diff options
| author | Marshall Lochbaum <mwlochbaum@gmail.com> | 2020-10-26 15:46:38 -0400 |
|---|---|---|
| committer | Marshall Lochbaum <mwlochbaum@gmail.com> | 2020-10-26 15:46:38 -0400 |
| commit | 1d6a9cf1441bd6d478977715d82031e77c20ce5c (patch) | |
| tree | 6fee5b999964c813594e9a5562b9e588d16d8536 /docs/tutorial/list.html | |
| parent | dd04717b7de252c300d197e5dcfaf9cab33d3ab5 (diff) | |
Don't include &run in documentation REPL links: it's no longer used
Diffstat (limited to 'docs/tutorial/list.html')
| -rw-r--r-- | docs/tutorial/list.html | 50 |
1 files changed, 25 insertions, 25 deletions
diff --git a/docs/tutorial/list.html b/docs/tutorial/list.html index deae0f11..71ad8237 100644 --- a/docs/tutorial/list.html +++ b/docs/tutorial/list.html @@ -6,11 +6,11 @@ <div class="nav"><a href="https://github.com/mlochbaum/BQN">BQN</a> / <a href="../index.html">main</a> / <a href="index.html">tutorial</a></div> <h1 id="tutorial-working-with-lists">Tutorial: Working with lists</h1> <p>Enough with all these preliminaries like learning how to read basic expressions. Let's get into what makes BQN special.</p> -<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4p+oMSwgMiwgM+KfqQ==&run">↗️</a><pre> <span class='Bracket'>⟨</span><span class='Number'>1</span><span class='Separator'>,</span> <span class='Number'>2</span><span class='Separator'>,</span> <span class='Number'>3</span><span class='Bracket'>⟩</span> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4p+oMSwgMiwgM+KfqQ==">↗️</a><pre> <span class='Bracket'>⟨</span><span class='Number'>1</span><span class='Separator'>,</span> <span class='Number'>2</span><span class='Separator'>,</span> <span class='Number'>3</span><span class='Bracket'>⟩</span> ⟨ 1 2 3 ⟩ </pre> <p>This is a list. Wait for it…</p> -<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4p+oMSwgMiwgM+KfqSArIDE=&run">↗️</a><pre> <span class='Bracket'>⟨</span><span class='Number'>1</span><span class='Separator'>,</span> <span class='Number'>2</span><span class='Separator'>,</span> <span class='Number'>3</span><span class='Bracket'>⟩</span> <span class='Function'>+</span> <span class='Number'>1</span> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4p+oMSwgMiwgM+KfqSArIDE=">↗️</a><pre> <span class='Bracket'>⟨</span><span class='Number'>1</span><span class='Separator'>,</span> <span class='Number'>2</span><span class='Separator'>,</span> <span class='Number'>3</span><span class='Bracket'>⟩</span> <span class='Function'>+</span> <span class='Number'>1</span> ⟨ 2 3 4 ⟩ </pre> <p>There we go. Now in BQN arrays are not just lists, which are a 1-dimensional data structure, but can have any number of dimensions. In this tutorial we're going to discuss lists only, leaving the 5-dimensional stuff for later. So we're really only seeing the power of <a href="https://aplwiki.com/wiki/K">K</a>, an APL-family language that only uses lists (and dictionaries, which BQN doesn't have). K was powerful enough for Arthur Whitney to found <a href="https://en.wikipedia.org/wiki/Kx_Systems">two</a> <a href="https://shakti.com/">companies</a> and make millions and millions of dollars, and BQN's compiler also runs almost entirely on lists, so this is probably enough power for one webpage.</p> @@ -79,7 +79,7 @@ </pre> <p>Strand notation is shorter and looks less cluttered in this example. As with lists, anything goes in a strand, but if it's the result of a function or operator, or another strand, then it has to be put in parentheses. With one set of parentheses, a strand will be just as long as the equivalent bracketed list, and with two you're better off using the list.</p> <p>A ligature is a kind of notation and doesn't do something specific like a function does. It's the sequence of ligatures that makes whatever they join together into a list. So if we parenthesize either ligature below, we get a different result! Ligatures aren't right-associative or left-associative.</p> -<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=MOKAvzHigL8yCigw4oC/MSnigL8yCjDigL8oMeKAvzIp&run">↗️</a><pre> <span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>1</span><span class='Ligature'>‿</span><span class='Number'>2</span> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=MOKAvzHigL8yCigw4oC/MSnigL8yCjDigL8oMeKAvzIp">↗️</a><pre> <span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>1</span><span class='Ligature'>‿</span><span class='Number'>2</span> ⟨ 0 1 2 ⟩ <span class='Paren'>(</span><span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>1</span><span class='Paren'>)</span><span class='Ligature'>‿</span><span class='Number'>2</span> ⟨ ⟨ 0 1 ⟩ 2 ⟩ @@ -113,7 +113,7 @@ <p>Lists are just one-dimensional arrays. Types are divided into <em>data types</em>, which tend to have a subject role, and <em>operation types</em>, which tend to have a role matching their type. Also, any value that's not an array, such as everything we used in the last tutorial, is called an <em>atom</em>.