1681 lines
56 KiB
HTML
1681 lines
56 KiB
HTML
<!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();
|
||
}
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||
}
|
||
};
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||
</script>
|
||
<script async id='MathJax-script' src='https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js'></script>
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||
|
||
<!-- 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"));
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||
</script>
|
||
|
||
<!-- highlight.js -->
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||
<link rel='stylesheet' href='https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.6.0/styles/hybrid.min.css' />
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||
<script src='https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.6.0/highlight.min.js'></script>
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||
<!-- Include languages that Emanote itself uses -->
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||
<script src='https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.6.0/languages/haskell.min.js'></script>
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||
<script src='https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.6.0/languages/nix.min.js'></script>
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||
<script>hljs.highlightAll();</script>
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||
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||
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||
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||
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||
<link href='tailwind.css?instanceId=9a96156f-f633-42f8-838d-f30867d3069d' rel='stylesheet' type='text/css' />
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||
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||
<style>
|
||
/* Heist error element */
|
||
strong.error {
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||
color: lightcoral;
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||
font-size: 90%;
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||
font-family: monospace;
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||
}
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||
|
||
/* External link icon */
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||
a[data-linkicon]:not([data-linkicon=""]):not([data-linkicon="none"])::after {
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||
/* filter converts black to rgb(156,163,175) */
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||
filter: invert(71%) sepia(3%) saturate(904%) hue-rotate(179deg) brightness(92%) contrast(87%);
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||
margin-left: 1px;
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||
}
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||
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||
a[data-linkicon]:not([data-linkicon=""]):not([data-linkicon="none"]):hover::after {
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||
/* filter converts black to rgb(175,85,99) */
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||
filter: invert(32%) sepia(10%) saturate(834%) hue-rotate(176deg) brightness(92%) contrast(88%);
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||
}
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||
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||
a[data-linkicon=""]::after {
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||
content: ""
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||
}
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||
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||
a[data-linkicon=none]::after {
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||
content: ""
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||
}
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||
|
||
a[data-linkicon="external"]::after {
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||
content: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' height='1em' fill='none' viewBox='0 0 24 24' stroke='black' stroke-width='2'%3E%3Cpath stroke-linecap='round' stroke-linejoin='round' d='M10 6H6a2 2 0 00-2 2v10a2 2 0 002 2h10a2 2 0 002-2v-4M14 4h6m0 0v6m0-6L10 14' /%3E%3C/svg%3E");
|
||
}
|
||
|
||
a[data-linkicon="external"][href^="mailto:"]::after {
|
||
content: url("data:image/svg+xml,%3Csvg xmlns='http://www.w3.org/2000/svg' height='1em' fill='none' viewBox='0 0 24 24' stroke='black' stroke-width='2'%3E%3Cpath stroke-linecap='round' stroke-linejoin='round' d='M3 8l7.89 5.26a2 2 0 002.22 0L21 8M5 19h14a2 2 0 002-2V7a2 2 0 00-2-2H5a2 2 0 00-2 2v10a2 2 0 002 2z' /%3E%3C/svg%3E");
|
||
}
|
||
</style>
|
||
<!-- What goes in this file will appear on near the end of <head>--><link rel='preload' href='_emanote-static/fonts/Work_Sans/WorkSans-VariableFont_wght.ttf' as='font' type='font/ttf' crossorigin />
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||
|
||
<style>
|
||
@font-face {
|
||
font-family: 'WorkSans';
|
||
/* FIXME: This ought to be: ${ema:emanoteStaticLayerUrl}/fonts/Work_Sans/WorkSans-VariableFont_wght.ttf */
|
||
src: url(_emanote-static/fonts/Work_Sans/WorkSans-VariableFont_wght.ttf) format("truetype");
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||
font-display: swap;
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||
}
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||
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||
body {
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||
font-family: 'WorkSans', sans-serif;
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||
font-variation-settings: 'wght' 350;
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||
}
