1159 lines
63 KiB
HTML
1159 lines
63 KiB
HTML
<!DOCTYPE html>
|
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<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"><head>
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|
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<meta charset="utf-8">
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<meta name="generator" content="quarto-1.7.23">
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|
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<meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes">
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<meta name="dcterms.date" content="2016-01-01">
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<title>Monoid? Da war doch was… – Nicole Dresselhaus</title>
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<style>
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code{white-space: pre-wrap;}
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span.smallcaps{font-variant: small-caps;}
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||
div.columns{display: flex; gap: min(4vw, 1.5em);}
|
||
div.column{flex: auto; overflow-x: auto;}
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||
div.hanging-indent{margin-left: 1.5em; text-indent: -1.5em;}
|
||
ul.task-list{list-style: none;}
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ul.task-list li input[type="checkbox"] {
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width: 0.8em;
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margin: 0 0.8em 0.2em -1em; /* quarto-specific, see https://github.com/quarto-dev/quarto-cli/issues/4556 */
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vertical-align: middle;
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}
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/* CSS for syntax highlighting */
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html { -webkit-text-size-adjust: 100%; }
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pre > code.sourceCode { white-space: pre; position: relative; }
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pre > code.sourceCode > span { display: inline-block; line-height: 1.25; }
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pre > code.sourceCode > span:empty { height: 1.2em; }
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.sourceCode { overflow: visible; }
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code.sourceCode > span { color: inherit; text-decoration: inherit; }
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div.sourceCode { margin: 1em 0; }
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pre.sourceCode { margin: 0; }
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@media screen {
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div.sourceCode { overflow: auto; }
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}
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@media print {
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pre > code.sourceCode { white-space: pre-wrap; }
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pre > code.sourceCode > span { text-indent: -5em; padding-left: 5em; }
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}
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pre.numberSource code
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{ counter-reset: source-line 0; }
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pre.numberSource code > span
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{ position: relative; left: -4em; counter-increment: source-line; }
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pre.numberSource code > span > a:first-child::before
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{ content: counter(source-line);
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position: relative; left: -1em; text-align: right; vertical-align: baseline;
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border: none; display: inline-block;
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-webkit-touch-callout: none; -webkit-user-select: none;
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-khtml-user-select: none; -moz-user-select: none;
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-ms-user-select: none; user-select: none;
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padding: 0 4px; width: 4em;
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}
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pre.numberSource { margin-left: 3em; padding-left: 4px; }
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div.sourceCode
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{ }
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@media screen {
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pre > code.sourceCode > span > a:first-child::before { text-decoration: underline; }
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}
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</style>
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|
||
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<script src="../../../site_libs/quarto-nav/quarto-nav.js"></script>
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<script src="../../../site_libs/quarto-nav/headroom.min.js"></script>
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<script src="../../../site_libs/clipboard/clipboard.min.js"></script>
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<script src="../../../site_libs/quarto-search/autocomplete.umd.js"></script>
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||
<script src="../../../site_libs/quarto-search/fuse.min.js"></script>
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<script src="../../../site_libs/quarto-search/quarto-search.js"></script>
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<meta name="quarto:offset" content="../../../">
