616 lines
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HTML
616 lines
25 KiB
HTML
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Julia für Numerik
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<span class="menu-text"><span class='chapter-number'>1</span> <span class='chapter-title'>Das Typsystem von Julia</span></span></a>
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<!-- main -->
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<main class="content" id="quarto-document-content"> <div id="nb1" class="cell" data-execution_count="1">
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<div class="sourceCode" id="cb1"><pre class="sourceCode julia cell-code"><code class="sourceCode julia"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="kw">function</span> <span class="fu">show_subtype_tree</span>(T, i<span class="op">=</span><span class="fl">0</span>)</span>
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<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a> <span class="fu">println</span>(<span class="st">" "</span><span class="op">^</span>i, T)</span>
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<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a> <span class="cf">for</span> Ts <span class="op">∈</span> <span class="fu">subtypes</span>(T)</span>
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<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a> <span class="fu">show_subtype_tree</span>(Ts, i<span class="op">+</span><span class="fl">1</span>)</span>
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<span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a> <span class="cf">end</span></span>
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<span id="cb1-6"><a href="#cb1-6" aria-hidden="true" tabindex="-1"></a><span class="kw">end</span></span>
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<span id="cb1-7"><a href="#cb1-7" aria-hidden="true" tabindex="-1"></a></span>
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<span id="cb1-8"><a href="#cb1-8" aria-hidden="true" tabindex="-1"></a><span class="fu">show_subtype_tree</span>(<span class="dt">Number</span>)</span></code></pre></div>
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<div class="cell-output cell-output-stdout">
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<pre class=""><code class=" ansi">Number
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Complex
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Real
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AbstractFloat
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BigFloat
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Float16
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Float32
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Float64
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AbstractIrrational
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Irrational
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Integer
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Bool
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Signed
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BigInt
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Int128
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Int16
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Int32
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Int64
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Int8
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Unsigned
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UInt128
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UInt16
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UInt32
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UInt64
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UInt8
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Rational</code></pre>
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</div>
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</div>
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<div id="nb2" class="cell" data-execution_count="2">
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<div class="sourceCode" id="cb2"><pre class="sourceCode julia cell-code"><code class="sourceCode julia"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a><span class="im">using</span> <span class="bu">AbstractTrees</span></span>
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<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a></span>
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<span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a>AbstractTrees.<span class="fu">children</span>(x<span class="op">::</span><span class="dt">Type</span>) <span class="op">=</span> <span class="fu">subtypes</span>(x)</span>
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<span id="cb2-4"><a href="#cb2-4" aria-hidden="true" tabindex="-1"></a><span class="fu">print_tree</span>(<span class="dt">Number</span>)</span></code></pre></div>
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<div class="cell-output cell-output-stdout">
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<pre class=""><code class=" ansi">Number
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├─ Complex
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└─ Real
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├─ AbstractFloat
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│ ├─ BigFloat