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||
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||
a.mavenLinkBold {
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||
font-variation-settings: 'wght' 400;
|
||
}
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||
|
||
strong {
|
||
font-variation-settings: 'wght' 500;
|
||
}
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||
|
||
h1,
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||
h2,
|
||
h3,
|
||
h4,
|
||
h5,
|
||
h6,
|
||
header,
|
||
.header-font {
|
||
font-family: 'WorkSans', sans-serif;
|
||
}
|
||
|
||
h1 {
|
||
font-variation-settings: 'wght' 500;
|
||
}
|
||
|
||
h2 {
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||
font-variation-settings: 'wght' 400;
|
||
}
|
||
|
||
h3 {
|
||
font-variation-settings: 'wght' 300;
|
||
}
|
||
</style>
|
||
|
||
|
||
|
||
<link rel='stylesheet' href='_emanote-static/inverted-tree.css' />
|
||
|
||
<link rel='stylesheet' href='_emanote-static/stork/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='_emanote-static/stork/stork.js'></script>
|
||
|
||
|
||
<script data-emanote-base-url='/'>
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||
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) {
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||
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.initialize(baseUrl + '_emanote-static/stork/stork.wasm');
|
||
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='Coding'>
|
||
Coding
|
||
</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='Coding/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-purple-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-purple-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-purple-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-purple-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-purple-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-500' viewBox='0 0 20 20' fill='currentColor'>
|
||
<path d='M2 6a2 2 0 012-2h5l2 2h5a2 2 0 012 2v6a2 2 0 01-2 2H4a2 2 0 01-2-2V6z'></path>
|
||
</svg>
|
||
|
||
|
||
<a class='hover:underline truncate' title='About' href='About'>
|
||
About
|
||
</a>
|
||
|
||
|
||
<span class='text-gray-300' title='3 children inside'>
|
||
3
|
||
</span>
|
||
|
||
|
||
</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-500' viewBox='0 0 20 20' fill='currentColor'>
|
||
<path d='M2 6a2 2 0 012-2h5l2 2h5a2 2 0 012 2v6a2 2 0 01-2 2H4a2 2 0 01-2-2V6z'></path>
|
||
</svg>
|
||
|
||
|
||
<a class='hover:underline truncate' title='Android' href='Android'>
|
||
Android
|
||
</a>
|
||
|
||
|
||
<span class='text-gray-300' title='1 children inside'>
|
||
1
|
||
</span>
|
||
|
||
|
||
</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='Coding' href='Coding'>
|
||
Coding
|
||
</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='Haskell' href='Coding/Haskell'>
|
||
Haskell
|
||
</a>
|
||
|
||
|
||
</div>
|
||
|
||
<!-- Node's children forest, displayed only on active trees
|
||
TODO: Use <details> to toggle visibility?
|
||
-->
|
||
|
||
|
||
<!-- Variable bindings for this tree-->
|
||
|
||
|
||
|
||
|
||
|
||
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||
|
||
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|
||
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|
||
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|
||
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|
||
<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='Coding/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>
|
||
|
||
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|
||
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|
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|
||
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||
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||
<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-500' viewBox='0 0 20 20' fill='currentColor'>
|
||
<path d='M2 6a2 2 0 012-2h5l2 2h5a2 2 0 012 2v6a2 2 0 01-2 2H4a2 2 0 01-2-2V6z'></path>
|
||
</svg>
|
||
|
||
|
||
<a class='hover:underline truncate' title='Code-Snippets' href='Coding/Haskell/Code%20Snippets'>
|
||
Code-Snippets
|
||
</a>
|
||
|
||
|
||
<span class='text-gray-300' title='2 children inside'>
|
||
2
|
||
</span>
|
||
|
||
|
||
</div>
|
||
|
||
<!-- Node's children forest, displayed only on active trees
|
||
TODO: Use <details> to toggle visibility?
|
||
-->
|
||
|
||
</div>
|
||
|
||
<!-- Variable bindings for this tree-->
|
||
|
||
|
||
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|
||
|
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|
||
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||
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|
||
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|
||
<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='Coding/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-->
|
||
|
||
|
||
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||
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||
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||
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||
|
||
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||
<div class='pl-2'>
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||
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|
||
<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'>
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||
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|
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<a class='font-bold text-purple-600 hover:underline truncate' title='Lenses' href='Coding/Haskell/Lenses'>
|
||
Lenses
|
||
</a>
|
||
|
||
|
||
</div>
|
||
|
||
<!-- Node's children forest, displayed only on active trees
|
||
TODO: Use <details> to toggle visibility?