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<script src="../../../site_libs/quarto-html/quarto.js" type="module"></script>
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<script src="../../../site_libs/quarto-html/tabsets/tabsets.js" type="module"></script>
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<script src="../../../site_libs/quarto-html/popper.min.js"></script>
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<script src="../../../site_libs/quarto-html/tippy.umd.min.js"></script>
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<script src="../../../site_libs/quarto-html/anchor.min.js"></script>
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||
<link href="../../../site_libs/quarto-html/tippy.css" rel="stylesheet">
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||
<link href="../../../site_libs/quarto-html/quarto-syntax-highlighting-dark-2c84ecb840a13f4c7993f9e5648f0c14.css" rel="stylesheet" class="quarto-color-scheme quarto-color-alternate" id="quarto-text-highlighting-styles">
|
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<link href="../../../site_libs/quarto-html/quarto-syntax-highlighting-6cf5824034cebd0380a5b9c74c43f006.css" rel="stylesheet" class="quarto-color-scheme" id="quarto-text-highlighting-styles">
|
||
<script src="../../../site_libs/bootstrap/bootstrap.min.js"></script>
|
||
<link href="../../../site_libs/bootstrap/bootstrap-icons.css" rel="stylesheet">
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<link href="../../../site_libs/bootstrap/bootstrap-ec71cb1e120c0dd41819aca960e74e38.min.css" rel="stylesheet" append-hash="true" class="quarto-color-scheme" id="quarto-bootstrap" data-mode="light">
|
||
<link href="../../../site_libs/bootstrap/bootstrap-dark-6ed95ce66646ab2447a87e45f81c21f3.min.css" rel="stylesheet" append-hash="true" class="quarto-color-scheme quarto-color-alternate" id="quarto-bootstrap" data-mode="dark">
|
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<link href="../../../site_libs/bootstrap/bootstrap-ec71cb1e120c0dd41819aca960e74e38.min.css" rel="stylesheet" append-hash="true" class="quarto-color-scheme-extra" id="quarto-bootstrap" data-mode="light">
|
||
<script id="quarto-search-options" type="application/json">{
|
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"location": "navbar",
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"copy-button": false,
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"collapse-after": 3,
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"panel-placement": "end",
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||
"type": "overlay",
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||
"limit": 50,
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||
"keyboard-shortcut": [
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"f",
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||
"/",
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"s"
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],
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||
"show-item-context": false,
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"language": {
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||
"search-no-results-text": "No results",
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||
"search-matching-documents-text": "matching documents",
|
||
"search-copy-link-title": "Copy link to search",
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||
"search-hide-matches-text": "Hide additional matches",
|
||
"search-more-match-text": "more match in this document",
|
||
"search-more-matches-text": "more matches in this document",
|
||
"search-clear-button-title": "Clear",
|
||
"search-text-placeholder": "",
|
||
"search-detached-cancel-button-title": "Cancel",
|
||
"search-submit-button-title": "Submit",
|
||
"search-label": "Search"
|
||
}
|
||
}</script>
|
||
|
||
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<meta property="og:title" content="Monoid? Da war doch was… – Nicole Dresselhaus">
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<meta property="og:description" content="Monoide tauchen überall auf. Ein Grund sich damit mal etwas eingehender an einen konkreten Beispiel zu beschäftigen.">
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<meta property="og:site_name" content="Nicole Dresselhaus">
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</head>
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<body class="nav-sidebar docked nav-fixed quarto-light"><script id="quarto-html-before-body" type="application/javascript">
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||
const toggleBodyColorMode = (bsSheetEl) => {
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||
const mode = bsSheetEl.getAttribute("data-mode");
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||
const bodyEl = window.document.querySelector("body");
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||
if (mode === "dark") {
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||
bodyEl.classList.add("quarto-dark");
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||
bodyEl.classList.remove("quarto-light");
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||
} else {
|
||
bodyEl.classList.add("quarto-light");
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||
bodyEl.classList.remove("quarto-dark");
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||
}
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||
}
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||
const toggleBodyColorPrimary = () => {
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||
const bsSheetEl = window.document.querySelector("link#quarto-bootstrap:not([rel=disabled-stylesheet])");
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if (bsSheetEl) {
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||
toggleBodyColorMode(bsSheetEl);
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||
}
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||
