More editing

1 files changed, 13 insertions, 11 deletions

diff --git a/docs/doc/shift.html b/docs/doc/shift.html
index 5b72e865..8e8b3640 100644
--- a/docs/doc/shift.html
+++ b/docs/doc/shift.html
@@ -5,23 +5,25 @@
 </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="shift-functions"><a class="header" href="#shift-functions">Shift functions</a></h1>
-<p>The shift functions <code><span class='Function'>«</span></code> and <code><span class='Function'>»</span></code> add major cells to one side an array, displacing cells on the opposite side and moving those in between. Shifts resemble but are more general than the bit-based shift operations used in low-level languages. They replace the APL pattern of a 2-wise reduction after appending or prepending an element (APL's <code><span class='Number'>2</span><span class='Function'>≠/</span><span class='Number'>0</span><span class='Separator'>,</span><span class='Value'>v</span></code> translates to <code><span class='Function'>»</span><span class='Modifier2'>⊸</span><span class='Function'>≠</span><span class='Value'>v</span></code>), one of the more common uses of 2-wise reduction.</p>
+<p>The shift functions <code><span class='Function'>«</span></code> and <code><span class='Function'>»</span></code> add <a href="array.html#cells">major cells</a> to one side an array, displacing cells on the opposite side and moving those in between. Shifts resemble but are more general than the bit-based shift operations used in low-level languages. They replace the APL pattern of a 2-wise reduction after appending or prepending an element (APL's <code><span class='Number'>2</span><span class='Function'>≠/</span><span class='Number'>0</span><span class='Separator'>,</span><span class='Value'>v</span></code> translates to <code><span class='Function'>»</span><span class='Modifier2'>⊸</span><span class='Function'>≠</span><span class='Value'>v</span></code>); a nice version of this common pattern is one reason BQN is free to replace windowed reduction with the sometimes less convenient <a href="windows.html">Windows</a>.</p>
 <p>The result of a shift function always has the same shape as <code><span class='Value'>𝕩</span></code>. The function adds major cells to the beginning (<code><span class='Function'>»</span></code>) or end (<code><span class='Function'>«</span></code>) of <code><span class='Value'>𝕩</span></code>, moving the cells already in <code><span class='Value'>𝕩</span></code> to accomodate them. Some cells on the opposite side from those added will &quot;fall off&quot; and not be included in the result.</p>
-<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=MOKAvzAgwrsgM+KAvzLigL8xICAgICAgICAgICAgICMgU2hpZnQgQmVmb3JlCiJlbmQiIMKrICJhZGQgdG8gdGhlICIgICAjIFNoaWZ0IEFmdGVy">↗️</a><pre>    <span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>0</span> <span class='Function'>»</span> <span class='Number'>3</span><span class='Ligature'>‿</span><span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>1</span>             <span class='Comment'># Shift Before
+<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=MOKAvzAgwrsgM+KAvzLigL8xICAgICAgICAgICAgICMgU2hpZnQgQmVmb3JlCgoiZW5kIiDCqyAiYWRkIHRvIHRoZSAiICAgIyBTaGlmdCBBZnRlcg==">↗️</a><pre>    <span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>0</span> <span class='Function'>»</span> <span class='Number'>3</span><span class='Ligature'>‿</span><span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>1</span>             <span class='Comment'># Shift Before
 </span>⟨ 0 0 3 ⟩
+
     <span class='String'>&quot;end&quot;</span> <span class='Function'>«</span> <span class='String'>&quot;add to the &quot;</span>   <span class='Comment'># Shift After
 </span>" to the end"
 </pre>
 <p>The cells to add come from <code><span class='Value'>𝕨</span></code> if it's present, as shown above. Otherwise, a single cell of <a href="fill.html">fill elements</a> for <code><span class='Value'>𝕩</span></code> is used. This kind of shift, which moves cells in <code><span class='Value'>𝕩</span></code> over by just one, is called a &quot;nudge&quot;.</p>
-<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=wrsgImFiY2QiICAgIyBOdWRnZQrCqyAx4oC/MuKAvzMgICAgIyBOdWRnZSBCYWNr">↗️</a><pre>    <span class='Function'>»</span> <span class='String'>&quot;abcd&quot;</span>   <span class='Comment'># Nudge