</p> <h2 id="arithmetic-on-lists">Arithmetic on lists</h2> <p>Arithmetic functions automatically apply to each element of a list argument. If both arguments are lists, they have to have the same length, and they're matched up one element at a time.</p> -<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=w7cg4p+oMiwzLDTin6kKCiJBUEwiICsgMQoKIjMxNDE1IiAtICcwJwoKNOKAvzPigL8y4oC/MSDii4YgMeKAvzLigL8z4oC/NA==&run">↗️</a><pre> <span class='Function'>÷</span> <span class='Bracket'>⟨</span><span class='Number'>2</span><span class='Separator'>,</span><span class='Number'>3</span><span class='Separator'>,</span><span class='Number'>4</span><span class='Bracket'>⟩</span> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=w7cg4p+oMiwzLDTin6kKCiJBUEwiICsgMQoKIjMxNDE1IiAtICcwJwoKNOKAvzPigL8y4oC/MSDii4YgMeKAvzLigL8z4oC/NA==">↗️</a><pre> <span class='Function'>÷</span> <span class='Bracket'>⟨</span><span class='Number'>2</span><span class='Separator'>,</span><span class='Number'>3</span><span class='Separator'>,</span><span class='Number'>4</span><span class='Bracket'>⟩</span> ⟨ 0.5 0.333333333333333 0.25 ⟩ <span class='String'>"APL"</span> <span class='Function'>+</span> <span class='Number'>1</span> @@ -126,7 +126,7 @@ ⟨ 4 9 8 1 ⟩ </pre> <p>This list application works recursively, so that lists of lists (and so on) are handled as well. We say that arithmetic functions are <em>pervasive</em>. They dig into their arguments until reaching the atoms.</p> -<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=MiDDlyDin6gw4oC/MiDii4QgMeKAvzPigL814p+pCgrin6ggMTAsIDIw4oC/MzAg4p+pICsg4p+oIDHigL8yLCAzIOKfqQ==&run">↗️</a><pre> <span class='Number'>2</span> <span class='Function'>×</span> <span class='Bracket'>⟨</span><span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>2</span> <span class='Separator'>⋄</span> <span class='Number'>1</span><span class='Ligature'>‿</span><span class='Number'>3</span><span class='Ligature'>‿</span><span class='Number'>5</span><span class='Bracket'>⟩</span> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=MiDDlyDin6gw4oC/MiDii4QgMeKAvzPigL814p+pCgrin6ggMTAsIDIw4oC/MzAg4p+pICsg4p+oIDHigL8yLCAzIOKfqQ==">↗️</a><pre> <span class='Number'>2</span> <span class='Function'>×</span> <span class='Bracket'>⟨</span><span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>2</span> <span class='Separator'>⋄</span> <span class='Number'>1</span><span class='Ligature'>‿</span><span class='Number'>3</span><span class='Ligature'>‿</span><span class='Number'>5</span><span class='Bracket'>⟩</span> ⟨ ⟨ 0 4 ⟩ ⟨ 2 6 10 ⟩ ⟩ <span class='Bracket'>⟨</span> <span class='Number'>10</span><span class='Separator'>,</span> <span class='Number'>20</span><span class='Ligature'>‿</span><span class='Number'>30</span> <span class='Bracket'>⟩</span> <span class='Function'>+</span> <span class='Bracket'>⟨</span> <span class='Number'>1</span><span class='Ligature'>‿</span><span class='Number'>2</span><span class='Separator'>,</span> <span class='Number'>3</span> <span class='Bracket'>⟩</span> @@ -156,14 +156,14 @@ <p>Let's introduce a few primitives to work with lists.</p> <p>Make one or two atom arguments into a list with <code><span class='Function'>≍</span></code>, pronounced Solo in the one-argument case and Couple in the two-argument case. This might not seem to merit a symbol but there's more to come. Don't call it on lists and ponder the results, igniting a hunger for ever more dimensions.</p> -<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4omNIDQKCjIg4omNIDQ=&run">↗️</a><pre> <span class='Function'>≍</span> <span class='Number'>4</span> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4omNIDQKCjIg4omNIDQ=">↗️</a><pre> <span class='Function'>≍</span> <span class='Number'>4</span> ⟨ 4 ⟩ <span class='Number'>2</span> <span class='Function'>≍</span> <span class='Number'>4</span> ⟨ 2 4 ⟩ </pre> <p>Concatenate lists with Join To (<code><span class='Function'>∾</span></code>). The little chain link symbol—technically "inverted lazy S"—is my favorite in BQN. Hook those lists together!