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| author | Marshall Lochbaum <mwlochbaum@gmail.com> | 2022-07-05 16:46:42 -0400 |
|---|---|---|
| committer | Marshall Lochbaum <mwlochbaum@gmail.com> | 2022-07-05 16:46:42 -0400 |
| commit | a25cb2b0bf26033c9bc778d816618a752d015d99 (patch) | |
| tree | 7056712bb10bf509764e04e56267f106e50dbea0 /docs/doc/map.html | |
| parent | df5ddc0ed2fe48411645228c6e2d596be239a0c6 (diff) | |
Somehow, all the docs have now been edited
Diffstat (limited to 'docs/doc/map.html')
| -rw-r--r-- | docs/doc/map.html | 28 |
1 files changed, 17 insertions, 11 deletions
diff --git a/docs/doc/map.html b/docs/doc/map.html index e91b4689..652651ca 100644 --- a/docs/doc/map.html +++ b/docs/doc/map.html @@ -62,7 +62,13 @@ </span>⟨ "0⊑𝕩" "1⊑𝕩" "2⊑𝕩" ⟩ </pre> <p>The applications are performed in index order: index <code><span class='Value'>…</span><span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>0</span></code>, then <code><span class='Value'>…</span><span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>1</span></code>, <code><span class='Value'>…</span><span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>2</span></code> and so on, until <code><span class='Value'>…</span><span class='Number'>1</span><span class='Ligature'>‿</span><span class='Number'>0</span></code>. This can affect a program where the operand has side effects, such as the following one that appends its argument to <code><span class='Value'>o</span></code>.</p> -<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=b+KGkOKfqOKfqSDii4Qge2/iiL7in5w84oap8J2VqX3CqCAiaW5kZXgi4omNIm9yZGVyIiDii4Qgbw==">↗️</a><pre> <span class='Value'>o</span><span class='Gets'>←</span><span class='Bracket'>⟨⟩</span> <span class='Separator'>⋄</span> <span class='Brace'>{</span><span class='Value'>o</span><span class='Function'>∾</span><span class='Modifier2'>⟜</span><span class='Function'><</span><span class='Gets'>↩</span><span class='Value'>𝕩</span><span class='Brace'>}</span><span class='Modifier'>¨</span> <span class='String'>"index"</span><span class='Function'>≍</span><span class='String'>"order"</span> <span class='Separator'>⋄</span> <span class='Value'>o</span> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=WyJpbmRleCIsIm9yZGVyIl0KCm/ihpDin6jin6kg4ouEIHtv4oi+4p+cPOKGqfCdlal9wqggWyJpbmRleCIsIm9yZGVyIl0g4ouEIG8=">↗️</a><pre> <span class='Bracket'>[</span><span class='String'>"index"</span><span class='Separator'>,</span><span class='String'>"order"</span><span class='Bracket'>]</span> +┌─ +╵"index + order" + ┘ + + <span class='Value'>o</span><span class='Gets'>←</span><span class='Bracket'>⟨⟩</span> <span class='Separator'>⋄</span> <span class='Brace'>{</span><span class='Value'>o</span><span class='Function'>∾</span><span class='Modifier2'>⟜</span><span class='Function'><</span><span class='Gets'>↩</span><span class='Value'>𝕩</span><span class='Brace'>}</span><span class='Modifier'>¨</span> <span class='Bracket'>[</span><span class='String'>"index"</span><span class='Separator'>,</span><span class='String'>"order"</span><span class='Bracket'>]</span> <span class='Separator'>⋄</span> <span class='Value'>o</span> "indexorder" </pre> <p>When an array is displayed, index order is the same as the top-to-bottom, left-to-right reading order of English. It's also the same as the ordering of <a href="reshape.html#deshape">Deshape</a>'s result, so that here <code><span class='Value'>o</span></code> ends up being <code><span class='Function'>⥊</span><span class='Value'>𝕩</span></code>. The dyadic cases described in the following sections will also have a defined evaluation order, but it's not as easy to describe it in terms of the arguments: instead, the <em>result</em> elements are produced in index order.</p> @@ -126,7 +132,7 @@ </svg> <p>The Table modifier applies its operand function to every possible combination of one element from <code><span class='Value'>𝕨</span></code> and one from <code><span class='Value'>𝕩</span></code>, sort of like a structure-preserving and function-applying <a href="https://en.wikipedia.org/wiki/Cartesian_product">Cartesian product</a>. Below, it combines a length-3 list and a length-5 list into a shape <code><span class='Number'>3</span><span class='Ligature'>‿</span><span class='Number'>5</span></code> table.