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<ul>
<li><strong>Choose</strong> (<code><span class='Modifier2'>◶</span></code>) is later redefined to use the complete <code><span class='Function'>⊑</span></code> rather than the simple version assumed (using this primitive means it's not a true combinator).</li>
<li><strong>Constant</strong> (<code><span class='Modifier'>˙</span></code>)</li>
-<li><strong>Valences</strong> (<code><span class='Modifier2'>⊘</span></code>) uses a trick with ambivalent <code><span class='Function'>-</span></code> to find out whether there's a left argument, described below.</li>
+<li><strong>Valences</strong> (<code><span class='Modifier2'>⊘</span></code>)</li>
<li><strong>Right</strong> (<code><span class='Function'>⊢</span></code>)</li>
<li><strong>Left</strong> (<code><span class='Function'>⊣</span></code>)</li>
<li><strong>Self</strong>/<strong>Swap</strong> (<code><span class='Modifier'>˜</span></code>)</li>
@@ -88,7 +88,6 @@
<li><strong>Before</strong>/<strong>Bind</strong> (<code><span class='Modifier2'>⊸</span></code>)</li>
<li><strong>After</strong>/<strong>Bind</strong> (<code><span class='Modifier2'>⟜</span></code>)</li>
</ul>
-<p>The somewhat complicated definition of Valences could be replaced with <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> using headers. However, reference.bqn uses a simple subset of BQN's syntax that doesn't include headers. Instead, the definition relies on the fact that <code><span class='Value'>𝕨</span></code> works like <code><span class='Nothing'>·</span></code> if no left argument is given: <code><span class='Paren'>(</span><span class='Number'>1</span><span class='Modifier'>˙</span><span class='Value'>𝕨</span><span class='Paren'>)</span><span class='Function'>-</span><span class='Number'>0</span></code> is <code><span class='Number'>1</span><span class='Function'>-</span><span class='Number'>0</span></code> or <code><span class='Number'>1</span></code> if <code><span class='Value'>𝕨</span></code> is present and <code><span class='Paren'>(</span><span class='Number'>1</span><span class='Modifier'>˙</span><span class='Nothing'>·</span><span class='Paren'>)</span><span class='Function'>-</span><span class='Number'>0</span></code> otherwise: this reduces to <code><span class='Nothing'>·</span><span class='Function'>-</span><span class='Number'>0</span></code> or <code><span class='Number'>0</span></code>.</p>
<h3 id="array-properties"><a class="header" href="#array-properties">Array properties</a></h3>
<p>The reference implementations extend Shape (<code><span class='Function'>≢</span></code>) to atoms as well as arrays, in addition to implementing other properties. In all cases, an atom behaves as if it has shape <code><span class='Bracket'>⟨⟩</span></code>. The functions in this section never cause an error.</p>
<ul>