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<head>
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<title>BQN: Pair</title>
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<h1 id="pair"><a class="header" href="#pair">Pair</a></h1>
<p>The function <code><span class='Function'>⋈</span></code> forms a list of all its arguments. When there's one argument, it's called "Enlist", and with two, it's called "Pair".</p>
<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4ouIICJlbmxpc3QiICAgICMg4p+o8J2VqeKfqQoKInBhIiDii4ggImlyIiAgICMg4p+o8J2VqCzwnZWp4p+p">↗️</a><pre> <span class='Function'>⋈</span> <span class='String'>"enlist"</span> <span class='Comment'># ⟨𝕩⟩
</span>⟨ "enlist" ⟩
<span class='String'>"pa"</span> <span class='Function'>⋈</span> <span class='String'>"ir"</span> <span class='Comment'># ⟨𝕨,𝕩⟩
</span>⟨ "pa" "ir" ⟩
</pre>
<p>It's usually preferable to use <a href="arrayrepr.html#brackets">list notation</a> directly for such arrays, because it's easy to add or remove any number of elements. Pair is useful when a standalone function is needed, for example to be used as an operand.</p>
<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=MuKAvzTigL8xIOKLiOKMnCAibm9ydGgi4oC/InNvdXRoIiAgIyBDYXJ0ZXNpYW4gcHJvZHVjdAoK4ouIwqggIistw5fDtyIgICMgR2x5cGhzIHRvIHN0cmluZ3M=">↗️</a><pre> <span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>4</span><span class='Ligature'>‿</span><span class='Number'>1</span> <span class='Function'>⋈</span><span class='Modifier'>⌜</span> <span class='String'>"north"</span><span class='Ligature'>‿</span><span class='String'>"south"</span> <span class='Comment'># Cartesian product
</span>┌─
╵ ⟨ 2 "north" ⟩ ⟨ 2 "south" ⟩
⟨ 4 "north" ⟩ ⟨ 4 "south" ⟩
⟨ 1 "north" ⟩ ⟨ 1 "south" ⟩
┘
<span class='Function'>⋈</span><span class='Modifier'>¨</span> <span class='String'>"+-×÷"</span> <span class='Comment'># Glyphs to strings
</span>⟨ "+" "-" "×" "÷" ⟩
</pre>
<p>Another common pattern is to use Pair in a <a href="train.html">train</a>, giving the results from applying each of two functions.</p>
<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=J2MnICgr4ouILSkgIDHigL8y">↗️</a><pre> <span class='String'>'c'</span> <span class='Paren'>(</span><span class='Function'>+⋈-</span><span class='Paren'>)</span> <span class='Number'>1</span><span class='Ligature'>‿</span><span class='Number'>2</span>
⟨ "de" "ba" ⟩
</pre>
<p>For longer lists, this pattern can be extended with the function <code><span class='Function'><</span><span class='Modifier2'>⊸</span><span class='Function'>∾</span></code>, which prepends a single element to a list.</p>
<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=ImUwIiA84oq44oi+ICJlMSIgPOKKuOKIviAiZTIiIOKLiCAiZTMi">↗️</a><pre> <span class='String'>"e0"</span> <span class='Function'><</span><span class='Modifier2'>⊸</span><span class='Function'>∾</span> <span class='String'>"e1"</span> <span class='Function'><</span><span class='Modifier2'>⊸</span><span class='Function'>∾</span> <span class='String'>"e2"</span> <span class='Function'>⋈</span> <span class='String'>"e3"</span>
⟨ "e0" "e1" "e2" "e3" ⟩
</pre>
<p>However, before making a long list of this sort, consider that your goal might be more easily accomplished with a list of functions.</p>
<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=NiAoKyA84oq44oi+IC0gPOKKuOKIviDDlyDii4ggw7cpIDMKCns28J2VjzN9wqggK+KAvy3igL/Dl+KAv8O3">↗️</a><pre> <span class='Number'>6</span> <span class='Paren'>(</span><span class='Function'>+</span> <span class='Function'><</span><span class='Modifier2'>⊸</span><span class='Function'>∾</span> <span class='Function'>-</span> <span class='Function'><</span><span class='Modifier2'>⊸</span><span class='Function'>∾</span> <span class='Function'>×</span> <span class='Function'>⋈</span> <span class='Function'>÷</span><span class='Paren'>)</span> <span class='Number'>3</span>
⟨ 9 3 18 2 ⟩
<span class='Brace'>{</span><span class='Number'>6</span><span class='Function'>𝕏</span><span class='Number'>3</span><span class='Brace'>}</span><span class='Modifier'>¨</span> <span class='Function'>+</span><span class='Ligature'>‿</span><span class='Function'>-</span><span class='Ligature'>‿</span><span class='Function'>×</span><span class='Ligature'>‿</span><span class='Function'>÷</span>
