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<head>
<link href="../favicon.ico" rel="shortcut icon" type="image/x-icon"/>
<link href="../style.css" rel="stylesheet"/>
<title>BQN–Dyalog APL dictionary</title>
</head>
<div class="nav">(<a href="https://github.com/mlochbaum/BQN">github</a>) / <a href="../index.html">BQN</a> / <a href="index.html">doc</a></div>
<h1 id="bqndyalog-apl-dictionary"><a class="header" href="#bqndyalog-apl-dictionary">BQN–Dyalog APL dictionary</a></h1>
<p>A few tables to help users of Dyalog APL (or similar) get started quickly on BQN. For a higher-level comparison, check <a href="../commentary/why.html#versus-apl-and-j">Why BQN?</a>. Here we assume <code><span class='Value'>⎕</span><span class='Function'>ML</span></code> is 1 for Dyalog.</p>
<h2 id="terminology"><a class="header" href="#terminology">Terminology</a></h2>
<h3 id="array-model"><a class="header" href="#array-model">Array model</a></h3>
<p>BQN uses the <a href="based.html">based array model</a>, so that a Dyalog simple scalar corresponds to many BQN values: an atom, its enclose, and so on.</p>
<table>
<thead>
<tr>
<th>Dyalog</th>
<th>BQN</th>
</tr>
</thead>
<tbody>
<tr>
<td>Simple scalar</td>
<td>Atom</td>
</tr>
<tr>
<td>Scalar</td>
<td>Unit</td>
</tr>
<tr>
<td>Vector</td>
<td>List</td>
</tr>
<tr>
<td>Matrix</td>
<td>Table</td>
</tr>
</tbody>
</table>
<p>BQN shares the terms "<a href="array.html#cells">cell</a>" and "major cell" with Dyalog, and uses "element" (which may mean different things to different Dyalog users) <em>not</em> for a 0-cell but for the value it contains.</p>
<h3 id="roles"><a class="header" href="#roles">Roles</a></h3>
<p>Dyalog uses value types (array, function, and so on) to determine syntax while BQN uses a separate concept called syntactic roles. See <a href="context.html">context-free grammar</a>.</p>
<table>
<thead>
<tr>
<th>Dyalog type</th>
<th>BQN role</th>
</tr>
</thead>
<tbody>
<tr>
<td>Array</td>
<td>Subject</td>
</tr>
<tr>
<td>Function</td>
<td>Function</td>
</tr>
<tr>
<td>Monadic operator</td>
<td>1-modifier</td>
</tr>
<tr>
<td>Dyadic operator</td>
<td>2-modifier</td>
</tr>
<tr>
<td>Niladic function</td>
<td><em>go away</em></td>
</tr>
</tbody>
</table>
<h2 id="syntax"><a class="header" href="#syntax">Syntax</a></h2>
<p>BQN comments are written with <code><span class='Comment'>#</span></code>, not <code><span class='Value'>⍝</span></code>. BQN strings use double quotes <code><span class='String'>""</span></code> while single quotes <code><span class='String'>''</span></code> enclose a character.</p>
<p>BQN's <a href="block.html">block</a> functions use <code><span class='Brace'>{}</span></code>, like Dyalog's dfns. The names for inputs and self-reference are different:</p>
<table>
<thead>
<tr>
<th>Dyalog</th>
<th>BQN</th>
</tr>
</thead>
<tbody>
<tr>
<td><code><span class='Value'>⍺</span></code></td>
<td><code><span class='Value'>𝕨</span></code></td>
</tr>
<tr>
<td><code><span class='Value'>⍵</span></code></td>
<td><code><span class='Value'>𝕩</span></code></td>
</tr>
<tr>
<td><code><span class='Value'>∇</span></code></td>
<td><code><span class='Function'>𝕊</span></code></td>
</tr>
<tr>
<td><code><span class='Value'>⍺⍺</span></code></td>
<td><code><span class='Function'>𝔽</span></code></td>
</tr>
<tr>
<td><code><span class='Value'>⍵⍵</span></code></td>
<td><code><span class='Function'>𝔾</span></code></td>
</tr>
<tr>
<td><code><span class='Value'>∇∇</span></code></td>
<td><code><span class='Value'>𝕣</span></code></td>
</tr>
</tbody>
</table>