|
||
-->
|
||
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||
|
||
|
||
</div>
|
||
|
||
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||
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||
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||
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||
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||
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||
<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-500' viewBox='0 0 20 20' fill='currentColor'>
|
||
<path d='M2 6a2 2 0 012-2h5l2 2h5a2 2 0 012 2v6a2 2 0 01-2 2H4a2 2 0 01-2-2V6z'></path>
|
||
</svg>
|
||
|
||
|
||
<a class='hover:underline truncate' title='Webapp-Development in Haskell' href='Coding/Haskell/Webapp-Example'>
|
||
Webapp-Development in Haskell
|
||
</a>
|
||
|
||
|
||
<span class='text-gray-300' title='2 children inside'>
|
||
2
|
||
</span>
|
||
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||
|
||
</div>
|
||
|
||
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|
||
TODO: Use <details> to toggle visibility?
|
||
-->
|
||
|
||
</div>
|
||
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||
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||
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||
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||
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||
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||
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||
<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='Openapi-generator' href='Coding/OpenAPI'>
|
||
Openapi-generator
|
||
</a>
|
||
|
||
|
||
|
||
|
||
</div>
|
||
|
||
<!-- Node's children forest, displayed only on active trees
|
||
TODO: Use <details> to toggle visibility?
|
||
-->
|
||
|
||
</div>
|
||
|
||
|
||
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|
||
|
||
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|
||
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|
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|
||
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||
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|
||
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|
||
<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?
|
||
-->
|
||
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||
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||
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||
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||
<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-500' viewBox='0 0 20 20' fill='currentColor'>
|
||
<path d='M2 6a2 2 0 012-2h5l2 2h5a2 2 0 012 2v6a2 2 0 01-2 2H4a2 2 0 01-2-2V6z'></path>
|
||
</svg>
|
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|
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|
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Opinions
|
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|
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<span class='text-gray-300' title='2 children inside'>
|
||
2
|
||
</span>
|
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||
|
||
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|
||
|
||
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|
||
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|
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-->
|
||
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||
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<div class='flex items-center my-2 space-x-2 justify-left'>
|
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|
||
|
||
<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>
|
||
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|
||
|
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|
||
<a class='hover:underline truncate' title='Todo' href='TODO'>
|
||
Todo
|
||
</a>
|
||
|
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|
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|
||
|
||
</div>
|
||
|
||
<!-- Node's children forest, displayed only on active trees
|
||
TODO: Use <details> to toggle visibility?
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-->
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</div>
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|
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<!-- Variable bindings for this tree-->
|
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|
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|
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<!-- Rendering of this tree -->
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|
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<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-500' viewBox='0 0 20 20' fill='currentColor'>
|
||
<path d='M2 6a2 2 0 012-2h5l2 2h5a2 2 0 012 2v6a2 2 0 01-2 2H4a2 2 0 01-2-2V6z'></path>
|
||
</svg>
|
||
|
||
|
||
<a class='hover:underline truncate' title='Uni' href='Uni'>
|
||
Uni
|
||
</a>
|
||
|
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|
||
<span class='text-gray-300' title='2 children inside'>
|
||
2
|
||
</span>
|
||
|
||
|
||
</div>
|
||
|
||
<!-- Node's children forest, displayed only on active trees
|
||
TODO: Use <details> to toggle visibility?
|
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-->
|
||
|
||
</div>
|
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|
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<!-- Variable bindings for this tree-->
|
||
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
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|
||
<svg xmlns='http://www.w3.org/2000/svg' class='w-4 h-4 flex-shrink-0 inline text-gray-500' viewBox='0 0 20 20' fill='currentColor'>
|
||
<path d='M2 6a2 2 0 012-2h5l2 2h5a2 2 0 012 2v6a2 2 0 01-2 2H4a2 2 0 01-2-2V6z'></path>
|
||
</svg>
|
||
|
||
|
||
<a class='hover:underline truncate' title='Unix' href='Unix'>
|
||
Unix
|
||
</a>
|
||
|
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|
||
<span class='text-gray-300' title='1 children inside'>
|
||
1
|
||
</span>
|
||
|
||
|
||
</div>
|
||
|
||
<!-- Node's children forest, displayed only on active trees
|
||
TODO: Use <details> to toggle visibility?