}
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||
window.setColorSchemeToggle = (alternate) => {
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||
const toggles = window.document.querySelectorAll('.quarto-color-scheme-toggle');
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||
for (let i=0; i < toggles.length; i++) {
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||
const toggle = toggles[i];
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||
if (toggle) {
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||
if (alternate) {
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toggle.classList.add("alternate");
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||
} else {
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toggle.classList.remove("alternate");
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||
}
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||
}
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||
}
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||
};
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||
const toggleColorMode = (alternate) => {
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||
// Switch the stylesheets
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||
const primaryStylesheets = window.document.querySelectorAll('link.quarto-color-scheme:not(.quarto-color-alternate)');
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||
const alternateStylesheets = window.document.querySelectorAll('link.quarto-color-scheme.quarto-color-alternate');
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||
manageTransitions('#quarto-margin-sidebar .nav-link', false);
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||
if (alternate) {
|
||
// note: dark is layered on light, we don't disable primary!
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||
enableStylesheet(alternateStylesheets);
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||
for (const sheetNode of alternateStylesheets) {
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||
if (sheetNode.id === "quarto-bootstrap") {
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||
toggleBodyColorMode(sheetNode);
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||
}
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||
}
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||
} else {
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||
disableStylesheet(alternateStylesheets);
|
||
enableStylesheet(primaryStylesheets)
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||
toggleBodyColorPrimary();
|
||
}
|
||
manageTransitions('#quarto-margin-sidebar .nav-link', true);
|
||
// Switch the toggles
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||
window.setColorSchemeToggle(alternate)
|
||
// Hack to workaround the fact that safari doesn't
|
||
// properly recolor the scrollbar when toggling (#1455)
|
||
if (navigator.userAgent.indexOf('Safari') > 0 && navigator.userAgent.indexOf('Chrome') == -1) {
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||
manageTransitions("body", false);
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||
window.scrollTo(0, 1);
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||
setTimeout(() => {
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||
window.scrollTo(0, 0);
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||
manageTransitions("body", true);
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||
}, 40);
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||
}
|
||
}
|
||
const disableStylesheet = (stylesheets) => {
|
||
for (let i=0; i < stylesheets.length; i++) {
|
||
const stylesheet = stylesheets[i];
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||
stylesheet.rel = 'disabled-stylesheet';
|
||
}
|
||
}
|
||
const enableStylesheet = (stylesheets) => {
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||
for (let i=0; i < stylesheets.length; i++) {
|
||
const stylesheet = stylesheets[i];
|
||
if(stylesheet.rel !== 'stylesheet') { // for Chrome, which will still FOUC without this check
|
||
stylesheet.rel = 'stylesheet';
|
||
}
|
||
}
|
||
}
|
||
const manageTransitions = (selector, allowTransitions) => {
|
||
const els = window.document.querySelectorAll(selector);
|
||
for (let i=0; i < els.length; i++) {
|
||
const el = els[i];
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||
if (allowTransitions) {
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||
el.classList.remove('notransition');
|
||
} else {
|
||
el.classList.add('notransition');
|
||
}
|
||
}
|
||
}
|
||
const isFileUrl = () => {
|
||
return window.location.protocol === 'file:';
|
||
}
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||
window.hasAlternateSentinel = () => {
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||
let styleSentinel = getColorSchemeSentinel();
|
||
if (styleSentinel !== null) {
|
||
return styleSentinel === "alternate";
|
||
} else {
|
||
return false;
|
||
}
|
||
}
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||
const setStyleSentinel = (alternate) => {
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||
const value = alternate ? "alternate" : "default";
|
||
if (!isFileUrl()) {
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||
window.localStorage.setItem("quarto-color-scheme", value);
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||
} else {
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||
localAlternateSentinel = value;
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||
}
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||
}
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||
const getColorSchemeSentinel = () => {
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||
if (!isFileUrl()) {
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||
const storageValue = window.localStorage.getItem("quarto-color-scheme");
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||
