docs/doc/valences.html


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  <title>BQN: Valences</title>
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<h1 id="valences"><a class="header" href="#valences">Valences</a></h1>
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      <text dy='0.32em' y='155' font-size='19px'><tspan class='Function'>𝔽</tspan><tspan class='Modifier2'>⊘</tspan><tspan class='Function'>𝔾</tspan> <tspan class='Value'>𝕩</tspan></text>
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      <text dy='0.32em' x='0' y='114'><tspan class='Value'>𝕩</tspan></text>
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      <text dy='0.32em' y='155' font-size='19px'><tspan class='Value'>𝕨</tspan> <tspan class='Function'>𝔽</tspan><tspan class='Modifier2'>⊘</tspan><tspan class='Function'>𝔾</tspan> <tspan class='Value'>𝕩</tspan></text>
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      <text dy='0.32em' x='32' y='114'><tspan class='Value'>𝕩</tspan></text>
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<p>Every BQN function can be called with one or two arguments, possibly doing completely different things in each case. The Valences (<code><span class='Modifier2'>⊘</span></code>) 2-modifier grafts together a one-argument function <code><span class='Function'>𝔽</span></code> and a two-argument function <code><span class='Function'>𝔾</span></code>, with the resulting function calling one or the other as appropriate. It's the <a href="tacit.html">tacit</a> equivalent of a block function with <a href="block.html#multiple-bodies">two bodies</a>. So the function <code><span class='Brace'>{</span><span class='Function'>÷</span><span class='Value'>𝕩</span> <span class='Head'>;</span> <span class='Value'>𝕩</span><span class='Function'>-</span><span class='Value'>𝕨</span><span class='Brace'>}</span></code> can also be written <code><span class='Function'>÷</span><span class='Modifier2'>⊘</span><span class='Paren'>(</span><span class='Function'>-</span><span class='Modifier'>˜</span><span class='Paren'>)</span></code>. A full definition of Valences as a block is <code><span class='Brace'>{</span><span class='Function'>𝔽</span><span class='Value'>𝕩</span><span class='Head'>;</span><span class='Value'>𝕨</span><span class='Function'>𝔾</span><span class='Value'>𝕩</span><span class='Brace'>}</span></code>.</p>
<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=ICAt4oqYKyA2ICAjIC0gc2lkZQoKMyAt4oqYKyAyICAjICsgc2lkZQ==">↗️</a><pre>      <span class='Function'>-</span><span class='Modifier2'>⊘</span><span class='Function'>+</span> <span class='Number'>6</span>  <span class='Comment'># - side
</span>¯6

    <span class='Number'>3</span> <span class='Function'>-</span><span class='Modifier2'>⊘</span><span class='Function'>+</span> <span class='Number'>2</span>  <span class='Comment'># + side
</span>5
</pre>
<p>Valences provides one way to check whether <code><span class='Value'>𝕨</span></code> is present in a block function. The expression <code><span class='Value'>𝕨</span><span class='Number'>0</span><span class='Modifier2'>⊘</span><span class='Number'>1</span><span class='Value'>𝕩</span></code> always ignores the values of the arguments, resulting in <code><span class='Number'>0</span></code> if <code><span class='Value'>𝕨</span></code> isn't given and <code><span class='Number'>1</span></code> if it is (if you want <code><span class='Number'>1</span></code> or <code><span class='Number'>2</span></code>, then <code><span class='Function'>≠</span><span class='Value'>𝕨</span><span class='Function'>⋈</span><span class='Value'>𝕩</span></code> is shorter, but I'm not sure if I like it).</p>
<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=ICAgIHvwnZWoMOKKmDHwnZWpfSAneCcKCid3JyB78J2VqDDiipgx8J2VqX0gJ3gn">↗️</a><pre>        <span class='Brace'>{</span><span class='Value'>𝕨</span><span class='Number'>0</span><span class='Modifier2'>⊘</span><span class='Number'>1</span><span class='Value'>𝕩</span><span class='Brace'>}</span> <span class='String'>'x'</span>
0

    <span class='String'>'w'</span> <span class='Brace'>{</span><span class='Value'>𝕨</span><span class='Number'>0</span><span class='Modifier2'>⊘</span><span class='Number'>1</span><span class='Value'>𝕩</span><span class='Brace'>}</span> <span class='String'>'x'</span>
1
</pre>