix (statt _) man haben will etc. pp.).
</p>
<p class='mb-3'>
Will man das aber haben, muss man selbst in den Control.Lens.TH-Code schauen.
</p>
<h2 id='lenses-für-den-beispielcode' class='inline-block mt-6 mb-4 text-4xl font-bold text-gray-700 border-b-2'>Lenses für den Beispielcode</h2><div class='py-0.5 mb-3 text-sm'><pre><code class='haskell language-haskell numberLines'>import Control.Lens.TH
data Person = P { _name :: String
, _addr :: Address
, _salary :: Int }
data Address = A { _road :: String
, _city :: String
, _postcode :: String }
$(makeLenses ''Person)
$(makeLenses ''Address)
setPostcode :: String -&gt; Person -&gt; Person
setPostcode pc p = set (addr . postcode) pc p</code></pre></div><h2 id='shortcuts-mit-line-noise' class='inline-block mt-6 mb-4 text-4xl font-bold text-gray-700 border-b-2'>Shortcuts mit “Line-Noise”</h2><div class='py-0.5 mb-3 text-sm'><pre><code class='haskell language-haskell numberLines'>-- ...
setPostcode :: String -&gt; Person -&gt; Person
setPostcode pc p = addr . postcode .~ pc $ p
-- | Focus |set|to what|in where
getPostcode :: Person -&gt; String
getPostcode p = p ^. $ addr . postcode
-- |from|get| Focus |</code></pre></div>
<p class='mb-3'>
Es gibt drölf-zillionen weitere Infix-Operatoren (für Folds, Listenkonvertierungen, -traversierungen, …)
</p>
<h2 id='virtuelle-felder' class='inline-block mt-6 mb-4 text-4xl font-bold text-gray-700 border-b-2'>Virtuelle Felder</h2>
<p class='mb-3'>
Man kann mit Lenses sogar Felder emulieren, die gar nicht da sind. Angenommen folgender Code:
</p>
<div class='py-0.5 mb-3 text-sm'><pre><code class='haskell language-haskell numberLines'>data Temp = T { _fahrenheit :: Float }
$(makeLenses ''Temp)
-- liefert Lens: fahrenheit :: Lens Temp Float
centigrade :: Lens Temp Float
centigrade centi_fn (T faren)
= (\centi' -&gt; T (cToF centi'))
&lt;$&gt; (centi_fn (fToC faren))
-- cToF & fToC as Converter-Functions defined someplace else</code></pre></div>
<p class='mb-3'>
Hiermit kann man dann auch Funktionen, die auf Grad-Celsius rechnen auf Daten anwenden, die eigenlich nur Fahrenheit speichern, aber eine Umrechnung bereitstellen. Analog kann man auch einen Zeit-Datentypen definieren, der intern mit Sekunden rechnet (und somit garantiert frei von Fehlern wie -3 Minuten oder 37 Stunden ist)
</p>
<h2 id='non-record-strukturen' class='inline-block mt-6 mb-4 text-4xl font-bold text-gray-700 border-b-2'>Non-Record Strukturen</h2>
<p class='mb-3'>
Das ganze kann man auch parametrisieren und auf Non-Record-Strukturen anwenden. Beispielhaft an einer Map verdeutlicht:
</p>
<div class='py-0.5 mb-3 text-sm'><pre><code class='haskell language-haskell numberLines'>-- from Data.Lens.At
at :: Ord k =&gt; k -&gt; Lens' (Map k v) (Maybe v)
-- oder identisch, wenn man die Lens' auflöst:
at :: Ord k, forall f. Functor f =&gt; k -&gt; (Maybe v -&gt; f Maybe v) -&gt; Map k v -&gt; f Map k v
at k mb_fn m
= wrap &lt;$&gt; (mb_fn mv)
where
mv = Map.lookup k m
wrap :: Maybe v -&gt; Map k v
wrap (Just v') = Map.insert k v' m
wrap Nothing = case mv of
Nothing -&gt; m
Just _ -&gt; Map.delete k m
-- mb_fn :: Maybe v -&gt; f Maybe v</code></pre></div><h2 id='weitere-beispiele' class='inline-block mt-6 mb-4 text-4xl font-bold text-gray-700 border-b-2'>Weitere Beispiele</h2>
<ul class='my-3 ml-6 space-y-1 list-disc'>
<li>
<p class='mb-3'>
Bitfields auf Strukturen die Bits haben (Ints, …) in Data.Bits.Lens
</p>
</li>
<li>
<p class='mb-3'>
Web-scraper in Package hexpat-lens
</p>
<div class='py-0.5 mb-3 text-sm'><pre><code class='haskell language-haskell numberLines'>p ^.. _HTML' . to allNodes
. traverse . named "a"
. traverse . ix "href"
. filtered isLocal
. to trimSpaces</code></pre></div>
<p class='mb-3'>
Zieht alle externen Links aus dem gegebenen HTML-Code in p um weitere ziele fürs crawlen zu finden.