<p>Blocks don't have guards exactly, but headers and predicates support some similar functionality (first-class functions can also be used for <a href="control.html">control structures</a>). Headers can also be used to make a block more explicit about its inputs, more like a tradfn.</p>
<p>The assignment arrow <code><span class='Gets'>←</span></code> defines a new variable in a block, while <code><span class='Gets'>↩</span></code> modifies an existing one.</p>
<p>BQN uses the ligature character <code><span class='Ligature'>‿</span></code> for stranding, instead of plain juxtaposition. It also has a <a href="arrayrepr.html#brackets">list notation</a> using <code><span class='Bracket'>⟨⟩</span></code>, and <code><span class='Bracket'>[]</span></code> for higher-rank arrays.</p>
<h2 id="for-reading"><a class="header" href="#for-reading">For reading</a></h2>
<p>Here are some closest equivalents in Dyalog APL for the BQN functions that don't use the same glyphs. Correspondence can be approximate, and <code><span class='Function'>⌽</span></code> is just used as a decorator to mean "reverse some things".</p>
<table>
<thead>
<tr>
<th align="center">BQN</th>
<th align="center"><code><span class='Function'>⋆</span></code></th>
<th align="center"><code><span class='Function'>√</span></code></th>
<th align="center"><code><span class='Function'>∧</span></code></th>
<th align="center"><code><span class='Function'>∨</span></code></th>
<th align="center"><code><span class='Function'>¬</span></code></th>
<th align="center"><code><span class='Function'>=</span></code></th>
<th align="center"><code><span class='Function'>≠</span></code></th>
<th align="center"><code><span class='Function'><</span></code></th>
<th align="center"><code><span class='Function'>></span></code></th>
<th align="center"><code><span class='Function'>≢</span></code></th>
<th align="center"><code><span class='Function'>⥊</span></code></th>
</tr>
</thead>
<tbody>
<tr>
<td align="center">Monad</td>
<td align="center"><code><span class='Value'>*</span></code></td>
<td align="center"><code><span class='Value'>*</span><span class='Modifier2'>∘</span><span class='Paren'>(</span><span class='Function'>÷</span><span class='Number'>2</span><span class='Paren'>)</span></code></td>
<td align="center"><code><span class='Bracket'>[</span><span class='Function'>⍋</span><span class='Bracket'>]</span></code></td>
<td align="center"><code><span class='Bracket'>[</span><span class='Function'>⍒</span><span class='Bracket'>]</span></code></td>
<td align="center"><code><span class='Value'>~</span></code></td>
<td align="center"><code><span class='Function'>≢</span><span class='Value'>⍤⍴</span></code></td>
<td align="center"><code><span class='Function'>≢</span></code></td>
<td align="center"><code><span class='Value'>⊂</span></code></td>
<td align="center"><code><span class='Function'>↑</span></code></td>
<td align="center"><code><span class='Value'>⍴</span></code></td>
<td align="center"><code><span class='Separator'>,</span></code></td>
</tr>
<tr>
<td align="center">Dyad</td>
<td align="center"><code><span class='Value'>*</span></code></td>
<td align="center"><code><span class='Value'>*</span><span class='Modifier2'>∘</span><span class='Function'>÷</span><span class='Value'>⍨</span></code></td>
<td align="center"><code><span class='Function'>∧</span></code></td>
<td align="center"><code><span class='Function'>∨</span></code></td>
<td align="center"><code><span class='Number'>1</span><span class='Function'>+-</span></code></td>
<td align="center"><code><span class='Function'>=</span></code></td>
<td align="center"><code><span class='Function'>≠</span></code></td>
<td align="center"><code><span class='Function'><</span></code></td>