</p> -<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4p+oMSwyLDPin6kg4oi+ICJhYmMiCgowIOKIviDin6gxLDIsM+KfqQoKInBsdXJhbCIg4oi+ICdzJw==&run">↗️</a><pre> <span class='Bracket'>⟨</span><span class='Number'>1</span><span class='Separator'>,</span><span class='Number'>2</span><span class='Separator'>,</span><span class='Number'>3</span><span class='Bracket'>⟩</span> <span class='Function'>∾</span> <span class='String'>"abc"</span> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4p+oMSwyLDPin6kg4oi+ICJhYmMiCgowIOKIviDin6gxLDIsM+KfqQoKInBsdXJhbCIg4oi+ICdzJw==">↗️</a><pre> <span class='Bracket'>⟨</span><span class='Number'>1</span><span class='Separator'>,</span><span class='Number'>2</span><span class='Separator'>,</span><span class='Number'>3</span><span class='Bracket'>⟩</span> <span class='Function'>∾</span> <span class='String'>"abc"</span> ⟨ 1 2 3 'a' 'b' 'c' ⟩ <span class='Number'>0</span> <span class='Function'>∾</span> <span class='Bracket'>⟨</span><span class='Number'>1</span><span class='Separator'>,</span><span class='Number'>2</span><span class='Separator'>,</span><span class='Number'>3</span><span class='Bracket'>⟩</span> @@ -174,11 +174,11 @@ </pre> <p>The last two examples show that you can join a list to an atom, making it the first or last element of the result. This is a little suspect because if you decide the data being stored is more complicated and start using a list instead of an atom, then it will no longer be used as a single element but rather a subsection of the result. So I would only use that shortcut for something like a numeric literal that's clearly an atom and will stay that way, and otherwise wrap those atomic arguments in some <code><span class='Bracket'>⟨⟩</span></code> brackets. Join will even work with two atoms, but in that case I'd say it makes more sense to use Couple instead.</p> <p>Reverse (<code><span class='Function'>⌽</span></code>) puts the list back to front.</p> -<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4oy9ICJkcmF3ZXIi&run">↗️</a><pre> <span class='Function'>⌽</span> <span class='String'>"drawer"</span> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4oy9ICJkcmF3ZXIi">↗️</a><pre> <span class='Function'>⌽</span> <span class='String'>"drawer"</span> "reward" </pre> <p>With a left argument <code><span class='Function'>⌽</span></code> means Rotate instead, and shifts values over by the specified amount, wrapping those that go off the end to the other side. A positive value rotates to the left, and a negative one rotates right.</p> -<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=MiDijL0g4p+oMCwxLDIsMyw04p+pCsKvMSDijL0gImJjZGVhIg==&run">↗️</a><pre> <span class='Number'>2</span> <span class='Function'>⌽</span> <span class='Bracket'>⟨</span><span class='Number'>0</span><span class='Separator'>,</span><span class='Number'>1</span><span class='Separator'>,</span><span class='Number'>2</span><span class='Separator'>,</span><span class='Number'>3</span><span class='Separator'>,</span><span class='Number'>4</span><span class='Bracket'>⟩</span> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=MiDijL0g4p+oMCwxLDIsMyw04p+pCsKvMSDijL0gImJjZGVhIg==">↗️</a><pre> <span class='Number'>2</span> <span class='Function'>⌽</span> <span class='Bracket'>⟨</span><span class='Number'>0</span><span class='Separator'>,</span><span class='Number'>1</span><span class='Separator'>,</span><span class='Number'>2</span><span class='Separator'>,</span><span class='Number'>3</span><span class='Separator'>,</span><span class='Number'>4</span><span class='Bracket'>⟩</span> ⟨ 2 3 4 0 1 ⟩ <span class='Number'>¯1</span> <span class='Function'>⌽</span> <span class='String'>"bcdea"</span> "abcde" @@ -204,7 +204,7 @@ </table> <p>The 1-modifier Each (<code><span class='Modifier'>¨</span></code>) applies its operand to every element of a list argument: it's the same as <code><span class='Value'>map</span></code> in a functional programming language. With two list arguments (which have to have the same length), Each pairs the corresponding elements from each, a bit like a <code><span class='Value'>zip</span></code> function. If one argument is a list and one's an atom, the atom is reused every time instead.</p> -<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4oy9wqggImFiY2Qi4oC/IkFCQ0RFRiLigL8iMDEiCgoic3RyaW5nIuKAvyJsaXN0IuKAvyJhcnJheSIg4oi+wqggJ3MnCgoiYWJjIiDiiY3CqCDijL0gImFiYyI=&run">↗️</a><pre> <span class='Function'>⌽</span><span class='Modifier'>¨</span> <span class='String'>"abcd"</span><span class='Ligature'>‿</span><span class='String'>"ABCDEF"</span><span class='Ligature'>‿</span><span class='String'>"01"</span> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4oy9wqggImFiY2Qi4oC/IkFCQ0RFRiLigL8iMDEiCgoic3RyaW5nIuKAvyJsaXN0IuKAvyJhcnJheSIg4oi+wqggJ3MnCgoiYWJjIiDiiY3CqCDijL0gImFiYyI=">↗️</a><pre> <span class='Function'>⌽</span><span class='Modifier'>¨</span> <span class='String'>"abcd"</span><span class='Ligature'>‿</span><span class='String'>"ABCDEF"</span><span class='Ligature'>‿</span><span class='String'>"01"</span> ⟨ "dcba" "FEDCBA" "10" ⟩ <span class='String'>"string"</span><span class='Ligature'>‿</span><span class='String'>"list"</span><span class='Ligature'>‿</span><span class='String'>"array"</span> <span class='Function'>∾</span><span class='Modifier'>¨</span> <span class='String'>'s'</span> @@ -214,13 +214,13 @@ ⟨ "ac" "bb" "ca" ⟩ </pre> <p>Fold (<code><span class='Modifier'>´</span></code>) is the higher-order function also known as reduce or accumulate. It applies its operand function between each pair of elements in a list argument. For example, <code><span class='Function'>+</span><span class='Modifier'>´</span></code> gives the sum of a list and <code><span class='Function'>×</span><span class='Modifier'>´</span></code> gives its product.