+<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=wrsgImFiY2QiICAgIyBOdWRnZQoKwqsgMeKAvzLigL8zICAgICMgTnVkZ2UgQmFjaw==">↗️</a><pre>    <span class='Function'>»</span> <span class='String'>&quot;abcd&quot;</span>   <span class='Comment'># Nudge
 </span>" abc"
+
     <span class='Function'>«</span> <span class='Number'>1</span><span class='Ligature'>‿</span><span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>3</span>    <span class='Comment'># Nudge Back
 </span>⟨ 2 3 0 ⟩
 </pre>
-<p>If <code><span class='Value'>𝕨</span></code> is longer than <code><span class='Value'>𝕩</span></code>, some cells from <code><span class='Value'>𝕨</span></code> will be discarded, as well as all of <code><span class='Value'>𝕩</span></code>. In this case <code><span class='Value'>𝕨</span><span class='Function'>»</span><span class='Value'>𝕩</span></code> is <code><span class='Paren'>(</span><span class='Function'>≠</span><span class='Value'>𝕩</span><span class='Paren'>)</span><span class='Function'>↑</span><span class='Value'>𝕨</span></code> and <code><span class='Value'>𝕨</span><span class='Function'>«</span><span class='Value'>𝕩</span></code> is <code><span class='Paren'>(</span><span class='Function'>-≠</span><span class='Value'>𝕩</span><span class='Paren'>)</span><span class='Function'>↑</span><span class='Value'>𝕨</span></code>. For similar reasons, nudging an array of length 0 returns it unchanged.</p>
+<p>If <code><span class='Value'>𝕨</span></code> is longer than <code><span class='Value'>𝕩</span></code>, some cells from <code><span class='Value'>𝕨</span></code> will be discarded, plus all of <code><span class='Value'>𝕩</span></code>. In this case <code><span class='Value'>𝕨</span><span class='Function'>»</span><span class='Value'>𝕩</span></code> is <code><span class='Paren'>(</span><span class='Function'>≠</span><span class='Value'>𝕩</span><span class='Paren'>)</span><span class='Function'>↑</span><span class='Value'>𝕨</span></code> and <code><span class='Value'>𝕨</span><span class='Function'>«</span><span class='Value'>𝕩</span></code> is <code><span class='Paren'>(</span><span class='Function'>-≠</span><span class='Value'>𝕩</span><span class='Paren'>)</span><span class='Function'>↑</span><span class='Value'>𝕨</span></code>. For similar reasons, nudging an array of length 0 returns it unchanged.</p>
 <h2 id="sequence-processing-with-shifts"><a class="header" href="#sequence-processing-with-shifts">Sequence processing with shifts</a></h2>
 <p>When working with a sequence of data such as text, daily measurements, or audio data, shift functions are generally the best way to handle the concept of &quot;next&quot; or &quot;previous&quot;. In the following example <code><span class='Value'>s</span></code> is shown alongside the shifted-right data <code><span class='Function'>»</span><span class='Value'>s</span></code>, and each element is compared to the previous with <code><span class='Function'>-</span><span class='Modifier2'>⟜</span><span class='Function'>»</span></code>, which we see is the <a href="undo.html">inverse</a> of Plus <a href="scan.html">Scan</a> <code><span class='Function'>+</span><span class='Modifier'>`</span></code>.</p>
-<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=cyDihpAgMeKAvzLigL8y4oC/NOKAvzPigL814oC/NgpzIOKJjSDCu3MKLeKfnMK7IHMKCitgIC3in5zCuyBz">↗️</a><pre>    <span class='Value'>s</span> <span class='Gets'>←</span> <span class='Number'>1</span><span class='Ligature'>‿</span><span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>4</span><span class='Ligature'>‿</span><span class='Number'>3</span><span class='Ligature'>‿</span><span class='Number'>5</span><span class='Ligature'>‿</span><span class='Number'>6</span>
+<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=cyDihpAgMeKAvzLigL8y4oC/NOKAvzPigL814oC/NgpzIOKJjSDCu3MKLeKfnMK7IHMKCitgIC3in5zCuyBzICAgIyBTYW1lIGFzIHM=">↗️</a><pre>    <span class='Value'>s</span> <span class='Gets'>←</span> <span class='Number'>1</span><span class='Ligature'>‿</span><span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>4</span><span class='Ligature'>‿</span><span class='Number'>3</span><span class='Ligature'>‿</span><span class='Number'>5</span><span class='Ligature'>‿</span><span class='Number'>6</span>