<td align="center"><code><span class='Function'>></span></code></td>
<td align="center"><code><span class='Function'>≢</span></code></td>
<td align="center"><code><span class='Value'>⍴</span></code></td>
</tr>
</tbody>
</table>
<table>
<thead>
<tr>
<th align="center">BQN</th>
<th align="center"><code><span class='Function'>∾</span></code></th>
<th align="center"><code><span class='Function'>≍</span></code></th>
<th align="center"><code><span class='Function'>⋈</span></code></th>
<th align="center"><code><span class='Function'>↑</span></code></th>
<th align="center"><code><span class='Function'>↓</span></code></th>
<th align="center"><code><span class='Function'>↕</span></code></th>
<th align="center"><code><span class='Function'>»</span></code></th>
<th align="center"><code><span class='Function'>«</span></code></th>
</tr>
</thead>
<tbody>
<tr>
<td align="center">Monad</td>
<td align="center"><code><span class='Value'>⊃</span><span class='Separator'>,</span><span class='Value'>⌿</span></code></td>
<td align="center"><code><span class='Function'>↑</span><span class='Separator'>,</span><span class='Value'>⍥⊂</span></code></td>
<td align="center"><code><span class='Separator'>,</span><span class='Value'>⍥⊂</span></code></td>
<td align="center"><code><span class='Separator'>,</span><span class='Value'>⍀</span></code></td>
<td align="center"><code><span class='Function'>⌽</span><span class='Separator'>,</span><span class='Function'>⌽</span><span class='Value'>⍀</span><span class='Function'>⌽</span></code></td>
<td align="center"><code><span class='Value'>⍳</span></code></td>
<td align="center"><code><span class='Function'>≢↑</span><span class='Paren'>(</span><span class='Number'>¯1</span><span class='Function'>-≢</span><span class='Paren'>)</span><span class='Function'>↑⊢</span></code></td>
<td align="center"><code><span class='Function'>-</span><span class='Value'>⍤</span><span class='Function'>≢↑</span><span class='Paren'>(</span><span class='Number'>1</span><span class='Function'>+≢</span><span class='Paren'>)</span><span class='Function'>↑⊢</span></code></td>
</tr>
<tr>
<td align="center">Dyad</td>
<td align="center"><code><span class='Value'>⍪</span></code></td>
<td align="center"><code><span class='Function'>↑</span><span class='Separator'>,</span><span class='Value'>⍥⊂</span></code></td>
<td align="center"><code><span class='Separator'>,</span><span class='Value'>⍥⊂</span></code></td>
<td align="center"><code><span class='Function'>↑</span></code></td>
<td align="center"><code><span class='Function'>↓</span></code></td>
<td align="center"><code><span class='Separator'>,</span><span class='Value'>⌿</span></code></td>
<td align="center"><code><span class='Function'>≢</span><span class='Value'>⍤</span><span class='Function'>⊢↑</span><span class='Value'>⍪</span></code></td>
<td align="center"><code><span class='Function'>-</span><span class='Value'>⍤</span><span class='Function'>≢</span><span class='Value'>⍤</span><span class='Function'>⊢↑</span><span class='Value'>⍪⍨</span></code></td>
</tr>
</tbody>
</table>
<table>
<thead>
<tr>
<th align="center">BQN</th>
<th align="center"><code><span class='Function'>/</span></code></th>
<th align="center"><code><span class='Function'>⍋</span></code></th>
<th align="center"><code><span class='Function'>⍒</span></code></th>
<th align="center"><code><span class='Function'>⊏</span></code></th>
<th align="center"><code><span class='Function'>⊑</span></code></th>
<th align="center"><code><span class='Function'>⊐</span></code></th>
<th align="center"><code><span class='Function'>⊒</span></code></th>