</p> -<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=K8K0IDLigL8z4oC/NArDl8K0IDLigL8z4oC/NA==&run">↗️</a><pre> <span class='Function'>+</span><span class='Modifier'>´</span> <span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>3</span><span class='Ligature'>‿</span><span class='Number'>4</span> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=K8K0IDLigL8z4oC/NArDl8K0IDLigL8z4oC/NA==">↗️</a><pre> <span class='Function'>+</span><span class='Modifier'>´</span> <span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>3</span><span class='Ligature'>‿</span><span class='Number'>4</span> 9 <span class='Function'>×</span><span class='Modifier'>´</span> <span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>3</span><span class='Ligature'>‿</span><span class='Number'>4</span> 24 </pre> <p>To match the order of BQN evaluation, Fold moves over its argument array from right to left. You'd get the same result by writing the operand function in between each element of the argument list, but you'd also write the function a lot of times.</p> -<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=LcK0IDHigL8y4oC/M+KAvzTigL81CjEtMi0zLTQtNQ==&run">↗️</a><pre> <span class='Function'>-</span><span class='Modifier'>´</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='Ligature'>‿</span><span class='Number'>4</span><span class='Ligature'>‿</span><span class='Number'>5</span> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=LcK0IDHigL8y4oC/M+KAvzTigL81CjEtMi0zLTQtNQ==">↗️</a><pre> <span class='Function'>-</span><span class='Modifier'>´</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='Ligature'>‿</span><span class='Number'>4</span><span class='Ligature'>‿</span><span class='Number'>5</span> 3 <span class='Number'>1</span><span class='Function'>-</span><span class='Number'>2</span><span class='Function'>-</span><span class='Number'>3</span><span class='Function'>-</span><span class='Number'>4</span><span class='Function'>-</span><span class='Number'>5</span> 3 @@ -228,11 +228,11 @@ <p>With this evaluation order, <code><span class='Function'>-</span><span class='Modifier'>´</span></code> gives the <em>alternating sum</em> of its argument. Think of it this way: the left argument of each <code><span class='Function'>-</span></code> is a single number, while the right argument is made up of all the numbers to the right subtracted together. So each <code><span class='Function'>-</span></code> flips the sign of every number to its right, and every number is negated by all the <code><span class='Function'>-</span></code>s to its left. The first number (<code><span class='Number'>1</span></code> above) never gets negated, the second is negated once, the third is negated twice, returning it to its original value… the signs alternate.</p> <p><em>Hey, isn't it dissonant that the first, second, and third numbers are negated zero, one, and two times? If they were the zeroth, first, and second it wouldn't be…</em></p> <p>You can fold with the Join To function to join several lists together:</p> -<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4oi+wrQg4p+oICJjb24iLCAiY2F0IiwgImVuYXQiLCAiZSIg4p+p&run">↗️</a><pre> <span class='Function'>∾</span><span class='Modifier'>´</span> <span class='Bracket'>⟨</span> <span class='String'>"con"</span><span class='Separator'>,</span> <span class='String'>"cat"</span><span class='Separator'>,</span> <span class='String'>"enat"</span><span class='Separator'>,</span> <span class='String'>"e"</span> <span class='Bracket'>⟩</span> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4oi+wrQg4p+oICJjb24iLCAiY2F0IiwgImVuYXQiLCAiZSIg4p+p">↗️</a><pre> <span class='Function'>∾</span><span class='Modifier'>´</span> <span class='Bracket'>⟨</span> <span class='String'>"con"</span><span class='Separator'>,</span> <span class='String'>"cat"</span><span class='Separator'>,</span> <span class='String'>"enat"</span><span class='Separator'>,</span> <span class='String'>"e"</span> <span class='Bracket'>⟩</span> "concatenate" </pre> <p>But you shouldn't! Just <code><span class='Function'>∾</span></code> will do the job for you—with no left argument it's just called "Join" (it's like Javascript's <code><span class='Number'>.join</span><span class='Paren'>()</span></code>, but with no separator and not specific to strings). And it could do more jobs if you had more dimensions. But I'm sure that's the furthest thing from your mind.