</p> -<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=IkFCQyIg4omN4oycICIwMTIzNCI=">↗️</a><pre> <span class='String'>"ABC"</span> <span class='Function'>≍</span><span class='Modifier'>⌜</span> <span class='String'>"01234"</span> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=IkFCQyIg4ouI4oycICIwMTIzNCI=">↗️</a><pre> <span class='String'>"ABC"</span> <span class='Function'>⋈</span><span class='Modifier'>⌜</span> <span class='String'>"01234"</span> ┌─ ╵ "A0" "A1" "A2" "A3" "A4" "B0" "B1" "B2" "B3" "B4" @@ -145,7 +151,7 @@ ┘ </pre> <p>The arguments don't have to be lists (that is, rank 1). There's no restriction on their shapes at all! Much like the result shape is <code><span class='Value'>m</span><span class='Ligature'>‿</span><span class='Value'>n</span></code> if <code><span class='Value'>𝕨</span></code> is a list of length <code><span class='Value'>m</span></code> and <code><span class='Value'>𝕩</span></code> is a list of length <code><span class='Value'>n</span></code>, the result shape for an array <code><span class='Value'>𝕨</span></code> of shape <code><span class='Value'>r</span></code> and <code><span class='Value'>𝕩</span></code> of shape <code><span class='Value'>s</span></code> is <code><span class='Value'>r</span><span class='Function'>∾</span><span class='Value'>s</span></code>.</p> -<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=IkEgIuKAvyJCICIg4oi+4oycICJ0aGUi4oC/ImZpcnN0IuKAvyJyb3ci4omNImFuZCLigL8idGhlIuKAvyJzZWNvbmQiCgriiaIgIkEgIuKAvyJCICIg4oi+4oycICJ0aGUi4oC/ImZpcnN0IuKAvyJyb3ci4omNImFuZCLigL8idGhlIuKAvyJzZWNvbmQi">↗️</a><pre> <span class='String'>"A "</span><span class='Ligature'>‿</span><span class='String'>"B "</span> <span class='Function'>∾</span><span class='Modifier'>⌜</span> <span class='String'>"the"</span><span class='Ligature'>‿</span><span class='String'>"first"</span><span class='Ligature'>‿</span><span class='String'>"row"</span><span class='Function'>≍</span><span class='String'>"and"</span><span class='Ligature'>‿</span><span class='String'>"the"</span><span class='Ligature'>‿</span><span class='String'>"second"</span> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=IkEgIuKAvyJCICIg4oi+4oycIFsidGhlIuKAvyJmaXJzdCLigL8icm93IiwiYW5kIuKAvyJ0aGUi4oC/InNlY29uZCJdCgriiaIgIkEgIuKAvyJCICIg4oi+4oycIFsidGhlIuKAvyJmaXJzdCLigL8icm93IiwiYW5kIuKAvyJ0aGUi4oC/InNlY29uZCJd">↗️</a><pre> <span class='String'>"A "</span><span class='Ligature'>‿</span><span class='String'>"B "</span> <span class='Function'>∾</span><span class='Modifier'>⌜</span> <span class='Bracket'>[</span><span class='String'>"the"</span><span class='Ligature'>‿</span><span class='String'>"first"</span><span class='Ligature'>‿</span><span class='String'>"row"</span><span class='Separator'>,</span><span class='String'>"and"</span><span class='Ligature'>‿</span><span class='String'>"the"</span><span class='Ligature'>‿</span><span class='String'>"second"</span><span class='Bracket'>]</span> ┌─ ╎ "A the" "A first" "A row" "A and" "A the" "A second" @@ -154,7 +160,7 @@ "B and" "B the" "B second" ┘ - <span class='Function'>≢</span> <span class='String'>"A "</span><span class='Ligature'>‿</span><span class='String'>"B "</span> <span class='Function'>∾</span><span class='Modifier'>⌜</span> <span class='String'>"the"</span><span class='Ligature'>‿</span><span class='String'>"first"</span><span class='Ligature'>‿</span><span class='String'>"row"</span><span class='Function'>≍</span><span class='String'>"and"</span><span class='Ligature'>‿</span><span class='String'>"the"</span><span class='Ligature'>‿</span><span class='String'>"second"</span> + <span class='Function'>≢</span> <span class='String'>"A "</span><span class='Ligature'>‿</span><span class='String'>"B "</span> <span class='Function'>∾</span><span class='Modifier'>⌜</span> <span class='Bracket'>[</span><span class='String'>"the"</span><span class='Ligature'>‿</span><span class='String'>"first"</span><span