<th align="center"><code><span class='Function'>∊</span></code></th>
<th align="center"><code><span class='Function'>⍷</span></code></th>
<th align="center"><code><span class='Function'>⊔</span></code></th>
</tr>
</thead>
<tbody>
<tr>
<td align="center">Monad</td>
<td align="center"><code><span class='Value'>⍸</span></code></td>
<td align="center"><code><span class='Function'>⍋</span></code></td>
<td align="center"><code><span class='Function'>⍒</span></code></td>
<td align="center"><code><span class='Function'>⊣</span><span class='Value'>⌿</span></code></td>
<td align="center"><code><span class='Value'>⊃</span></code></td>
<td align="center"><code><span class='Value'>∪⍳</span><span class='Function'>⊢</span></code></td>
<td align="center"><code><span class='Value'>…</span></code></td>
<td align="center"><code><span class='Function'>≠</span></code></td>
<td align="center"><code><span class='Value'>∪</span></code></td>
<td align="center"><code><span class='Value'>⌸</span></code></td>
</tr>
<tr>
<td align="center">Dyad</td>
<td align="center"><code><span class='Value'>⌿</span></code></td>
<td align="center"><code><span class='Value'>⍸</span></code></td>
<td align="center"><code><span class='Function'>⌽</span><span class='Value'>⍸</span><span class='Function'>⌽</span></code></td>
<td align="center"><code><span class='Value'>⌷</span></code></td>
<td align="center"><code><span class='Value'>⊃</span></code></td>
<td align="center"><code><span class='Value'>⍳</span></code></td>
<td align="center"><code><span class='Value'>…</span></code></td>
<td align="center"><code><span class='Function'>∊</span></code></td>
<td align="center"><code><span class='Function'>⍷</span></code></td>
<td align="center"><code><span class='Value'>⌸</span></code> or <code><span class='Value'>⊆</span></code></td>
</tr>
</tbody>
</table>
<p>Modifiers are a little harder. Many have equivalents in some cases, but Dyalog sometimes chooses different functionality based on whether the operand is an array. In BQN an array is always treated as a constant function.</p>
<table>
<thead>
<tr>
<th align="center">BQN</th>
<th align="center"><code><span class='Modifier'>¨</span></code></th>
<th align="center"><code><span class='Modifier'>⌜</span></code></th>
<th align="center"><code><span class='Modifier'>˝</span></code></th>
<th align="center"><code><span class='Modifier2'>⎉</span></code></th>
<th align="center"><code><span class='Modifier2'>⍟</span></code></th>
<th align="center"><code><span class='Modifier'>˜</span></code></th>
<th align="center"><code><span class='Modifier2'>∘</span></code></th>
<th align="center"><code><span class='Modifier2'>○</span></code></th>
<th align="center"><code><span class='Modifier2'>⟜</span></code></th>
</tr>
</thead>
<tbody>
<tr>
<td align="center">Dyalog</td>
<td align="center"><code><span class='Modifier'>¨</span></code></td>
<td align="center"><code><span class='Modifier2'>∘</span><span class='Value'>.</span></code></td>
<td align="center"><code><span class='Value'>⌿</span></code></td>
<td align="center"><code><span class='Value'>⍤</span><span class='Function'>A</span></code></td>
<td align="center"><code><span class='Value'>⍣</span></code></td>
<td align="center"><code><span class='Value'>⍨</span></code></td>
<td align="center"><code><span class='Value'>⍤f</span></code></td>
<td align="center"><code><span class='Value'>⍥</span></code></td>
<td align="center"><code><span class='Modifier2'>∘</span></code></td>
</tr>
</tbody>
</table>
<p>Some other BQN modifiers have been proposed as future Dyalog extensions:</p>
<table>
<thead>
<tr>
<th align="center">BQN</th>
<th align="center"><code><span class='Modifier2'>⌾</span></code></th>