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|
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|
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|
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|
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|
||
<a href='Coding/Haskell/Advantages'>
|
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Talks und Posts zu Haskell
|
||
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|
||
</div>
|
||
|
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|
||
<ul>
|
||
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<li>
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|
||
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|
||
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|
||
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|
||
</div>
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|
||
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|
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</ul>
|
||
|
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</li>
|
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|
||
<li>
|
||
|
||
<div class='text-gray-900 forest-link'>
|
||
<a href='Coding/Haskell/FFPiH'>
|
||
Fortgeschrittene funktionale Programmierung in Haskell
|
||
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Uni
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</ul>
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</li>
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||
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|
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<h1 class='flex items-end justify-center mb-4 p-3 bg-purple-100 text-5xl font-extrabold text-black rounded'>
|
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<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'>data Person = P { name :: String
|
||
, addr :: Address
|
||
, salary :: Int }
|
||
data Address = A { road :: String
|
||
, city :: String
|
||
, postcode :: String }
|
||
-- autogeneriert unten anderem: addr :: Person -> Address
|
||
|
||
setName :: String -> Person -> Person
|
||
setName n p = p { name = n } --record update notation
|
||
|
||
setPostcode :: String -> Person -> 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'>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 -> s -> a
|
||
set :: Lens' s a -> a -> s -> s
|
||
-- lens-composition
|
||
composeL :: Lens' s1 s2 -> Lens s2 a -> 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'>data Person = P { name :: String
|
||
, addr :: Address
|
||
, salary :: Int }
|
||
data Address = A { road :: String
|
||
, city :: String
|
||
, postcode :: String }
|
||
setPostcode :: String -> Person -> 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'>data LensR s a = L { viewR :: s -> a
|
||
, setR :: a -> s -> s }
|
||
|
||
composeL (L v1 u1) (L v2 u2)
|
||
= L (\s -> v2 (v1 s))
|
||
(\a s -> 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'>over :: LensR s a -> (a -> a) -> s -> 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'>data LensR s a
|
||
= L { viewR :: s -> a
|
||
, setR :: a -> s -> s
|
||
, mod :: (a->a) -> s -> s
|
||
, modM :: (a->Maybe a) -> s -> Maybe s
|
||
, modIO :: (a->IO a) -> s -> 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'>data LensR s a
|
||
= L { viewR :: s -> a
|
||
, setR :: a -> s -> s
|
||
, mod :: (a->a) -> s -> s
|
||
, modF :: Functor f => (a->f a) -> s -> 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
|
||
=> (a -> f a) -> s -> 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 -> a
|
||
, setR :: a -> s -> 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'>set :: Lens' s a -> (a -> s -> s)
|
||
set ln a s = --...umm...
|
||
--:t ln => (a -> f a) -> s -> f s
|
||
-- => 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'>newtype Identity a = Identity a
|
||
-- Id :: a -> Identity a
|
||
|
||
runIdentity :: Identity s -> 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'>set :: Lens' s a -> (a -> s -> s)
|
||
set ln x s
|
||
= runIdentity (ls set_fld s)
|
||
where
|
||
set_fld :: a -> 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 -> (a -> s -> 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 -> (a -> a) -> s -> 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'>view :: Lens' s a -> (s -> a)
|
||
view ln s = --...umm...
|
||
--:t ln => (a -> f a) -> s -> f s
|
||
-- => 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'>newtype Const v a = Const v
|
||
|
||
getConst :: Const v a -> 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'>view :: Lens' s a -> (s -> a)
|
||
view ln s
|
||
= getConst (ln Const s)
|
||
-- Const :: s -> 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 -> (s -> 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
|
||
=> (a -> f a) -> s -> 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'>data Person = P { _name :: String, _salary :: Int }
|
||
|
||
name :: Lens' Person String
|
||
-- name :: Functor f => (String -> f String)
|
||
-- -> Person -> f Person
|
||
|
||
name elt_fn (P n s)
|
||
= fmap (\n' -> P n' s) (elt_fn n)
|
||
-- fmap :: Functor f => (a->b) -> f a -> f b - der Funktor, der alles verknüpft
|
||
-- \n' -> .. :: String -> 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' -> P n' s) <$> (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'>view name (P {_name="Fred", _salary=100})
|
||
-- inline view-function
|
||
= getConst (name Const (P {_name="Fred", _salary=100})
|
||
-- inline name
|
||
= getConst (fmap (\n' -> 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 -> Lens’ s2 a -> 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 -> f s2) -> (s1 -> f s1) ln2 :: (a -> f a) -> (s2 -> 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 -> f s) -> (s1 -> 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'>data Person = P { _name :: String, _salary :: Int }
|
||
|
||
name :: Lens' Person String
|
||
name elt_fn (P n s) = (\n' -> P n' s) <$> (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'>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'>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 -> Person -> 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'>-- ...