return storageValue != null ? storageValue : localAlternateSentinel;
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||
} else {
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||
return localAlternateSentinel;
|
||
}
|
||
}
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||
const toggleGiscusIfUsed = (isAlternate, darkModeDefault) => {
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||
const baseTheme = document.querySelector('#giscus-base-theme')?.value ?? 'light';
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||
const alternateTheme = document.querySelector('#giscus-alt-theme')?.value ?? 'dark';
|
||
let newTheme = '';
|
||
if(darkModeDefault) {
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||
newTheme = isAlternate ? baseTheme : alternateTheme;
|
||
} else {
|
||
newTheme = isAlternate ? alternateTheme : baseTheme;
|
||
}
|
||
const changeGiscusTheme = () => {
|
||
// From: https://github.com/giscus/giscus/issues/336
|
||
const sendMessage = (message) => {
|
||
const iframe = document.querySelector('iframe.giscus-frame');
|
||
if (!iframe) return;
|
||
iframe.contentWindow.postMessage({ giscus: message }, 'https://giscus.app');
|
||
}
|
||
sendMessage({
|
||
setConfig: {
|
||
theme: newTheme
|
||
}
|
||
});
|
||
}
|
||
const isGiscussLoaded = window.document.querySelector('iframe.giscus-frame') !== null;
|
||
if (isGiscussLoaded) {
|
||
changeGiscusTheme();
|
||
}
|
||
};
|
||
const queryPrefersDark = window.matchMedia('(prefers-color-scheme: dark)');
|
||
const darkModeDefault = queryPrefersDark.matches;
|
||
document.querySelector('link.quarto-color-scheme-extra').rel = 'disabled-stylesheet';
|
||
let localAlternateSentinel = darkModeDefault ? 'alternate' : 'default';
|
||
// Dark / light mode switch
|
||
window.quartoToggleColorScheme = () => {
|
||
// Read the current dark / light value
|
||
let toAlternate = !window.hasAlternateSentinel();
|
||
toggleColorMode(toAlternate);
|
||
setStyleSentinel(toAlternate);
|
||
toggleGiscusIfUsed(toAlternate, darkModeDefault);
|
||
};
|
||
queryPrefersDark.addEventListener("change", e => {
|
||
if(window.localStorage.getItem("quarto-color-scheme") !== null)
|
||
return;
|
||
const alternate = e.matches
|
||
toggleColorMode(alternate);
|
||
localAlternateSentinel = e.matches ? 'alternate' : 'default'; // this is used alongside local storage!
|
||
toggleGiscusIfUsed(alternate, darkModeDefault);
|
||
});
|
||
// Switch to dark mode if need be
|
||
if (window.hasAlternateSentinel()) {
|
||
toggleColorMode(true);
|
||
} else {
|
||
toggleColorMode(false);
|
||
}
|
||
</script>
|
||
|
||
<div id="quarto-search-results"></div>
|
||
<header id="quarto-header" class="headroom fixed-top">
|
||
<nav class="navbar navbar-expand-lg " data-bs-theme="dark">
|
||
<div class="navbar-container container-fluid">
|
||
<div class="navbar-brand-container mx-auto">
|
||
<a class="navbar-brand" href="../../../index.html">
|
||
<span class="navbar-title">Nicole Dresselhaus</span>
|
||
</a>
|
||
</div>
|
||
<div id="quarto-search" class="" title="Search"></div>
|
||
<button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbarCollapse" aria-controls="navbarCollapse" role="menu" aria-expanded="false" aria-label="Toggle navigation" onclick="if (window.quartoToggleHeadroom) { window.quartoToggleHeadroom(); }">
|
||
<span class="navbar-toggler-icon"></span>
|
||
</button>
|
||
<div class="collapse navbar-collapse" id="navbarCollapse">
|
||
<ul class="navbar-nav navbar-nav-scroll me-auto">
|
||
<li class="nav-item">
|
||
<a class="nav-link" href="../../../index.html"> <i class="bi bi-house" role="img">
|
||
</i>
|
||
<span class="menu-text">Home</span></a>
|
||
</li>
|
||
<li class="nav-item">
|
||
<a class="nav-link active" href="../../../About/index.html" aria-current="page"> <i class="bi bi-file-person" role="img">
|
||
</i>
|
||
<span class="menu-text">About</span></a>
|
||
</li>
|
||
</ul>
|
||
<ul class="navbar-nav navbar-nav-scroll ms-auto">
|
||
<li class="nav-item compact">
|
||
<a class="nav-link" href="../../../index.xml"> <i class="bi bi-rss" role="img">
|
||
</i>
|
||
<span class="menu-text"></span></a>
|
||
</li>
|
||
</ul>
|
||
</div> <!-- /navcollapse -->
|
||
<div class="quarto-navbar-tools">
|
||
<a href="" class="quarto-color-scheme-toggle quarto-navigation-tool px-1" onclick="window.quartoToggleColorScheme(); return false;" title="Toggle dark mode"><i class="bi"></i></a>
|
||
<a href="" class="quarto-reader-toggle quarto-navigation-tool px-1" onclick="window.quartoToggleReader(); return false;" title="Toggle reader mode">
|
||
<div class="quarto-reader-toggle-btn">
|
||
<i class="bi"></i>
|
||
</div>
|
||
</a>
|
||
</div>
|
||
</div> <!-- /container-fluid -->
|
||
</nav>
|
||
<nav class="quarto-secondary-nav">
|
||
<div class="container-fluid d-flex">
|
||
<button type="button" class="quarto-btn-toggle btn" data-bs-toggle="collapse" role="button" data-bs-target=".quarto-sidebar-collapse-item" aria-controls="quarto-sidebar" aria-expanded="false" aria-label="Toggle sidebar navigation" onclick="if (window.quartoToggleHeadroom) { window.quartoToggleHeadroom(); }">
|
||
<i class="bi bi-layout-text-sidebar-reverse"></i>
|
||
</button>
|
||
<nav class="quarto-page-breadcrumbs" aria-label="breadcrumb"><ol class="breadcrumb"><li class="breadcrumb-item">Serious</li><li class="breadcrumb-item">Coding</li><li class="breadcrumb-item"><a href="../../../Coding/Haskell/Advantages.html">Haskell</a></li><li class="breadcrumb-item"><a href="../../../Coding/Haskell/Code Snippets/Monoid.html">Code Snippets</a></li><li class="breadcrumb-item"><a href="../../../Coding/Haskell/Code Snippets/Monoid.html">Monoid? Da war doch was…</a></li></ol></nav>
|
||
<a class="flex-grow-1" role="navigation" data-bs-toggle="collapse" data-bs-target=".quarto-sidebar-collapse-item" aria-controls="quarto-sidebar" aria-expanded="false" aria-label="Toggle sidebar navigation" onclick="if (window.quartoToggleHeadroom) { window.quartoToggleHeadroom(); }">