<th align="center"><code><span class='Modifier2'>⚇</span></code></th>
<th align="center"><code><span class='Modifier2'>⊸</span></code></th>
</tr>
</thead>
<tbody>
<tr>
<td align="center">Dyalog proposed</td>
<td align="center"><code><span class='Value'>⍢</span></code> <a href="https://aplwiki.com/wiki/Under">Under</a></td>
<td align="center"><code><span class='Value'>⍥</span></code> Depth</td>
<td align="center"><code><span class='Value'>⍛</span></code> <a href="https://aplwiki.com/wiki/Reverse_Compose">Reverse Compose</a></td>
</tr>
</tbody>
</table>
<h2 id="for-writing"><a class="header" href="#for-writing">For writing</a></h2>
<p>The tables below give approximate implementations of Dyalog primitives for the ones that aren't the same. First- and last-axis pairs are also mostly omitted. BQN just has the first-axis form, and you can get the last-axis form with <code><span class='Modifier2'>⎉</span><span class='Number'>1</span></code>.</p>
<p>The form <code><span class='Function'>F</span><span class='Value'>⍣</span><span class='Function'>G</span></code> (Power with a function right operand; Power limit) must be implemented with recursion instead of primitives because it performs unbounded iteration. The modifier <code><span class='Modifier2'>_while_</span> <span class='Gets'>←</span> <span class='Brace'>{</span><span class='Function'>𝔽</span><span class='Modifier2'>⍟</span><span class='Function'>𝔾</span><span class='Modifier2'>∘</span><span class='Function'>𝔽</span><span class='Modifier2'>_𝕣_</span><span class='Function'>𝔾</span><span class='Modifier2'>∘</span><span class='Function'>𝔽</span><span class='Modifier2'>⍟</span><span class='Function'>𝔾</span><span class='Value'>𝕩</span><span class='Brace'>}</span></code> provides similar functionality without risk of stack overflow. It's discussed <a href="control.html#low-stack-version">here</a> and called as <code><span class='Function'>Fn</span> <span class='Modifier2'>_while_</span> <span class='Function'>Cond</span> <span class='Value'>arg</span></code>.</p>
<table>
<tr><th colspan=3>Functions</th></tr>
<tr><th> Glyph </th><th> Monadic </th><th> Dyadic </th> </tr>
<tr><td> <code><span class='Value'>*</span></code> </td><td colspan=2><code><span class='Function'>⋆</span></code></td> </tr>
<tr><td> <code><span class='Modifier2'>⍟</span></code> </td><td colspan=2><code><span class='Function'>⋆</span><span class='Modifier'>⁼</span></code></td> </tr>
<tr><td> <code><span class='Function'>!</span></code> </td><td><code><span class='Function'>×</span><span class='Modifier'>´</span><span class='Number'>1</span><span class='Function'>+↕</span></code> </td><td> <code><span class='Paren'>(</span><span class='Function'>-÷</span><span class='Modifier2'>○</span><span class='Paren'>(</span><span class='Function'>×</span><span class='Modifier'>´</span><span class='Paren'>)</span><span class='Number'>1</span><span class='Modifier2'>⊸</span><span class='Function'>+</span><span class='Paren'>)</span><span class='Modifier2'>⟜</span><span class='Function'>↕</span><span class='Modifier'>˜</span></code></td></tr>
<tr><td> <code><span class='Modifier2'>○</span></code> </td><td> <code><span class='Number'>π</span><span class='Modifier2'>⊸</span><span class='Function'>×</span></code> </td><td> <code><span class='Value'>•math</span></code></td> </tr>
<tr><td> <code><span class='Value'>~</span></code> </td><td> <code><span class='Function'>¬</span></code> </td><td> <code><span class='Function'>¬</span><span class='Modifier2'>∘</span><span class='Function'>∊/⊣</span></code></td> </tr>