     <span class='Value'>s</span> <span class='Function'>≍</span> <span class='Function'>»</span><span class='Value'>s</span>
 ┌─               
 ╵ 1 2 2 4 3 5 6  
@@ -30,8 +32,8 @@
     <span class='Function'>-</span><span class='Modifier2'>⟜</span><span class='Function'>»</span> <span class='Value'>s</span>
 ⟨ 1 1 0 2 ¯1 2 1 ⟩
 
-    <span class='Function'>+</span><span class='Modifier'>`</span> <span class='Function'>-</span><span class='Modifier2'>⟜</span><span class='Function'>»</span> <span class='Value'>s</span>
-⟨ 1 2 2 4 3 5 6 ⟩
+    <span class='Function'>+</span><span class='Modifier'>`</span> <span class='Function'>-</span><span class='Modifier2'>⟜</span><span class='Function'>»</span> <span class='Value'>s</span>   <span class='Comment'># Same as s
+</span>⟨ 1 2 2 4 3 5 6 ⟩
 </pre>
 <p>In this way <code><span class='Function'>»</span></code> refers to a sequence containing the previous element at each position. By default the array's fill is used for the element before the first, and a right argument can be given to provide a different one.</p>
 <a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4oieIMK7IHMKCuKKj+KKuMK7IHM=">↗️</a><pre>    <span class='Number'>∞</span> <span class='Function'>»</span> <span class='Value'>s</span>
@@ -59,7 +61,7 @@
 </pre>
 <p>A feature these examples all share is that they maintain the length of <code><span class='Value'>s</span></code>. This is a common condition in sequence processing, particularly when the processed sequence needs to be combined or compared with the original in some way. However, it's not always the case. In some instances, for example when searching <code><span class='Value'>s</span></code> to see if there is any value less than the previous, the list should get shorter during processing. In these cases, <a href="windows.html">Windows</a> (<code><span class='Function'>↕</span></code>) is usually a better choice.</p>
 <h2 id="arithmetic-and-logical-shifts"><a class="header" href="#arithmetic-and-logical-shifts">Arithmetic and logical shifts</a></h2>
-<p>The glyphs <code><span class='Function'>«</span></code> and <code><span class='Function'>»</span></code>, suggesting movement, were chosen for the same reasons as the digraphs <code><span class='Function'>&lt;&lt;</span></code> and <code><span class='Function'>&gt;&gt;</span></code>, and can be used to implement the same operations on boolean lists.</p>
+<p>The glyphs <code><span class='Function'>«</span></code> and <code><span class='Function'>»</span></code>, suggesting movement, were chosen for the same reasons as the digraphs <code><span class='Function'>&lt;&lt;</span></code> and <code><span class='Function'>&gt;&gt;</span></code> in C-like languages, and can be used to implement the same bit-shift operations on boolean lists.</p>
 <a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4oqiIGkg4oaQICIxMDAxMTAxMSItJzAnCgrCq+KNnzMgaSAgICAgICAgIyBRdWljayBhbmQgZGlydHkgbGVmdCBzaGlmdAoKMyDipYrin5ww4oq4wqsgaSAgICAjIEFsdGVybmF0ZSBsZWZ0IHNoaWZ0">↗️</a><pre>    <span class='Function'>⊢</span> <span class='Value'>i</span> <span class='Gets'>←</span> <span class='String'>&quot;10011011&quot;</span><span class='Function'>-</span><span class='String'>'0'</span>
 ⟨ 1 0 0 1 1 0 1 1 ⟩
 
@@ -77,7 +79,7 @@
 </span>⟨ 1 1 1 1 0 0 1 1 ⟩
 </pre>
 <h2 id="other-examples"><a class="header" href="#other-examples">Other examples</a></h2>
-<p>In <a href="take.html">Take</a> (<code><span class='Function'>↑</span></code>), there's no way to specify the fill element when the result is longer than the argument. To take along the first axis with a specified, constant fill value, you can use Shift Before instead, where the right argument is an array of fills with the desired final shape.</p>
+<p>In <a href="take.html">Take</a> (<code><span class='Function'>↑</span></code>), there's no way to specify the fill element when the result is longer than the argument. To take along the first axis with a specified, constant fill value, you can use Shift Before instead, where the right argument is an array of fills with the desired final shape (a more general approach is <a href="under.html">Under</a>).</p>