</p>
</li>
</ul>
<h2 id='erweiterungen' class='inline-block mt-6 mb-4 text-4xl font-bold text-gray-700 border-b-2'>Erweiterungen</h2>
<p class='mb-3'>
Bisher hatten wir Lenses nur auf Funktoren F. Die nächstmächtigere Klasse ist Applicative.
</p>
<div class='py-0.5 mb-3 text-sm'><pre><code class='haskell language-haskell numberLines'>type Traversal' s a = forall f. Applicative f
=&gt; (a -&gt; f a) -&gt; (s -&gt; f s)</code></pre></div>
<p class='mb-3'>
Da wir den Container identisch lassen (weder s noch a wurde angefasst) muss sich etwas anderes ändern. Statt eines einzelnen Focus erhalten wir viele Foci.
</p>
<p class='mb-3'>
Was ist ein Applicative überhaupt? Eine schwächere Monade (nur 1x Anwendung und kein Bind - dafür kann man die beliebig oft hintereinanderhängen).
</p>
<div class='py-0.5 mb-3 text-sm'><pre><code class='haskell language-haskell numberLines'>class Functor f =&gt; Applicative f where
pure :: a -&gt; f a
(&lt;*&gt;) :: f (a -&gt; b) -&gt; f a -&gt; f b
-- Monade als Applicative:
pure = return
mf &lt;*&gt; mx = do { f &lt;- mf; x &lt;- mx; return (f x) }</code></pre></div>
<p class='mb-3'>
Recap: Was macht eine Lens:
</p>
<div class='py-0.5 mb-3 text-sm'><pre><code class='haskell language-haskell numberLines'>data Adress = A { _road :: String
, _city :: String
, _postcode :: String }
road :: Lens' Adress String
road elt_fn (A r c p) = (\r' -&gt; A r' c p) &lt;$&gt; (elt_fn r)
-- | "Hole" | | Thing to put in|</code></pre></div>
<p class='mb-3'>
Wenn man nun road & city gleichzeitig bearbeiten will:
</p>
<div class='py-0.5 mb-3 text-sm'><pre><code class='haskell language-haskell numberLines'>addr_strs :: Traversal' Address String
addr_strs elt_fn (A r c p)
= ... (\r' c' -&gt; A r' c' p) .. (elt_fn r) .. (elt_fn c) ..
-- | function with 2 "Holes"| first Thing | second Thing</code></pre></div>
<p class='mb-3'>
fmap kann nur 1 Loch stopfen, aber nicht mit n Löchern umgehen. Applicative mit &lt;*&gt; kann das.<br />Somit gibt sich
</p>
<div class='py-0.5 mb-3 text-sm'><pre><code class='haskell language-haskell numberLines'>addr_strs :: Traversal' Address String
addr_strs elt_fn (A r c p)
= pure (\r' c' -&gt; A r' c' p) &lt;*&gt; (elt_fn r) &lt;*&gt; (elt_fn c)
-- lift in Appl. | function with 2 "Holes"| first Thing | second Thing
-- oder kürzer
addr_strs :: Traversal' Address String
addr_strs elt_fn (A r c p)
= (\r' c' -&gt; A r' c' p) &lt;$&gt; (elt_fn r) &lt;*&gt; (elt_fn c)
-- pure x &lt;*&gt; y == x &lt;$&gt; y</code></pre></div>
<p class='mb-3'>
Wie würd eine modify-funktion aussehen?
</p>
<div class='py-0.5 mb-3 text-sm'><pre><code class='haskell language-haskell'>over :: Lens' s a -&gt; (a -&gt; a) -&gt; s -&gt; s
over ln f = runIdentity . ln (Identity . f)
over :: Traversal' s a -&gt; (a -&gt; a) -&gt; s -&gt; s
over ln f = runIdentity . ln (Identity . f)</code></pre></div>
<p class='mb-3'>
Der Code ist derselbe - nur der Typ ist generischer. Auch die anderen Dinge funktioniert diese Erweiterung (für Identity und Const muss man noch ein paar dummy-Instanzen schreiben um sie von Functor auf Applicative oder Monad zu heben
</p>
<ul class='my-3 ml-6 space-y-1 list-disc'>
<li>
konkret reicht hier die Instanzierung von Monoid). In der Lens-Library ist daher meist Monad m statt Functor f gefordert.