<tr><td> <code><span class='Head'>?</span></code> </td><td> <code><span class='Value'>•rand.</span><span class='Function'>Range</span><span class='Modifier2'>⚇</span><span class='Number'>0</span></code> </td><td> <code><span class='Value'>•rand.</span><span class='Function'>Deal</span></code></td></tr>
<tr><td> <code><span class='Value'>⍲</span></code> </td><td> </td><td> <code><span class='Function'>¬</span><span class='Modifier2'>∘</span><span class='Function'>∧</span></code></td> </tr>
<tr><td> <code><span class='Value'>⍱</span></code> </td><td> </td><td> <code><span class='Function'>¬</span><span class='Modifier2'>∘</span><span class='Function'>∨</span></code></td> </tr>
<tr><td> <code><span class='Value'>⍴</span></code> </td><td> <code><span class='Function'>≢</span></code> </td><td> <code><span class='Function'>⥊</span></code></td> </tr>
<tr><td> <code><span class='Separator'>,</span></code> </td><td> <code><span class='Function'>⥊</span></code> </td><td> <code><span class='Function'>∾</span><span class='Modifier2'>⎉</span><span class='Number'>1</span></code></td> </tr>
<tr><td> <code><span class='Value'>⍪</span></code> </td><td> <code><span class='Function'>⥊</span><span class='Modifier'>˘</span></code> </td><td> <code><span class='Function'>∾</span></code></td> </tr>
<tr><td> <code><span class='Function'>⌽</span></code> </td><td colspan=2><code><span class='Function'>⌽</span><span class='Modifier2'>⎉</span><span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>1</span></code></td> </tr>
<tr><td> <code><span class='Function'>↑</span></code> </td><td> <code><span class='Function'>></span></code> </td><td> <code><span class='Function'>↑</span></code></td> </tr>
<tr><td> <code><span class='Function'>↓</span></code> </td><td> <code><span class='Function'><</span><span class='Modifier'>˘</span></code> </td><td> <code><span class='Function'>↓</span></code></td> </tr>
<tr><td> <code><span class='Value'>⊂</span></code> </td><td> <code><span class='Function'><</span></code> </td><td> <code><span class='Function'>+</span><span class='Modifier'>`</span><span class='Modifier2'>⊸</span><span class='Function'>⊔</span></code></td> </tr>
<tr><td> <code><span class='Value'>⊆</span></code> </td><td> <code><span class='Function'><</span><span class='Modifier2'>⍟</span><span class='Paren'>(</span><span class='Number'>0</span><span class='Function'><≡</span><span class='Paren'>)</span></code> </td><td> <code><span class='Paren'>(</span><span class='Function'>¬-</span><span class='Modifier'>˜</span><span class='Function'>⊢×</span><span class='Nothing'>·</span><span class='Function'>+</span><span class='Modifier'>`</span><span class='Function'>»</span><span class='Modifier2'>⊸</span><span class='Function'>></span><span class='Paren'>)</span><span class='Modifier2'>⊸</span><span class='Function'>⊔</span></code></td></tr>
<tr><td> <code><span class='Function'>∊</span></code> </td><td> <code><span class='Brace'>{</span><span class='Paren'>(</span><span class='Function'>∾𝕊</span><span class='Modifier'>¨</span><span class='Paren'>)</span><span class='Modifier2'>⍟</span><span class='Paren'>(</span><span class='Number'>0</span><span class='Function'><≡</span><span class='Paren'>)</span><span class='Function'>⥊</span><span class='Value'>𝕩</span><span class='Brace'>}</span></code> </td><td> <code><span class='Function'>∊</span></code></td> </tr>
<tr><td> <code><span class='Value'>⊃</span></code> </td><td colspan=2><code><span class='Function'>⊑</span></code></td> </tr>