|
||
|
||
setPostcode :: String -> Person -> Person
|
||
setPostcode pc p = addr . postcode .~ pc $ p
|
||
-- | Focus |set|to what|in where
|
||
|
||
getPostcode :: Person -> 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'>data Temp = T { _fahrenheit :: Float }
|
||
|
||
$(makeLenses ''Temp)
|
||
-- liefert Lens: fahrenheit :: Lens Temp Float
|
||
|
||
centigrade :: Lens Temp Float
|
||
centigrade centi_fn (T faren)
|
||
= (\centi' -> T (cToF centi'))
|
||
<$> (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'>-- from Data.Lens.At
|
||
at :: Ord k => k -> Lens' (Map k v) (Maybe v)
|
||
|
||
-- oder identisch, wenn man die Lens' auflöst:
|
||
at :: Ord k, forall f. Functor f => k -> (Maybe v -> f Maybe v) -> Map k v -> f Map k v
|
||
|
||
at k mb_fn m
|
||
= wrap <$> (mb_fn mv)
|
||
where
|
||
mv = Map.lookup k m
|
||
|
||
wrap :: Maybe v -> Map k v
|
||
wrap (Just v') = Map.insert k v' m
|
||
wrap Nothing = case mv of
|
||
Nothing -> m
|
||
Just _ -> Map.delete k m
|
||
|
||
-- mb_fn :: Maybe v -> 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'>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'>type Traversal' s a = forall f. Applicative f
|
||
=> (a -> f a) -> (s -> 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'>class Functor f => Applicative f where
|
||
pure :: a -> f a
|
||
(<*>) :: f (a -> b) -> f a -> f b
|
||
|
||
-- Monade als Applicative:
|
||
pure = return
|
||
mf <*> mx = do { f <- mf; x <- 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'>data Adress = A { _road :: String
|
||
, _city :: String
|
||
, _postcode :: String }
|
||
|
||
road :: Lens' Adress String
|
||
road elt_fn (A r c p) = (\r' -> A r' c p) <$> (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'>addr_strs :: Traversal' Address String
|
||
addr_strs elt_fn (A r c p)
|
||
= ... (\r' c' -> 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 <*> kann das.<br />Somit gibt sich
|
||
</p>
|
||
<div class='py-0.5 mb-3 text-sm'><pre><code class='haskell language-haskell'>addr_strs :: Traversal' Address String
|
||
addr_strs elt_fn (A r c p)
|
||
= pure (\r' c' -> A r' c' p) <*> (elt_fn r) <*> (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' -> A r' c' p) <$> (elt_fn r) <*> (elt_fn c)
|
||
-- pure x <*> y == x <$> 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 -> (a -> a) -> s -> s
|
||
over ln f = runIdentity . ln (Identity . f)
|
||
|
||
over :: Traversal' s a -> (a -> a) -> s -> 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 > 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> => <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> => <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 => (a -> f b) -> (s -> 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'>> over :: Profunctor p => Setting p s t a b -> p a b -> s -> 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'>-- traverseOf :: Functor f => Iso s t a b -> (a -> f b) -> s -> f t
|
||
-- traverseOf :: Functor f => Lens s t a b -> (a -> f b) -> s -> f t
|
||
-- traverseOf :: Applicative f => Traversal s t a b -> (a -> f b) -> s -> f t
|
||
|
||
traverseOf :: Over p f s t a b -> p a (f b) -> s -> f t</code></pre></div>
|
||
<p class='mb-3'>
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||
dafuq?
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<div>Umschreiben von explizitem Argument-Passing hin zu Monad-Transformers mit stateful <a href='Coding/Haskell/Lenses' class='text-gray-600 font-bold hover:bg-gray-50' data-wikilink-type='WikiLinkBranch'>lenses</a></div>
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