⟨ 9 3 18 2 ⟩
</pre>
<h2 id="pair-versus-couple"><a class="header" href="#pair-versus-couple">Pair versus Couple</a></h2>
<p>Enlist and Pair closely related to <a href="couple.html">Solo and Couple</a>, in that <code><span class='Function'>⋈</span></code> is equivalent to <code><span class='Function'>≍</span><span class='Modifier2'>○</span><span class='Function'><</span></code> and <code><span class='Function'>≍</span></code> is equivalent to <code><span class='Function'>></span><span class='Modifier2'>∘</span><span class='Function'>⋈</span></code>. However, the result of <code><span class='Function'>⋈</span></code> is always a list (rank 1) while Solo or Couple return an array of rank at least 1.</p>
<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=ImFiYyIg4omNICJkZWYiCgoiYWJjIiDii4ggImRlZiI=">↗️</a><pre> <span class='String'>"abc"</span> <span class='Function'>≍</span> <span class='String'>"def"</span>
┌─
╵"abc
def"
┘
<span class='String'>"abc"</span> <span class='Function'>⋈</span> <span class='String'>"def"</span>
⟨ "abc" "def" ⟩
</pre>
<p>And the arguments to Couple must have the same shape, while Enlist takes any two arguments.</p>
<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=ImFiYyIg4omNICJkZWZnIgoKImFiYyIg4ouIICJkZWZnIg==">↗️</a><pre> <span class='String'>"abc"</span> <span class='Function'>≍</span> <span class='String'>"defg"</span>
<span class='Error'>Error: ≍: 𝕨 and 𝕩 must have equal shapes (⟨3⟩ ≡ ≢𝕨, ⟨4⟩ ≡ ≢𝕩)</span>
<span class='String'>"abc"</span> <span class='Function'>⋈</span> <span class='String'>"defg"</span>
⟨ "abc" "defg" ⟩
</pre>
<p>The difference is that Couple treats the arguments as cells, and adds a dimension, while Pair treats them as elements, adding a layer of depth. Couple is a "flat" version of Pair, much like Cells (<code><span class='Modifier'>˘</span></code>) is a flat version of Each (<code><span class='Modifier'>¨</span></code>). Pair is more versatile, but—precisely because of its restrictions—Couple may allow more powerful array operations on the result.</p>
<h2 id="fill-element"><a class="header" href="#fill-element">Fill element</a></h2>
<p>Enlist and Pair set the result's <a href="fill.html">fill</a> element, while list notation doesn't have to. So the following result is guaranteed:</p>
<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=NCDihpEgImEi4oC/NSDii4ggImIi4oC/Nw==">↗️</a><pre> <span class='Number'>4</span> <span class='Function'>↑</span> <span class='String'>"a"</span><span class='Ligature'>‿</span><span class='Number'>5</span> <span class='Function'>⋈</span> <span class='String'>"b"</span><span class='Ligature'>‿</span><span class='Number'>7</span>
⟨ ⟨ "a" 5 ⟩ ⟨ "b" 7 ⟩ ⟨ " " 0 ⟩ ⟨ " " 0 ⟩ ⟩
</pre>
<p>This means that <code><span class='Function'>⋈</span></code> may always behave the same as the obvious implementation <code><span class='Brace'>{</span><span class='Bracket'>⟨</span><span class='Value'>𝕩</span><span class='Bracket'>⟩</span><span class='Head'>;</span><span class='Bracket'>⟨</span><span class='Value'>𝕨</span><span class='Separator'>,</span><span class='Value'>𝕩</span><span class='Bracket'>⟩</span><span class='Brace'>}</span></code>. However, <code><span class='Function'>≍</span><span class='Modifier2'>○</span><span class='Function'><</span></code> and even <code><span class='Function'>></span><span class='Modifier2'>∘</span><span class='Brace'>{</span><span class='Bracket'>⟨</span><span class='Value'>𝕩</span><span class='Bracket'>⟩</span><span class='Head'>;</span><span class='Bracket'>⟨</span><span class='Value'>𝕨</span><span class='Separator'>,</span><span class='Value'>𝕩</span><span class='Bracket'>⟩</span><span class='Brace'>}</span><span class='Modifier2'>○</span><span class='Function'><</span></code> compute the result fill as <code><span class='Function'>⋈</span></code> does and are identical implementations.</p>
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