<tr><td> <code><span class='Value'>⍀</span></code> </td><td> </td><td> <code><span class='Brace'>{</span><span class='Value'>𝕩</span><span class='Modifier2'>⌾</span><span class='Paren'>(</span><span class='Value'>𝕨</span><span class='Modifier2'>⊸</span><span class='Function'>/</span><span class='Paren'>)</span><span class='Value'>𝕨</span><span class='Function'>≠</span><span class='Modifier2'>⊸</span><span class='Function'>↑</span><span class='Number'>0</span><span class='Function'>↑</span><span class='Value'>𝕩</span><span class='Brace'>}</span></code></td></tr>
<tr><td> <code><span class='Value'>∩</span></code> </td><td> </td><td> <code><span class='Function'>∊/⊣</span></code></td> </tr>
<tr><td> <code><span class='Value'>∪</span></code> </td><td> <code><span class='Function'>⍷</span></code> </td><td> <code><span class='Function'>⊣∾∊</span><span class='Modifier'>˜</span><span class='Function'>¬</span><span class='Modifier2'>⊸</span><span class='Function'>/⊢</span></code></td> </tr>
<tr><td> <code><span class='Value'>⍳</span></code> </td><td> <code><span class='Function'>↕</span></code> </td><td> <code><span class='Function'>⊐</span></code></td> </tr>
<tr><td> <code><span class='Value'>⍸</span></code> </td><td> <code><span class='Function'>/</span></code> </td><td> <code><span class='Function'>⍋</span></code></td> </tr>
<tr><td> <code><span class='Function'>⍋</span></code> </td><td> <code><span class='Function'>⍋</span></code> </td><td> Give up </td> </tr>
<tr><td> <code><span class='Function'>⍒</span></code> </td><td> <code><span class='Function'>⍒</span></code> </td><td> Give up </td> </tr>
<tr><td> <code><span class='Function'>≢</span></code> </td><td> <code><span class='Function'>≠</span></code> </td><td> <code><span class='Function'>≢</span></code></td> </tr>
<tr><td> <code><span class='Value'>⍎</span></code> </td><td colspan=2><code><span class='Function'>•BQN</span></code></td> </tr>
<tr><td> <code><span class='Value'>⍕</span></code> </td><td colspan=2><code><span class='Function'>•Fmt</span></code></td> </tr>
<tr><td> <code><span class='Value'>⊥</span></code> </td><td> </td><td> <code><span class='Brace'>{</span><span class='Function'>+</span><span class='Modifier2'>⟜</span><span class='Paren'>(</span><span class='Value'>𝕨</span><span class='Modifier2'>⊸</span><span class='Function'>×</span><span class='Paren'>)</span><span class='Modifier'>´</span><span class='Function'>⌽</span><span class='Value'>𝕩</span><span class='Brace'>}</span></code> </td></tr>
<tr><td> <code><span class='Value'>⊤</span></code> </td><td> </td><td> <code><span class='Brace'>{</span><span class='Value'>𝕨</span><span class='Function'>|>⌊</span><span class='Modifier2'>∘</span><span class='Function'>÷</span><span class='Modifier'>`</span><span class='Modifier2'>⌾</span><span class='Function'>⌽</span><span class='Value'>𝕨</span><span class='Function'>«</span><span class='Modifier'>˜</span><span class='Function'><</span><span class='Value'>𝕩</span><span class='Brace'>}</span></code></td></tr>
<tr><td> <code><span class='Value'>⌹</span></code> </td><td><code><span class='Function'>Inverse</span></code>, </td><td> <code><span class='Function'>Solve</span></code> from <a href="https://github.com/mlochbaum/bqn-libs/blob/master/matrix.bqn">here</a></td></tr>
<tr><td> <code><span class='Value'>⌷</span></code> </td><td> N/A </td><td> <code><span class='Function'>⊏</span></code></td> </tr>
</table>
<table>
<tr><th colspan=3>Operators</th></tr>
<tr><th> Syntax </th><th> Monadic </th><th> Dyadic </th></tr>
<tr><td> <code><span class='Value'>⌿</span></code> </td><td> <code><span class='Modifier'>¨˝</span></code> </td><td> <code><span class='Function'>↕</span></code> </td></tr>