|
||
</a>
|
||
</div>
|
||
</nav>
|
||
</header>
|
||
<!-- content -->
|
||
<div id="quarto-content" class="quarto-container page-columns page-rows-contents page-layout-article page-navbar">
|
||
<!-- sidebar -->
|
||
<nav id="quarto-sidebar" class="sidebar collapse collapse-horizontal quarto-sidebar-collapse-item sidebar-navigation docked overflow-auto">
|
||
<div class="sidebar-menu-container">
|
||
<ul class="list-unstyled mt-1">
|
||
<li class="sidebar-item sidebar-item-section">
|
||
<div class="sidebar-item-container">
|
||
<a class="sidebar-item-text sidebar-link text-start" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-1" role="navigation" aria-expanded="true">
|
||
<span class="menu-text">Serious</span></a>
|
||
<a class="sidebar-item-toggle text-start" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-1" role="navigation" aria-expanded="true" aria-label="Toggle section">
|
||
<i class="bi bi-chevron-right ms-2"></i>
|
||
</a>
|
||
</div>
|
||
<ul id="quarto-sidebar-section-1" class="collapse list-unstyled sidebar-section depth1 show">
|
||
<li class="sidebar-item sidebar-item-section">
|
||
<div class="sidebar-item-container">
|
||
<a class="sidebar-item-text sidebar-link text-start collapsed" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-2" role="navigation" aria-expanded="false">
|
||
<span class="menu-text">Writing</span></a>
|
||
<a class="sidebar-item-toggle text-start collapsed" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-2" role="navigation" aria-expanded="false" aria-label="Toggle section">
|
||
<i class="bi bi-chevron-right ms-2"></i>
|
||
</a>
|
||
</div>
|
||
<ul id="quarto-sidebar-section-2" class="collapse list-unstyled sidebar-section depth2 ">
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../../../Writing/documentation.html" class="sidebar-item-text sidebar-link">
|
||
<span class="menu-text">Anforderungskatalog für die Dokumentation von Forschungssoftware (Digital Humanities)</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../../../Writing/ner4all-case-study.html" class="sidebar-item-text sidebar-link">
|
||
<span class="menu-text">Case Study: Local LLM-Based NER with n8n and Ollama</span></a>
|
||
</div>
|
||
</li>
|
||
<li class="sidebar-item">
|
||
<div class="sidebar-item-container">
|
||
<a href="../../../Writing/Obsidian-RAG.html" class="sidebar-item-text sidebar-link">
|
||
<span class="menu-text">RAG für eine Obsidian-Wissensdatenbank: Technische Ansätze</span></a>
|
||
</div>
|
||
</li>
|
||
</ul>
|
||
</li>
|
||
<li class="sidebar-item sidebar-item-section">
|
||
<div class="sidebar-item-container">
|
||
<a class="sidebar-item-text sidebar-link text-start" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar-section-3" role="navigation" aria-expanded="true">
|
||
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<p>Monoide tauchen überall auf. Ein Grund sich damit mal etwas eingehender an einen konkreten Beispiel zu beschäftigen.</p>
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<p>Stellen wir uns vor, dass wir eine Funktion schreiben, die einen String bekommt (mehrere Lines mit ACSII-Text) und dieses Wort-für-Wort rückwärts ausgeben soll. Das ist ein einfacher Einzeiler:</p>
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<div class="sourceCode" id="cb1"><pre class="sourceCode haskell code-with-copy"><code class="sourceCode haskell"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="kw">module</span> <span class="dt">Main</span> <span class="kw">where</span></span>
|
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<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a></span>
|
||
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a><span class="kw">import</span> <span class="dt">System.Environment</span> (getArgs)</span>
|
||
<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a><span class="kw">import</span> <span class="dt">Data.Monoid</span> (mconcat)</span>
|
||
<span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a><span class="kw">import</span> <span class="dt">Data.Functor</span> ((<$>))</span>
|
||
<span id="cb1-6"><a href="#cb1-6" aria-hidden="true" tabindex="-1"></a></span>
|
||
<span id="cb1-7"><a href="#cb1-7" aria-hidden="true" tabindex="-1"></a>main <span class="ot">=</span> <span class="kw">do</span></span>
|
||
<span id="cb1-8"><a href="#cb1-8" aria-hidden="true" tabindex="-1"></a> ls <span class="ot"><-</span> <span class="fu">readFile</span> <span class="op">=<<</span> <span class="fu">head</span> <span class="op"><$></span> getArgs</span>
|
||
<span id="cb1-9"><a href="#cb1-9" aria-hidden="true" tabindex="-1"></a> <span class="fu">mconcat</span> <span class="op"><$></span> <span class="fu">mapM</span> (<span class="fu">putStrLn</span> <span class="op">.</span> <span class="fu">unwords</span> <span class="op">.</span> <span class="fu">reverse</span> <span class="op">.</span> <span class="fu">words</span>) (<span class="fu">lines</span> ls) <span class="co">--die eigentliche Funktion, ls ist das argument.</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<p>Was passiert hier an Vodoo? Und was machen die ganzen wilden Zeichen da?</p>
|
||
<p>Gehen wir die Main zeilenweise durch: Wir lesen die Datei, die im ersten Kommandozeilen-Argument gegeben wird. getArgs hat folgende Signatur:</p>
|
||
<div class="sourceCode" id="cb2"><pre class="sourceCode haskell code-with-copy"><code class="sourceCode haskell"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a><span class="ot">getArgs ::</span> <span class="dt">IO</span> [<span class="dt">String</span>]</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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||
<p>Wir bekommen als eine Liste der Argumente. Wir wollen nur das erste. Also machen wir head getArgs. Allerdings fliegt uns dann ein Fehler. head sieht nämlich so aus:</p>
|
||