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│ ├─ Float16
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│ ├─ Float32
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│ └─ Float64
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├─ AbstractIrrational
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│ └─ Irrational
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├─ Integer
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│ ├─ Bool
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│ ├─ Signed
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│ │ ├─ BigInt
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│ │ ├─ Int128
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│ │ ├─ Int16
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│ │ ├─ Int32
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│ │ ├─ Int64
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│ │ └─ Int8
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│ └─ Unsigned
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│ ├─ UInt128
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│ ├─ UInt16
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│ ├─ UInt32
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│ ├─ UInt64
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│ └─ UInt8
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└─ Rational</code></pre>
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</div>
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</div>
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<p><span class="hidden" data-render-id="quarto-int-sidebar-title">Julia für Numerik</span> <span class="hidden" data-render-id="quarto-int-navbar-title">Julia für Numerik</span> <span class="hidden" data-render-id="quarto-int-sidebar:/index.html">Was ist Julia?</span> <span class="hidden" data-render-id="quarto-int-sidebar:/chapters/types.html"><span class="chapter-number">1</span> <span class="chapter-title">Das Typsystem von Julia</span></span> <span class="hidden" data-render-id="footer-left">All content licenced under <a href="https://creativecommons.org/licenses/by-nc-sa/4.0/">CC BY-NC-SA 4.0</a>.</span> <span class="hidden" data-render-id="footer-right">Created with <a href="https://quarto.org/">Quarto</a><br />
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<p><span class="hidden" data-render-id="quarto-twittercardtitle"></span> <span class="hidden" data-render-id="quarto-ogcardtitle"></span> <span class="hidden" data-render-id="quarto-metasitename">Julia für Numerik</span> <span class="hidden" data-render-id="quarto-twittercarddesc"></span> <span class="hidden" data-render-id="quarto-ogcardddesc"></span></p>
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||
clipboard.on('success', function(e) {
|
||
// button target
|
||
const button = e.trigger;
|
||
// don't keep focus
|
||
button.blur();
|
||
// flash "checked"
|
||
button.classList.add('code-copy-button-checked');
|
||
var currentTitle = button.getAttribute("title");
|
||
button.setAttribute("title", "Kopiert");
|
||
let tooltip;
|
||
if (window.bootstrap) {
|
||
button.setAttribute("data-bs-toggle", "tooltip");
|
||
button.setAttribute("data-bs-placement", "left");
|
||
button.setAttribute("data-bs-title", "Kopiert");
|
||
tooltip = new bootstrap.Tooltip(button,
|
||
{ trigger: "manual",
|
||
customClass: "code-copy-button-tooltip",
|
||
offset: [0, -8]});
|
||
tooltip.show();
|
||
}
|
||
setTimeout(function() {
|
||
if (tooltip) {
|
||
tooltip.hide();
|
||
button.removeAttribute("data-bs-title");
|
||
button.removeAttribute("data-bs-toggle");
|
||
button.removeAttribute("data-bs-placement");
|
||
}
|
||
button.setAttribute("title", currentTitle);
|
||
button.classList.remove('code-copy-button-checked');
|
||
}, 1000);
|
||
// clear code selection
|
||
e.clearSelection();
|
||
});
|
||
function tippyHover(el, contentFn) {
|
||
const config = {
|
||
allowHTML: true,
|
||
content: contentFn,
|
||
maxWidth: 500,
|
||
delay: 100,
|
||
arrow: false,
|
||
appendTo: function(el) {
|
||
return el.parentElement;
|
||
},
|
||
interactive: true,
|
||
interactiveBorder: 10,
|
||
theme: 'quarto',
|
||
placement: 'bottom-start'
|
||
};
|
||
window.tippy(el, config);
|
||
}
|
||
const noterefs = window.document.querySelectorAll('a[role="doc-noteref"]');
|
||
for (var i=0; i<noterefs.length; i++) {
|
||
const ref = noterefs[i];
|
||
tippyHover(ref, function() {
|
||
// use id or data attribute instead here
|
||
let href = ref.getAttribute('data-footnote-href') || ref.getAttribute('href');
|
||
try { href = new URL(href).hash; } catch {}
|
||
const id = href.replace(/^#\/?/, "");
|
||
const note = window.document.getElementById(id);
|
||
return note.innerHTML;
|
||
});
|
||
}
|
||
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";
|
||
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;
|
||
};
|
||
// 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 -->
|
||
<footer class="footer">
|
||
<div class="nav-footer">
|
||
<div class="nav-footer-left">
|
||
<div class='footer-contents'>All content licenced under [CC BY-NC-SA 4.0](https://creativecommons.org/licenses/by-nc-sa/4.0/).
|
||
</div>
|
||
</div>
|
||
<div class="nav-footer-center">
|
||
|
||
</div>
|
||
<div class="nav-footer-right">
|
||
<div class='footer-contents'>Created with [Quarto](https://quarto.org/)
|
||
</div>
|
||
</div>
|
||
</div>
|
||
</footer>
|
||
</body>
|
||
</html>
|