</li>
</ul>
<h2 id='wozu-dienen-die-erweiterungen' class='inline-block mt-6 mb-4 text-4xl font-bold text-gray-700 border-b-2'>Wozu dienen die Erweiterungen?</h2>
<p class='mb-3'>
Man kann mit Foci sehr selektiv vorgehen. Auch kann man diese durch Funktionen steuern. Beispisweise eine Funktion anwenden auf
</p>
<ul class='my-3 ml-6 space-y-1 list-disc'>
<li>
Jedes 2. Listenelement
</li>
<li>
Alle graden Elemente in einem Baum
</li>
<li>
Alle Namen in einer Tabelle, deren Gehalt &gt; 10.000€ ist
</li>
</ul>
<p class='mb-3'>
Traversals und Lenses kann man trivial kombinieren (<code class='py-0.5 px-0.5 bg-gray-100'>lens . lens</code> =&gt; <code class='py-0.5 px-0.5 bg-gray-100'>lens</code>, <code class='py-0.5 px-0.5 bg-gray-100'>lens . traversal</code> =&gt; <code class='py-0.5 px-0.5 bg-gray-100'>traversal</code> etc.)
</p>
<h2 id='wie-es-in-lens-wirklich-aussieht' class='inline-block mt-6 mb-4 text-4xl font-bold text-gray-700 border-b-2'>Wie es in Lens wirklich aussieht</h2>
<p class='mb-3'>
In diesem Artikel wurde nur auf Monomorphic Lenses eingegangen. In der richtigen Library ist eine Lens
</p>
<div class='py-0.5 mb-3 text-sm'><pre><code class='haskell language-haskell'>type Lens' s a = Lens s s a a
type Lens s t a b = forall f. Functor f =&gt; (a -&gt; f b) -&gt; (s -&gt; f t)</code></pre></div>
<p class='mb-3'>
sodass sich auch die Typen ändern können um z.B. automatisch einen Konvertierten (sicheren) Typen aus einer unsicheren Datenstruktur zu geben.
</p>
<p class='mb-3'>
Die modify-Funktion over ist auch
</p>
<div class='py-0.5 mb-3 text-sm'><pre><code class='haskell language-haskell'>&gt; over :: Profunctor p =&gt; Setting p s t a b -&gt; p a b -&gt; s -&gt; t</code></pre></div>
<blockquote class='py-0.5 px-4 mb-3 italic border-l-4 bg-gray-50 text-gray-600 border-gray-400 quote'>
<p class='mb-3'>
<em>Edward is deeply in thrall to abstractionitis</em> - Simon Peyton Jones
</p>
</blockquote>
<p class='mb-3'>
Lens alleine definiert 39 newtypes, 34 data-types und 194 Typsynonyme…<br />Ausschnitt
</p>
<div class='py-0.5 mb-3 text-sm'><pre><code class='haskell language-haskell numberLines'>-- traverseOf :: Functor f =&gt; Iso s t a b -&gt; (a -&gt; f b) -&gt; s -&gt; f t
-- traverseOf :: Functor f =&gt; Lens s t a b -&gt; (a -&gt; f b) -&gt; s -&gt; f t
-- traverseOf :: Applicative f =&gt; Traversal s t a b -&gt; (a -&gt; f b) -&gt; s -&gt; f t
traverseOf :: Over p f s t a b -&gt; p a (f b) -&gt; s -&gt; f t</code></pre></div>
<p class='mb-3'>
dafuq?