<div class="sourceCode" id="cb3"><pre class="sourceCode haskell code-with-copy"><code class="sourceCode haskell"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a><span class="fu">head</span><span class="ot"> ::</span> [a] <span class="ot">-></span> a</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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||
<p>Irgendwie müssen wird as <strong>in</strong> das IO bekommen. Hierzu gibt es fmap. Somit ist</p>
|
||
<div class="sourceCode" id="cb4"><pre class="sourceCode haskell code-with-copy"><code class="sourceCode haskell"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a><span class="fu">fmap</span><span class="ot"> head ::</span> <span class="dt">IO</span> [a] <span class="ot">-></span> <span class="dt">IO</span> a</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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||
<p>Ein inline-Alias (um die Funktion links und das Argument rechts zu schreiben und sich ne Menge Klammern zu sparen) ist <$>. Somit ist schlussendlich der Inhalt der Datei aus dem ersten Argument (lazy) in ls.</p>
|
||
<p>Eine andere Möglichkeit sich das (in diesem Fall) zu merken, bzw. drauf zu kommen ist, dass [] AUCH ein Funktor (sogar eine Monade) ist. Man könnte das also auch so schreiben:</p>
|
||
<div class="sourceCode" id="cb5"><pre class="sourceCode haskell code-with-copy"><code class="sourceCode haskell"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a><span class="fu">head</span><span class="ot"> ::</span> [] a <span class="ot">-></span> a</span>
|
||
<span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a><span class="fu">head</span><span class="ot"> ::</span> <span class="dt">Functor</span> f <span class="ot">=></span> [] (f a) <span class="ot">-></span> f a <span class="co">-- das "a" geschickt ersetzt zur Verdeutlichung</span></span>
|
||
<span id="cb5-3"><a href="#cb5-3" aria-hidden="true" tabindex="-1"></a><span class="ot">getArgs ::</span> <span class="dt">IO</span> [] <span class="dt">String</span></span>
|
||
<span id="cb5-4"><a href="#cb5-4" aria-hidden="true" tabindex="-1"></a><span class="fu">fmap</span><span class="ot"> head ::</span> <span class="dt">Functor</span> f <span class="ot">=></span> f [] a <span class="ot">-></span> f a</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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||
<p>fmap “packt” die Funktion quasi 1 Umgebung (Funktor, Monade, ..) weiter rein - Sei es nun in Maybe, Either oder irgendwas anderes.</p>
|
||
<p>Alternatives (ausführliches) Beispiel am Ende.</p>
|
||
<p>Wenn wir uns die Signatur ansehen, dann haben wir nun</p>
|
||
<div class="sourceCode" id="cb6"><pre class="sourceCode haskell code-with-copy"><code class="sourceCode haskell"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a><span class="fu">head</span> <span class="op"><$></span><span class="ot"> getArgs ::</span> <span class="dt">IO</span> <span class="dt">String</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<p>readFile will aber nun ein String haben. Man kann nun</p>
|
||
<div class="sourceCode" id="cb7"><pre class="sourceCode haskell code-with-copy"><code class="sourceCode haskell"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a>f <span class="ot"><-</span> <span class="fu">head</span> <span class="op"><$></span> getArgs</span>
|
||
<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a>ls <span class="ot"><-</span> <span class="fu">readFile</span> f</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<p>kann man auch “inline” mit =<< die Sachen “auspacken”.</p>
|
||
<p>Die 2. Zeile lesen wir nun einfach “von hinten”, wie man das meistens tun sollte. Hier ist ein</p>
|
||
<div class="sourceCode" id="cb8"><pre class="sourceCode haskell code-with-copy"><code class="sourceCode haskell"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a><span class="fu">lines</span><span class="ot"> ls ::</span> [<span class="dt">String</span>]</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<p>was uns den Inhalt der Datei zeilenweise gibt. Mit jeder Zeile möchten wir nun folgendes machen:</p>
|
||
<ol type="1">
|
||
<li>nach Wörtern trennen (words)</li>
|
||
<li>Wörter in der reihenfolge umkehren (reverse)</li>
|
||
<li>Wörter wider zu einer Zeile zusammensetzen (unwords)</li>
|
||
<li>diese Zeile ausgeben (putStrLn)</li>
|
||
</ol>
|
||
<p>Wenn wir uns die Signatur ansehen:</p>
|
||
<div class="sourceCode" id="cb9"><pre class="sourceCode haskell code-with-copy"><code class="sourceCode haskell"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a>(<span class="fu">putStrLn</span> <span class="op">.</span> <span class="fu">unwords</span> <span class="op">.</span> <span class="fu">reverse</span> <span class="op">.</span> <span class="fu">words</span>)<span class="ot"> ::</span> <span class="dt">String</span> <span class="ot">-></span> <span class="dt">IO</span> ()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<p>Das mag im ersten Moment verwirren, daher noch die Signaturen der Einzelfunktionen:</p>
|
||
<div class="sourceCode" id="cb10"><pre class="sourceCode haskell code-with-copy"><code class="sourceCode haskell"><span id="cb10-1"><a href="#cb10-1" aria-hidden="true" tabindex="-1"></a><span class="fu">words</span><span class="ot"> ::</span> <span class="dt">String</span> <span class="ot">-></span> [<span class="dt">String</span>]</span>
|
||
<span id="cb10-2"><a href="#cb10-2" aria-hidden="true" tabindex="-1"></a><span class="fu">reverse</span><span class="ot"> ::</span> [a] <span class="ot">-></span> [a]</span>
|
||
<span id="cb10-3"><a href="#cb10-3" aria-hidden="true" tabindex="-1"></a><span class="fu">unwords</span><span class="ot"> ::</span> [<span class="dt">String</span>] <span class="ot">-></span> <span class="dt">String</span></span>
|
||
<span id="cb10-4"><a href="#cb10-4" aria-hidden="true" tabindex="-1"></a><span class="fu">putStrLn</span><span class="ot"> ::</span> <span class="dt">String</span> <span class="ot">-></span> <span class="dt">IO</span> ()</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<p>Da wir am Ende in der IO-Monade landen müssen wir das auf unsere Zeilen mit mapM statt map anwenden. Dies sorgt auch dafür, dass die Liste der reihe nach durchgegangen wird. mapM mit unserer Funktion schaut dann so aus:</p>