</p> -<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4oi+IOKfqCAiY29uIiwgImNhdCIsICJlbmF0IiwgImUiIOKfqQ==&run">↗️</a><pre> <span class='Function'>∾</span> <span class='Bracket'>⟨</span> <span class='String'>"con"</span><span class='Separator'>,</span> <span class='String'>"cat"</span><span class='Separator'>,</span> <span class='String'>"enat"</span><span class='Separator'>,</span> <span class='String'>"e"</span> <span class='Bracket'>⟩</span> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4oi+IOKfqCAiY29uIiwgImNhdCIsICJlbmF0IiwgImUiIOKfqQ==">↗️</a><pre> <span class='Function'>∾</span> <span class='Bracket'>⟨</span> <span class='String'>"con"</span><span class='Separator'>,</span> <span class='String'>"cat"</span><span class='Separator'>,</span> <span class='String'>"enat"</span><span class='Separator'>,</span> <span class='String'>"e"</span> <span class='Bracket'>⟩</span> "concatenate" </pre> <h2 id="example-base-decoding">Example: base decoding</h2> @@ -253,19 +253,19 @@ </table> <p>Almost. It's really close. There are just two things missing, so I'll cover those and can we agree one and three-quarters is pretty good? First is Range (<code><span class='Function'>↕</span></code>), which is called on a number to give all the natural numbers less than it:</p> -<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4oaVIDg=&run">↗️</a><pre> <span class='Function'>↕</span> <span class='Number'>8</span> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4oaVIDg=">↗️</a><pre> <span class='Function'>↕</span> <span class='Number'>8</span> ⟨ 0 1 2 3 4 5 6 7 ⟩ </pre> <p>Natural numbers in BQN start at 0. I'll get to the second function in a moment, but first let's consider how we'd decode just one number in binary. I'll pick a smaller one: 9 is 1001 in binary. Like the first 1 in decimal 1001 counts for one thousand or <code><span class='Number'>10</span><span class='Function'>⋆</span><span class='Number'>3</span></code>, the first one in binary 1001 counts for 8, which is <code><span class='Number'>2</span><span class='Function'>⋆</span><span class='Number'>3</span></code>. We can put each number next to its place value like this:</p> -<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=OOKAvzTigL8y4oC/MSDiiY3CqCAx4oC/MOKAvzDigL8x&run">↗️</a><pre> <span class='Number'>8</span><span class='Ligature'>‿</span><span class='Number'>4</span><span class='Ligature'>‿</span><span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>1</span> <span class='Function'>≍</span><span class='Modifier'>¨</span> <span class='Number'>1</span><span class='Ligature'>‿</span><span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>1</span> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=OOKAvzTigL8y4oC/MSDiiY3CqCAx4oC/MOKAvzDigL8x">↗️</a><pre> <span class='Number'>8</span><span class='Ligature'>‿</span><span class='Number'>4</span><span class='Ligature'>‿</span><span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>1</span> <span class='Function'>≍</span><span class='Modifier'>¨</span> <span class='Number'>1</span><span class='Ligature'>‿</span><span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>1</span> ⟨ ⟨ 8 1 ⟩ ⟨ 4 0 ⟩ ⟨ 2 0 ⟩ ⟨ 1 1 ⟩ ⟩ </pre> <p>To get the value we multiply each number by its place value and then add them up.</p> -<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=K8K0IDjigL804oC/MuKAvzEgw5cgMeKAvzDigL8w4oC/MQ==&run">↗️</a><pre> <span class='Function'>+</span><span class='Modifier'>´</span> <span class='Number'>8</span><span class='Ligature'>‿</span><span class='Number'>4</span><span class='Ligature'>‿</span><span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>1</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'>0</span><span class='Ligature'>‿</span><span class='Number'>1</span> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=K8K0IDjigL804oC/MuKAvzEgw5cgMeKAvzDigL8w4oC/MQ==">↗️</a><pre> <span class='Function'>+</span><span class='Modifier'>´</span> <span class='Number'>8</span><span class='Ligature'>‿</span><span class='Number'>4</span><span class='Ligature'>‿</span><span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>1</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'>0</span><span class='Ligature'>‿</span><span class='Number'>1</span> 9 </pre> <p>Now we'd like to generate that list <code><span class='Number'>8</span><span class='Ligature'>‿</span><span class='Number'>4</span><span class='Ligature'>‿</span><span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>1</span></code> instead of writing it out, particularly because it needs to be twice as long to decode eight-bit ASCII characters (where the first bit is always zero come on robots would never use such an inefficient format). It's the first four powers of two, or two to the power of the first four natural numbers, in reverse. While we're at it, let's get <code><span class='Number'>1</span><span class='Ligature'>‿</span><span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>1</span></code> from <code><span class='String'>"1001"</span></code> by subtracting <code><span class='String'>'0'</span></code>. Nice.