<tr><td> <code><span class='Value'>⍀</span></code> </td><td colspan=2> <code><span class='Function'>↑</span></code>, or <code><span class='Modifier'>`</span></code> if associative </td></tr>
<tr><td> <code><span class='Modifier'>¨</span></code> </td><td colspan=2> <code><span class='Modifier'>¨</span></code> </td></tr>
<tr><td> <code><span class='Value'>⍨</span></code> </td><td colspan=2> <code><span class='Modifier'>˜</span></code> </td></tr>
<tr><td> <code><span class='Value'>⍣</span></code> </td><td colspan=2> <code><span class='Modifier2'>⍟</span></code> </td></tr>
<tr><td> <code><span class='Value'>f.g</span></code> </td><td> </td><td> <code><span class='Value'>f</span><span class='Modifier'>˝</span><span class='Modifier2'>∘</span><span class='Value'>g</span><span class='Modifier2'>⎉</span><span class='Number'>1</span><span class='Ligature'>‿</span><span class='Number'>∞</span></code> </td></tr>
<tr><td> <code><span class='Modifier2'>∘</span><span class='Value'>.f</span></code> </td><td> </td><td> <code><span class='Value'>f</span><span class='Modifier'>⌜</span></code> </td></tr>
<tr><td> <code><span class='Function'>A</span><span class='Modifier2'>∘</span><span class='Value'>g</span></code> </td><td> <code><span class='Function'>A</span><span class='Modifier2'>⊸</span><span class='Value'>g</span></code> </td><td> </td></tr>
<tr><td> <code><span class='Value'>f</span><span class='Modifier2'>∘</span><span class='Function'>B</span></code> </td><td> <code><span class='Value'>f</span><span class='Modifier2'>⟜</span><span class='Function'>B</span></code> </td><td> </td></tr>
<tr><td> <code><span class='Value'>f</span><span class='Modifier2'>∘</span><span class='Value'>g</span></code> </td><td colspan=2> <code><span class='Value'>f</span><span class='Modifier2'>⟜</span><span class='Value'>g</span></code> </td></tr>
<tr><td> <code><span class='Value'>f⍤</span><span class='Function'>B</span></code> </td><td colspan=2> <code><span class='Value'>f</span><span class='Modifier2'>⎉</span><span class='Function'>B</span></code> </td></tr>
<tr><td> <code><span class='Value'>f⍤g</span></code> </td><td colspan=2> <code><span class='Value'>f</span><span class='Modifier2'>∘</span><span class='Value'>g</span></code> </td></tr>
<tr><td> <code><span class='Value'>f⍥g</span></code> </td><td colspan=2> <code><span class='Value'>f</span><span class='Modifier2'>○</span><span class='Value'>g</span></code> </td></tr>
<tr><td> <code><span class='Value'>f</span><span class='String'>@</span><span class='Value'>v</span></code> </td><td colspan=2> <code><span class='Value'>f</span><span class='Modifier2'>⌾</span><span class='Paren'>(</span><span class='Value'>v</span><span class='Modifier2'>⊸</span><span class='Function'>⊏</span><span class='Paren'>)</span></code> </td></tr>
<tr><td> <code><span class='Value'>f⍠</span><span class='Function'>B</span></code> </td><td colspan=2> Uh </td></tr>
<tr><td> <code><span class='Value'>f⌸</span></code> </td><td><code><span class='Function'>⊐⊔↕</span><span class='Modifier2'>∘</span><span class='Function'>≠</span></code></td><td><code><span class='Function'>⊐</span><span class='Modifier2'>⊸</span><span class='Function'>⊔</span></code> </td></tr>
<tr><td> <code><span class='Value'>f⌺</span><span class='Function'>B</span></code> </td><td colspan=2> <code><span class='Function'>↕</span></code> </td></tr>
<tr><td> <code><span class='Function'>A</span><span class='Value'>⌶</span></code> </td><td colspan=2> <code><span class='Function'>•Something</span></code> </td></tr>
<tr><td> <code><span class='Value'>f&</span></code> </td><td colspan=2> Nothing yet </td></tr>
</table>
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