|
||
<div class="sourceCode" id="cb11"><pre class="sourceCode haskell code-with-copy"><code class="sourceCode haskell"><span id="cb11-1"><a href="#cb11-1" aria-hidden="true" tabindex="-1"></a><span class="fu">mapM</span> (<span class="fu">putStrLn</span> <span class="op">.</span> <span class="fu">unwords</span> <span class="op">.</span> <span class="fu">reverse</span> <span class="op">.</span> <span class="fu">words</span>)<span class="ot"> ::</span> [<span class="dt">String</span>] <span class="ot">-></span> [<span class="dt">IO</span> ()]</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<p>eek! Das [IO ()] sieht ekelig aus. Wir haben eine Liste von IO-gar nichts. Das können wir eigentlich entsorgen. Da wir innerhalb der main-Funktion in einer IO-Monade sind, wollen wir IO () anstatt [IO ()] zurück haben.</p>
|
||
<p>Wenn wir uns jetzt erinnern, dass [] auch nur eine Monade ist und dass jede Monade ein Monoid ist, dann ist die Lösung einfach. Monoide haben eine “append”-funktion (mappend oder (<>) genannt). Wenn wir “nichts” an “nichts” anhängen, dann erhalten wir …. <em>Trommelwirbel</em> “nichts”! Wir müssen die [IO ()]-Liste also “nur noch” mit mappend falten. Hierzu gibt es schon eine vorgefertigte Funktion:</p>
|
||
<div class="sourceCode" id="cb12"><pre class="sourceCode haskell code-with-copy"><code class="sourceCode haskell"><span id="cb12-1"><a href="#cb12-1" aria-hidden="true" tabindex="-1"></a><span class="fu">mconcat</span><span class="ot"> ::</span> [a] <span class="ot">-></span> a</span>
|
||
<span id="cb12-2"><a href="#cb12-2" aria-hidden="true" tabindex="-1"></a><span class="fu">mconcat</span> <span class="ot">=</span> <span class="fu">foldr</span> <span class="fu">mappend</span> <span class="fu">mempty</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<p>Was genau die gewünschte Faltung macht. Wir müssen nun wieder fmap nehmen, da wir die Liste selbst falten wollen - und nicht map, welches auf den IO () innerhalb der Liste arbeiten würde. Durch die Faltung fällt die Liste nun auf IO () zusammen.</p>
|
||
<p>Viel Voodoo in wenig Code, aber wenn man sich dran gewöhnt hat, sind Monaden in Monaden auch nicht schlimm. Man muss sich immer nur richtig “rein” fmap’en.</p>
|
||
<hr>
|
||
<p>Kleinen Tipp gab es noch: mapM_ macht genau das, was oben mit mconcat erreicht werden sollte. Somit kann man auch</p>
|
||
<div class="sourceCode" id="cb13"><pre class="sourceCode haskell code-with-copy"><code class="sourceCode haskell"><span id="cb13-1"><a href="#cb13-1" aria-hidden="true" tabindex="-1"></a><span class="fu">mapM_</span> (<span class="fu">putStrLn</span> <span class="op">.</span> <span class="fu">unwords</span> <span class="op">.</span> <span class="fu">reverse</span> <span class="op">.</span> <span class="fu">words</span>) (<span class="fu">lines</span> ls)</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<p>schreiben. Ich hab es aber mal wegen der klarheit oben so gelassen.</p>
|
||
<section id="alternatives-fmap-beispiel" class="level2">
|
||
<h2 class="anchored" data-anchor-id="alternatives-fmap-beispiel">Alternatives fmap-Beispiel</h2>
|
||
<p>Nehmen wir als alternatives Beispiel mal an:</p>
|
||
<div class="sourceCode" id="cb14"><pre class="sourceCode haskell code-with-copy"><code class="sourceCode haskell"><span id="cb14-1"><a href="#cb14-1" aria-hidden="true" tabindex="-1"></a><span class="ot">a ::</span> <span class="dt">IO</span> <span class="dt">Maybe</span> <span class="dt">State</span> t</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<p>Um Funktionen vom Typ</p>
|
||
<div class="sourceCode" id="cb15"><pre class="sourceCode haskell code-with-copy"><code class="sourceCode haskell"><span id="cb15-1"><a href="#cb15-1" aria-hidden="true" tabindex="-1"></a><span class="ot">f ::</span> <span class="dt">IO</span> a <span class="ot">-></span> <span class="dt">IO</span> a</span>
|
||
<span id="cb15-2"><a href="#cb15-2" aria-hidden="true" tabindex="-1"></a>f a <span class="co">-- valide</span></span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<p>zu nehmen, brauchen wir nichts machen. Bei</p>
|
||
<div class="sourceCode" id="cb16"><pre class="sourceCode haskell code-with-copy"><code class="sourceCode haskell"><span id="cb16-1"><a href="#cb16-1" aria-hidden="true" tabindex="-1"></a><span class="ot">f' ::</span> <span class="dt">Maybe</span> a <span class="ot">-></span> <span class="dt">Maybe</span> a</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<p>brauchen wir 1 fmap, also ein</p>
|
||
<div class="sourceCode" id="cb17"><pre class="sourceCode haskell code-with-copy"><code class="sourceCode haskell"><span id="cb17-1"><a href="#cb17-1" aria-hidden="true" tabindex="-1"></a>f' a <span class="co">-- error</span></span>
|
||
<span id="cb17-2"><a href="#cb17-2" aria-hidden="true" tabindex="-1"></a>f' <span class="op"><$></span> a</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<p>um eine Funktion</p>
|
||
<div class="sourceCode" id="cb18"><pre class="sourceCode haskell code-with-copy"><code class="sourceCode haskell"><span id="cb18-1"><a href="#cb18-1" aria-hidden="true" tabindex="-1"></a><span class="ot">f'' ::</span> <span class="dt">State</span> t <span class="ot">-></span> <span class="dt">State</span> t</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
||
<p>zu benutzen folglich:</p>
|
||
<div class="sourceCode" id="cb19"><pre class="sourceCode haskell code-with-copy"><code class="sourceCode haskell"><span id="cb19-1"><a href="#cb19-1" aria-hidden="true" tabindex="-1"></a>f'' a <span class="co">-- error</span></span>
|
||
<span id="cb19-2"><a href="#cb19-2" aria-hidden="true" tabindex="-1"></a>f'' <span class="op"><$></span> a <span class="co">-- error</span></span>
|
||