</p> -<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=MiDii4Yg4oaVNAoK4oy9MuKLhuKGlTQKCijijL0y4ouG4oaVNCkgw5cgIjEwMDEiLScwJwoKK8K0ICjijL0y4ouG4oaVNCkgw5cgIjEwMDEiLScwJw==&run">↗️</a><pre> <span class='Number'>2</span> <span class='Function'>⋆</span> <span class='Function'>↕</span><span class='Number'>4</span> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=MiDii4Yg4oaVNAoK4oy9MuKLhuKGlTQKCijijL0y4ouG4oaVNCkgw5cgIjEwMDEiLScwJwoKK8K0ICjijL0y4ouG4oaVNCkgw5cgIjEwMDEiLScwJw==">↗️</a><pre> <span class='Number'>2</span> <span class='Function'>⋆</span> <span class='Function'>↕</span><span class='Number'>4</span> ⟨ 1 2 4 8 ⟩ <span class='Function'>⌽</span><span class='Number'>2</span><span class='Function'>⋆↕</span><span class='Number'>4</span> @@ -279,34 +279,34 @@ </pre> <p>Lot of functions up there. Notice how I need to use parentheses for the left argument of a function if it's compound, but never for the right argument, and consequently never with a one-argument function.</p> <p>Representing our ASCII statement as a list of lists, we convert each digit to a number as before:</p> -<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=JzAnIC3LnCAiMDEwMDExMTAi4oC/IjAxMTAwMTAxIuKAvyIwMTExMDAxMCLigL8iMDExMDAxMDAi4oC/IjAwMTAwMDAxIg==&run">↗️</a><pre> <span class='String'>'0'</span> <span class='Function'>-</span><span class='Modifier'>˜</span> <span class='String'>"01001110"</span><span class='Ligature'>‿</span><span class='String'>"01100101"</span><span class='Ligature'>‿</span><span class='String'>"01110010"</span><span class='Ligature'>‿</span><span class='String'>"01100100"</span><span class='Ligature'>‿</span><span class='String'>"00100001"</span> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=JzAnIC3LnCAiMDEwMDExMTAi4oC/IjAxMTAwMTAxIuKAvyIwMTExMDAxMCLigL8iMDExMDAxMDAi4oC/IjAwMTAwMDAxIg==">↗️</a><pre> <span class='String'>'0'</span> <span class='Function'>-</span><span class='Modifier'>˜</span> <span class='String'>"01001110"</span><span class='Ligature'>‿</span><span class='String'>"01100101"</span><span class='Ligature'>‿</span><span class='String'>"01110010"</span><span class='Ligature'>‿</span><span class='String'>"01100100"</span><span class='Ligature'>‿</span><span class='String'>"00100001"</span> ⟨ ⟨ 0 1 0 0 1 1 1 0 ⟩ ⟨ 0 1 1 0 0 1 0 1 ⟩ ⟨ 0 1 1 1 0 0 1 0 ⟩ ⟨ 0 1 1 0 0 1 0 0 ⟩ ⟨ 0 0 1 0 0 0 0 1 ⟩ ⟩ </pre> <p>Now we need to multiply each digit by the right place value, and add them up. The adding part is easy, just requiring an Each.</p> -<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=K8K0wqggJzAnIC3LnCAiMDEwMDExMTAi4oC/IjAxMTAwMTAxIuKAvyIwMTExMDAxMCLigL8iMDExMDAxMDAi4oC/IjAwMTAwMDAxIg==&run">↗️</a><pre> <span class='Function'>+</span><span class='Modifier'>´¨</span> <span class='String'>'0'</span> <span class='Function'>-</span><span class='Modifier'>˜</span> <span class='String'>"01001110"</span><span class='Ligature'>‿</span><span class='String'>"01100101"</span><span class='Ligature'>‿</span><span class='String'>"01110010"</span><span class='Ligature'>‿</span><span class='String'>"01100100"</span><span class='Ligature'>‿</span><span class='String'>"00100001"</span> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=K8K0wqggJzAnIC3LnCAiMDEwMDExMTAi4oC/IjAxMTAwMTAxIuKAvyIwMTExMDAxMCLigL8iMDExMDAxMDAi4oC/IjAwMTAwMDAxIg==">↗️</a><pre> <span class='Function'>+</span><span class='Modifier'>´¨</span> <span class='String'>'0'</span> <span class='Function'>-</span><span class='Modifier'>˜</span> <span class='String'>"01001110"</span><span class='Ligature'>‿</span><span class='String'>"01100101"</span><span class='Ligature'>‿</span><span class='String'>"01110010"</span><span class='Ligature'>‿</span><span class='String'>"01100100"</span><span class='Ligature'>‿</span><span class='String'>"00100001"</span> ⟨ 4 4 4 3 2 ⟩ </pre> <p>Multiplication is harder, and if we try to multiply by the place value list directly it doesn't go so well.