 <a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=ImFiYyIgwrsgNeKliidGJw==">↗️</a><pre>    <span class='String'>&quot;abc&quot;</span> <span class='Function'>»</span> <span class='Number'>5</span><span class='Function'>⥊</span><span class='String'>'F'</span>
 "abcFF"
 </pre>
@@ -91,12 +93,12 @@
     <span class='Number'>2</span> <span class='Function'>+</span><span class='Modifier'>`</span><span class='Modifier2'>∘</span><span class='Function'>»</span> <span class='Number'>1</span><span class='Ligature'>‿</span><span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>1</span><span class='Ligature'>‿</span><span class='Number'>0</span>  <span class='Comment'># Final value not created
 </span>⟨ 2 3 3 4 ⟩
 </pre>
-<p>The <em>strides</em> of an array are the distances between one element and the next along any given axis. It's the product of all axis lengths below that axis, since these are all the axes that have to be &quot;skipped&quot; to jump along the axis. The strides of an array <code><span class='Value'>𝕩</span></code> are <code><span class='Paren'>(</span><span class='Function'>×</span><span class='Modifier'>`</span><span class='Number'>1</span><span class='Function'>»⊢</span><span class='Paren'>)</span><span class='Modifier2'>⌾</span><span class='Function'>⌽</span><span class='Modifier2'>∘</span><span class='Function'>≢</span><span class='Value'>𝕩</span></code>.</p>
+<p>The <em>strides</em> of an array are the distances between one element and the next along any given axis. It's the product of all axis lengths below that axis, since these are all the axes that have to be &quot;skipped&quot; to jump along the axis. The strides of an array <code><span class='Value'>𝕩</span></code> are <code><span class='Paren'>(</span><span class='Function'>×</span><span class='Modifier'>`</span><span class='Number'>1</span><span class='Function'>»⊢</span><span class='Paren'>)</span><span class='Modifier2'>⌾</span><span class='Function'>⌽</span> <span class='Function'>≢</span><span class='Value'>𝕩</span></code>.</p>
 <a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=KMOXYDHCu+KKoinijL7ijL0gNeKAvzLigL804oC/Mw==">↗️</a><pre>    <span class='Paren'>(</span><span class='Function'>×</span><span class='Modifier'>`</span><span class='Number'>1</span><span class='Function'>»⊢</span><span class='Paren'>)</span><span class='Modifier2'>⌾</span><span class='Function'>⌽</span> <span class='Number'>5</span><span class='Ligature'>‿</span><span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>4</span><span class='Ligature'>‿</span><span class='Number'>3</span>
 ⟨ 24 12 3 1 ⟩
 </pre>
 <h2 id="higher-rank"><a class="header" href="#higher-rank">Higher rank</a></h2>
-<p>Shifting always works on the first axis of <code><span class='Value'>𝕩</span></code> (which must have rank 1 or more), and shifts in major cells. A left argument can have rank equal to <code><span class='Value'>𝕩</span></code>, or one less than it, in which case it becomes a single cell of the result. With no left argument, a cell of fills <code><span class='Number'>1</span><span class='Function'>↑</span><span class='Number'>0</span><span class='Function'>↑</span><span class='Value'>𝕩</span></code> is nudged in.</p>
+<p>Shifting always works on the <a href="leading.html">first axis</a> of <code><span class='Value'>𝕩</span></code> (which must have rank 1 or more), and shifts in major cells. A left argument can have rank equal to <code><span class='Value'>𝕩</span></code>, or one less than it, in which case it becomes a single cell of the result. With no left argument, a cell of fills <code><span class='Number'>1</span><span class='Function'>↑</span><span class='Number'>0</span><span class='Function'>↑</span><span class='Value'>𝕩</span></code> is nudged in.</p>
 <a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4oqiIGEg4oaQIOKliuKfnCjihpXDl8K0KSA04oC/MwoKwrsgYSAgICAgICAgICAgICAgICAjIE51ZGdlIGFkZHMgYSBjZWxsIG9mIGZpbGxzCgoib25lIiDCqyBhICAgICAgICAgICMgU2hpZnQgaW4gYSBjZWxsCgooInR3byLiiY0iY2VsIikgwqsgYSAgIyBTaGlmdCBpbiBtdWx0aXBsZSBjZWxscw==">↗️</a><pre>    <span class='Function'>⊢</span> <span class='Value'>a</span> <span class='Gets'>←</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'>4</span><span class='Ligature'>‿</span><span class='Number'>3</span>
 ┌─         
 ╵ 0  1  2