</p>
<!-- div class="flex items-center justify-center mt-2">
<ema:metadata>
<with var="template">
<a class="text-gray-300 hover:text-${theme}-600 text-sm" title="Edit this page on GitHub"
href="${value:editBaseUrl}/${ema:note:source-path}">
<svg xmlns="http://www.w3.org/2000/svg" class="h-6 w-6" fill="none" viewBox="0 0 24 24" stroke="currentColor">
<path stroke-linecap="round" stroke-linejoin="round" stroke-width="2"
d="M11 5H6a2 2 0 00-2 2v11a2 2 0 002 2h11a2 2 0 002-2v-5m-1.414-9.414a2 2 0 112.828 2.828L11.828 15H9v-2.828l8.586-8.586z" />
</svg>
</a>
</with>
</ema:metadata>
</div -->
</article>
<div class='flex flex-col lg:flex-row lg:space-x-2'>
<div class='flex-1 p-4 mt-8 bg-gray-100 rounded'>
<header class='mb-2 text-xl font-semibold text-gray-500'>Links to this page</header>
<ul class='space-y-1'>
<li>
<a class='text-red-600 mavenLinkBold hover:bg-red-50' href='Haskell/Advantages'>
Talks und Posts zu Haskell
</a>
<div class='mb-4 overflow-auto text-sm text-gray-500'>
<div class='pl-2 mt-2 border-l-2 border-red-200 hover:border-red-500'>
<div><a href='https://skillsmatter.com/skillscasts/4251-lenses-compositional-data-access-and-manipulation' class='text-gray-600 hover:underline' target='_blank' rel='noopener'>Lenses</a> (Registrierung nötig - kostenfrei), siehe auch: <a href='Haskell/Lenses' class='text-gray-600 font-bold hover:bg-gray-50' data-wikilink-type='WikiLinkBranch'>Lenses</a></div>
</div>
</div>
</li>
<li>
<a class='text-red-600 mavenLinkBold hover:bg-red-50' href='Haskell/FFPiH'>
Fortgeschrittene funktionale Programmierung in Haskell
</a>
<div class='mb-4 overflow-auto text-sm text-gray-500'>
<div class='pl-2 mt-2 border-l-2 border-red-200 hover:border-red-500'>
<div>Umschreiben von explizitem Argument-Passing hin zu Monad-Transformers mit stateful <a href='Haskell/Lenses' class='text-gray-600 font-bold hover:bg-gray-50' data-wikilink-type='WikiLinkBranch'>lenses</a></div>
</div>
</div>
</li>
</ul>
</div>
</div>
<section class='flex flex-wrap items-end justify-center my-4 space-x-2 space-y-2 font-mono text-sm'>
</section>
<!-- What goes in this file will at the very end of the main div -->
</main>
</div>
</div>
<footer class='flex items-center justify-center mt-2 mb-8 space-x-4 text-center text-gray-800'>
<div>
<a href='' title='Go to Home page'>
<svg xmlns='http://www.w3.org/2000/svg' class='w-6 h-6 hover:text-red-700' fill='none' viewBox='0 0 24 24' stroke='currentColor'>
<path stroke-linecap='round' stroke-linejoin='round' stroke-width='2' d='M3 12l2-2m0 0l7-7 7 7M5 10v10a1 1 0 001 1h3m10-11l2 2m-2-2v10a1 1 0 01-1 1h-3m-6 0a1 1 0 001-1v-4a1 1 0 011-1h2a1 1 0 011 1v4a1 1 0 001 1m-6 0h6'></path>
</svg>
</a>
</div>
<div>
<a href='-/all' title='View Index'>
<svg class='w-6 h-6 hover:text-red-700' fill='none' stroke='currentColor' viewBox='0 0 24 24' xmlns='http://www.w3.org/2000/svg'>
<path stroke-linecap='round' stroke-linejoin='round' stroke-width='2' d='M4 8V4m0 0h4M4 4l5 5m11-1V4m0 0h-4m4 0l-5 5M4 16v4m0 0h4m-4 0l5-5m11 5l-5-5m5 5v-4m0 4h-4'>
</path>
</svg>
</a>
</div>
<div>
<a href='https://emanote.srid.ca' target='_blank' title='Generated by Emanote 0.7.3.0'>
<img class='w-6 h-6 hover:text-red-700' src='_emanote-static/emanote-logo.svg' />
</a>
</div>
<div>
<a href='-/tags' title='View tags'>
<svg class='w-6 h-6 hover:text-red-700' fill='none' stroke='currentColor' viewBox='0 0 24 24' xmlns='http://www.w3.org/2000/svg'>
<path stroke-linecap='round' stroke-linejoin='round' stroke-width='2' d='M7 7h.01M7 3h5c.512 0 1.024.195 1.414.586l7 7a2 2 0 010 2.828l-7 7a2 2 0 01-2.828 0l-7-7A1.994 1.994 0 013 12V7a4 4 0 014-4z'>
</path>
</svg>
</a>
</div>
<div>
<a href='-/tasks' title='View tasks'>
<svg xmlns='http://www.w3.org/2000/svg' class='w-6 h-6 hover:text-red-700' fill='none' viewBox='0 0 24 24' stroke='currentColor'>
<path stroke-linecap='round' stroke-linejoin='round' stroke-width='2' d='M9 12l2 2 4-4m6 2a9 9 0 11-18 0 9 9 0 0118 0z'></path>
</svg>
</a>
</div>
</footer>
</div>
<div id='stork-search-container' class='hidden fixed w-screen h-screen inset-0 backdrop-filter backdrop-blur-sm'>
<div class='fixed w-screen h-screen inset-0' onclick='window.emanote.stork.toggleSearch()'></div>
<div class='container mx-auto p-10 mt-10'>
<div class='stork-wrapper-flat container mx-auto'>
<input id='stork-search-input' data-stork='emanote-search' class='stork-input' placeholder='Search (Ctrl+K) ...' />
<div data-stork='emanote-search-output' class='stork-output'></div>
</div>
</div>
</div>
</body>
</html>
Reference in New Issue Copy Permalink