</p> -<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=KOKMvTLii4bihpU4KSDDlyAnMCcgLcucICIwMTAwMTExMCLigL8iMDExMDAxMDEi4oC/IjAxMTEwMDEwIuKAvyIwMTEwMDEwMCLigL8iMDAxMDAwMDEi&run">↗️</a><pre> <span class='Paren'>(</span><span class='Function'>⌽</span><span class='Number'>2</span><span class='Function'>⋆↕</span><span class='Number'>8</span><span class='Paren'>)</span> <span class='Function'>×</span> <span class='String'>'0'</span> <span class='Function'>-</span><span class='Modifier'>˜</span> <span class='String'>"01001110"</span><span class='Ligature'>‿</span><span class='String'>"01100101"</span><span class='Ligature'>‿</span><span class='String'>"01110010"</span><span class='Ligature'>‿</span><span class='String'>"01100100"</span><span class='Ligature'>‿</span><span class='String'>"00100001"</span> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=KOKMvTLii4bihpU4KSDDlyAnMCcgLcucICIwMTAwMTExMCLigL8iMDExMDAxMDEi4oC/IjAxMTEwMDEwIuKAvyIwMTEwMDEwMCLigL8iMDAxMDAwMDEi">↗️</a><pre> <span class='Paren'>(</span><span class='Function'>⌽</span><span class='Number'>2</span><span class='Function'>⋆↕</span><span class='Number'>8</span><span class='Paren'>)</span> <span class='Function'>×</span> <span class='String'>'0'</span> <span class='Function'>-</span><span class='Modifier'>˜</span> <span class='String'>"01001110"</span><span class='Ligature'>‿</span><span class='String'>"01100101"</span><span class='Ligature'>‿</span><span class='String'>"01110010"</span><span class='Ligature'>‿</span><span class='String'>"01100100"</span><span class='Ligature'>‿</span><span class='String'>"00100001"</span> ERROR</pre> <p>This is because the list on the left has length 8 while the list on the right has length 5. The <em>elements</em> of the list on the right have length 8, but BQN can't be expected to know you want to connect the two arguments in that particular way. Especially considering that if you happen to have 8 characters then the right argument <em>will</em> have length 8!</p> <p>There are a few ways to handle this. What we'll do is <em>bind</em> the place values to <code><span class='Function'>×</span></code> using the 2-modifier <code><span class='Modifier2'>⊸</span></code>. This modifier attaches a left argument to a function.</p> -<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=ImFiIiDiiL7CqCDin6ggImNkIiwgInV0IiDin6kKCiJhYiLiirjiiL7CqCDin6ggImNkIiwgInV0IiDin6k=&run">↗️</a><pre> <span class='String'>"ab"</span> <span class='Function'>∾</span><span class='Modifier'>¨</span> <span class='Bracket'>⟨</span> <span class='String'>"cd"</span><span class='Separator'>,</span> <span class='String'>"ut"</span> <span class='Bracket'>⟩</span> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=ImFiIiDiiL7CqCDin6ggImNkIiwgInV0IiDin6kKCiJhYiLiirjiiL7CqCDin6ggImNkIiwgInV0IiDin6k=">↗️</a><pre> <span class='String'>"ab"</span> <span class='Function'>∾</span><span class='Modifier'>¨</span> <span class='Bracket'>⟨</span> <span class='String'>"cd"</span><span class='Separator'>,</span> <span class='String'>"ut"</span> <span class='Bracket'>⟩</span> ⟨ "acd" "but" ⟩ <span class='String'>"ab"</span><span class='Modifier2'>⊸</span><span class='Function'>∾</span><span class='Modifier'>¨</span> <span class='Bracket'>⟨</span> <span class='String'>"cd"</span><span class='Separator'>,</span> <span class='String'>"ut"</span> <span class='Bracket'>⟩</span> ⟨ "abcd" "abut" ⟩ </pre> <p>In the first bit of code above, <code><span class='Modifier'>¨</span></code> matches up its left and right arguments. In the second, we bind <code><span class='String'>"ab"</span></code> to <code><span class='Function'>∾</span></code> first—remember that modifiers associate from left to right, so that <code><span class='String'>"ab"</span><span class='Modifier2'>⊸</span><span class='Function'>∾</span><span class='Modifier'>¨</span></code> and <code><span class='Paren'>(</span><span class='String'>"ab"</span><span class='Modifier2'>⊸</span><span class='Function'>∾</span><span class='Paren'>)</span><span class='Modifier'>¨</span></code> are the same—and Each only sees one argument. <code><span class='String'>"ab"</span></code>, packed inside Each's operand, is reused each time. The same principle applies to our binary problem:</p> -<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=K8K0wqggKOKMvTLii4bihpU4KeKKuMOXwqggJzAnIC3LnCAiMDEwMDExMTAi4oC/IjAxMTAwMTAxIuKAvyIwMTExMDAxMCLigL8iMDExMDAxMDAi4oC/IjAwMTAwMDAxIg==&run">↗️</a><pre> <span class='Function'>+</span><span class='Modifier'>´¨</span> <span class='Paren'>(</span><span class='Function'>⌽</span><span class='Number'>2</span><span class='Function'>⋆↕</span><span class='Number'>8</span><span class='Paren'>)</span><span class='Modifier2'>⊸</span><span class='Function'>×</span><span class='Modifier'>¨</span> <span class='String'>'0'</span> <span class='Function'>-</span><span class='Modifier'>˜</span> <span class='String'>"01001110"</span><span class='Ligature'>‿</span><span class='String'>"01100101"</span><span class='Ligature'>‿</span><span class='String'>"01110010"</span><span