<span id="cb19-3"><a href="#cb19-3" aria-hidden="true" tabindex="-1"></a><span class="fu">fmap</span> f'' <span class="op"><$></span> a</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
|
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|
||
// (since there is no id in the URL)
|
||
// remove the first header
|
||
if (note.children.length > 0 && note.children[0].tagName === "HEADER") {
|
||
note.children[0].remove();
|
||
}
|
||
const html = processXRef(null, note);
|
||
instance.setContent(html);
|
||
}
|
||
}).finally(() => {
|
||
instance.enable();
|
||
instance.show();
|
||
});
|
||
}
|
||
}, function(instance) {
|
||
});
|
||
}
|
||
let selectedAnnoteEl;
|
||
const selectorForAnnotation = ( cell, annotation) => {
|
||
let cellAttr = 'data-code-cell="' + cell + '"';
|
||
let lineAttr = 'data-code-annotation="' + annotation + '"';
|
||
const selector = 'span[' + cellAttr + '][' + lineAttr + ']';
|
||
return selector;
|
||
}
|
||
const selectCodeLines = (annoteEl) => {
|
||
const doc = window.document;
|
||
const targetCell = annoteEl.getAttribute("data-target-cell");
|
||
const targetAnnotation = annoteEl.getAttribute("data-target-annotation");
|
||
const annoteSpan = window.document.querySelector(selectorForAnnotation(targetCell, targetAnnotation));
|
||
const lines = annoteSpan.getAttribute("data-code-lines").split(",");
|
||
const lineIds = lines.map((line) => {
|
||
return targetCell + "-" + line;
|
||
})
|
||
let top = null;
|
||
let height = null;
|
||
let parent = null;
|
||
if (lineIds.length > 0) {
|
||
//compute the position of the single el (top and bottom and make a div)
|
||
const el = window.document.getElementById(lineIds[0]);
|
||
top = el.offsetTop;
|
||
height = el.offsetHeight;
|
||
parent = el.parentElement.parentElement;
|
||
if (lineIds.length > 1) {
|
||
const lastEl = window.document.getElementById(lineIds[lineIds.length - 1]);
|
||
const bottom = lastEl.offsetTop + lastEl.offsetHeight;
|
||
height = bottom - top;
|
||
}
|
||
if (top !== null && height !== null && parent !== null) {
|
||
// cook up a div (if necessary) and position it
|
||
let div = window.document.getElementById("code-annotation-line-highlight");
|
||
if (div === null) {
|
||
div = window.document.createElement("div");
|
||
div.setAttribute("id", "code-annotation-line-highlight");
|
||
div.style.position = 'absolute';
|
||
parent.appendChild(div);
|
||
}
|
||
div.style.top = top - 2 + "px";
|
||
div.style.height = height + 4 + "px";
|
||
div.style.left = 0;
|
||
let gutterDiv = window.document.getElementById("code-annotation-line-highlight-gutter");
|
||
if (gutterDiv === null) {
|
||
gutterDiv = window.document.createElement("div");
|
||
gutterDiv.setAttribute("id", "code-annotation-line-highlight-gutter");
|
||
gutterDiv.style.position = 'absolute';
|
||
const codeCell = window.document.getElementById(targetCell);
|
||
const gutter = codeCell.querySelector('.code-annotation-gutter');
|
||
gutter.appendChild(gutterDiv);
|
||
}
|
||
gutterDiv.style.top = top - 2 + "px";
|
||
gutterDiv.style.height = height + 4 + "px";
|
||
}
|
||
selectedAnnoteEl = annoteEl;
|
||
}
|
||
};
|
||
const unselectCodeLines = () => {
|
||
const elementsIds = ["code-annotation-line-highlight", "code-annotation-line-highlight-gutter"];
|
||
elementsIds.forEach((elId) => {
|
||
const div = window.document.getElementById(elId);
|
||
if (div) {
|
||
div.remove();
|
||
}
|
||
});
|
||
selectedAnnoteEl = undefined;
|
||
};
|
||
// Handle positioning of the toggle
|
||
window.addEventListener(
|
||
"resize",
|
||
throttle(() => {
|
||
elRect = undefined;
|
||
if (selectedAnnoteEl) {
|
||
selectCodeLines(selectedAnnoteEl);
|
||
}
|
||
}, 10)
|
||
);
|
||
function throttle(fn, ms) {
|
||
let throttle = false;
|
||
let timer;
|
||
return (...args) => {
|
||
if(!throttle) { // first call gets through
|
||
fn.apply(this, args);
|
||
throttle = true;
|
||
} else { // all the others get throttled
|
||
if(timer) clearTimeout(timer); // cancel #2
|
||
timer = setTimeout(() => {
|
||
fn.apply(this, args);
|
||
timer = throttle = false;
|
||
}, ms);
|
||
}
|
||
};
|
||
}
|
||
// Attach click handler to the DT
|
||
const annoteDls = window.document.querySelectorAll('dt[data-target-cell]');
|
||
for (const annoteDlNode of annoteDls) {
|
||
annoteDlNode.addEventListener('click', (event) => {
|
||
const clickedEl = event.target;
|
||
if (clickedEl !== selectedAnnoteEl) {
|
||
unselectCodeLines();
|
||
const activeEl = window.document.querySelector('dt[data-target-cell].code-annotation-active');
|
||
if (activeEl) {
|
||
activeEl.classList.remove('code-annotation-active');
|
||
}
|
||
selectCodeLines(clickedEl);
|
||
clickedEl.classList.add('code-annotation-active');
|
||
} else {
|
||
// Unselect the line
|
||
unselectCodeLines();
|
||
clickedEl.classList.remove('code-annotation-active');
|
||
}
|
||
});
|
||
}
|
||
const findCites = (el) => {
|
||
const parentEl = el.parentElement;
|
||
if (parentEl) {
|
||
const cites = parentEl.dataset.cites;
|
||
if (cites) {
|
||
return {
|
||
el,
|
||
cites: cites.split(' ')
|
||
};
|
||
} else {
|
||
return findCites(el.parentElement)
|
||
}
|
||
} else {
|
||
return undefined;
|
||
}
|
||
};
|
||
var bibliorefs = window.document.querySelectorAll('a[role="doc-biblioref"]');
|
||
for (var i=0; i<bibliorefs.length; i++) {
|
||
const ref = bibliorefs[i];
|
||
const citeInfo = findCites(ref);
|
||
if (citeInfo) {
|
||
tippyHover(citeInfo.el, function() {
|
||
var popup = window.document.createElement('div');
|
||
citeInfo.cites.forEach(function(cite) {
|
||
var citeDiv = window.document.createElement('div');
|
||
citeDiv.classList.add('hanging-indent');
|
||
citeDiv.classList.add('csl-entry');
|
||
var biblioDiv = window.document.getElementById('ref-' + cite);
|
||
if (biblioDiv) {
|
||
citeDiv.innerHTML = biblioDiv.innerHTML;
|
||
}
|
||
popup.appendChild(citeDiv);
|
||
});
|
||
return popup.innerHTML;
|
||
});
|
||
}
|
||
}
|
||
});
|
||
</script>
|
||
</div> <!-- /content -->
|
||
|
||
|
||
|
||
|
||
</body></html> |