class='Ligature'>‿</span><span class='String'>"01100100"</span><span class='Ligature'>‿</span><span class='String'>"00100001"</span> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=K8K0wqggKOKMvTLii4bihpU4KeKKuMOXwqggJzAnIC3LnCAiMDEwMDExMTAi4oC/IjAxMTAwMTAxIuKAvyIwMTExMDAxMCLigL8iMDExMDAxMDAi4oC/IjAwMTAwMDAxIg==">↗️</a><pre> <span class='Function'>+</span><span class='Modifier'>´¨</span> <span class='Paren'>(</span><span class='Function'>⌽</span><span class='Number'>2</span><span class='Function'>⋆↕</span><span class='Number'>8</span><span class='Paren'>)</span><span class='Modifier2'>⊸</span><span class='Function'>×</span><span class='Modifier'>¨</span> <span class='String'>'0'</span> <span class='Function'>-</span><span class='Modifier'>˜</span> <span class='String'>"01001110"</span><span class='Ligature'>‿</span><span class='String'>"01100101"</span><span class='Ligature'>‿</span><span class='String'>"01110010"</span><span class='Ligature'>‿</span><span class='String'>"01100100"</span><span class='Ligature'>‿</span><span class='String'>"00100001"</span> ⟨ 78 101 114 100 33 ⟩ </pre> <p>To wrap things up, we just convert from numbers to characters by adding the null character.</p> -<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=QCArICvCtMKoICjijL0y4ouG4oaVOCniirjDl8KoICcwJyAty5wgIjAxMDAxMTEwIuKAvyIwMTEwMDEwMSLigL8iMDExMTAwMTAi4oC/IjAxMTAwMTAwIuKAvyIwMDEwMDAwMSI=&run">↗️</a><pre> <span class='String'>@</span> <span class='Function'>+</span> <span class='Function'>+</span><span class='Modifier'>´¨</span> <span class='Paren'>(</span><span class='Function'>⌽</span><span class='Number'>2</span><span class='Function'>⋆↕</span><span class='Number'>8</span><span class='Paren'>)</span><span class='Modifier2'>⊸</span><span class='Function'>×</span><span class='Modifier'>¨</span> <span class='String'>'0'</span> <span class='Function'>-</span><span class='Modifier'>˜</span> <span class='String'>"01001110"</span><span class='Ligature'>‿</span><span class='String'>"01100101"</span><span class='Ligature'>‿</span><span class='String'>"01110010"</span><span class='Ligature'>‿</span><span class='String'>"01100100"</span><span class='Ligature'>‿</span><span class='String'>"00100001"</span> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=QCArICvCtMKoICjijL0y4ouG4oaVOCniirjDl8KoICcwJyAty5wgIjAxMDAxMTEwIuKAvyIwMTEwMDEwMSLigL8iMDExMTAwMTAi4oC/IjAxMTAwMTAwIuKAvyIwMDEwMDAwMSI=">↗️</a><pre> <span class='String'>@</span> <span class='Function'>+</span> <span class='Function'>+</span><span class='Modifier'>´¨</span> <span class='Paren'>(</span><span class='Function'>⌽</span><span class='Number'>2</span><span class='Function'>⋆↕</span><span class='Number'>8</span><span class='Paren'>)</span><span class='Modifier2'>⊸</span><span class='Function'>×</span><span class='Modifier'>¨</span> <span class='String'>'0'</span> <span class='Function'>-</span><span class='Modifier'>˜</span> <span class='String'>"01001110"</span><span class='Ligature'>‿</span><span class='String'>"01100101"</span><span class='Ligature'>‿</span><span class='String'>"01110010"</span><span class='Ligature'>‿</span><span class='String'>"01100100"</span><span class='Ligature'>‿</span><span class='String'>"00100001"</span> "Nerd!" </pre> <p>Was it as anticlimactic as you'd hoped? In fact there's a simpler way to do the base decoding as well, using <code><span class='Modifier2'>⊸</span></code>'s mirror image <code><span class='Modifier2'>⟜</span></code> in a different way. We'll discuss that in the next tutorial!</p> -<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=K8K0ICjijL0y4ouG4oaVNCkgw5cgIjEwMDEiLScwJwor4p+cKCvLnCnCtCDijL0gIjEwMDEiLScwJw==&run">↗️</a><pre> <span class='Function'>+</span><span class='Modifier'>´</span> <span class='Paren'>(</span><span class='Function'>⌽</span><span class='Number'>2</span><span class='Function'>⋆↕</span><span class='Number'>4</span><span class='Paren'>)</span> <span class='Function'>×</span> <span class='String'>"1001"</span><span class='Function'>-</span><span class='String'>'0'</span> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=K8K0ICjijL0y4ouG4oaVNCkgw5cgIjEwMDEiLScwJwor4p+cKCvLnCnCtCDijL0gIjEwMDEiLScwJw==">↗️</a><pre> <span class='Function'>+</span><span class='Modifier'>´</span> <span class='Paren'>(</span><span class='Function'>⌽</span><span class='Number'>2</span><span class='Function'>⋆↕</span><span class='Number'>4</span><span class='Paren'>)</span> <span class='Function'>×</span> <span class='String'>"1001"</span><span class='Function'>-</span><span class='String'>'0'</span> 9 <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='Modifier'>´</span> <span class='Function'>⌽</span> <span class='String'>"1001"</span><span class='Function'>-</span><span class='String'>'0'</span> 9 |