class='Ligature'>‿</span><span class='String'>"row"</span><span class='Separator'>,</span><span class='String'>"and"</span><span class='Ligature'>‿</span><span class='String'>"the"</span><span class='Ligature'>‿</span><span class='String'>"second"</span><span class='Bracket'>]</span> ⟨ 2 2 3 ⟩ </pre> <p>Except for the more sophisticated shape, this result is exactly what you'd get if you deshaped each argument to a list. In each case, every element of <code><span class='Value'>𝕨</span></code> is visited in turn, and each time the element is paired with every element of <code><span class='Value'>𝕩</span></code>.</p> @@ -210,31 +216,31 @@ </svg> <p>Given two arguments of matching shapes, Each performs what's sometimes called a "zip", matching each element of <code><span class='Value'>𝕨</span></code> to the corresponding element of <code><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=IkFCQ0QiIOKJjcKoICIwMTIzIg==">↗️</a><pre> <span class='String'>"ABCD"</span> <span class='Function'>≍</span><span class='Modifier'>¨</span> <span class='String'>"0123"</span> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=IkFCQ0QiIOKLiMKoICIwMTIzIg==">↗️</a><pre> <span class='String'>"ABCD"</span> <span class='Function'>⋈</span><span class='Modifier'>¨</span> <span class='String'>"0123"</span> ⟨ "A0" "B1" "C2" "D3" ⟩ </pre> <p>This makes for a lot fewer applications than Table. Only the diagonal elements from Table's result are seen, as we can check with <a href="transpose.html#reorder-axes">Reorder Axes</a>.</p> -<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=MOKAvzAg4o2JICJBQkNEIiDiiY3ijJwgIjAxMjMi">↗️</a><pre> <span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>0</span> <span class='Function'>⍉</span> <span class='String'>"ABCD"</span> <span class='Function'>≍</span><span class='Modifier'>⌜</span> <span class='String'>"0123"</span> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=MOKAvzAg4o2JICJBQkNEIiDii4jijJwgIjAxMjMi">↗️</a><pre> <span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>0</span> <span class='Function'>⍉</span> <span class='String'>"ABCD"</span> <span class='Function'>⋈</span><span class='Modifier'>⌜</span> <span class='String'>"0123"</span> ⟨ "A0" "B1" "C2" "D3" ⟩ </pre> <p>If the argument lengths don't match then Each gives an error. This differs from zip in many languages, which drops elements from the longer argument (this is natural for linked lists). This flexibility is rarely wanted in BQN, and having an error right away saves debugging time.</p> -<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=IkFCQyIg4omNwqggIjAxMjM0Ig==">↗️</a><pre> <span class='String'>"ABC"</span> <span class='Function'>≍</span><span class='Modifier'>¨</span> <span class='String'>"01234"</span> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=IkFCQyIg4ouIwqggIjAxMjM0Ig==">↗️</a><pre> <span class='String'>"ABC"</span> <span class='Function'>⋈</span><span class='Modifier'>¨</span> <span class='String'>"01234"</span> <span class='Error'>Error: Mapping: Expected equal shape prefix (⟨3⟩ ≡ ≢𝕨, ⟨5⟩ ≡ ≢𝕩)</span> </pre> <p>Arguments can have any shape as long as the axis lengths match up. As with Table, the result elements don't depend on these shapes but the result shape does.</p> -<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=WzIw4oC/MzDigL8xMCw1MOKAvzQw4oC/NjBdICvin5zihpXCqCAy4oC/MeKAvzDiiY0z4oC/MuKAvzE=">↗️</a><pre> <span class='Bracket'>[</span><span class='Number'>20</span><span class='Ligature'>‿</span><span class='Number'>30</span><span class='Ligature'>‿</span><span class='Number'>10</span><span class='Separator'>,</span><span class='Number'>50</span><span class='Ligature'>‿</span><span class='Number'>40</span><span class='Ligature'>‿</span><span class='Number'>60</span><span class='Bracket'>]</span> <span class='Function'>+</span><span class='Modifier2'>⟜</span><span class='Function'>↕</span><span class='Modifier'>¨</span> <span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>1</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> +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=WzIw4oC/MzDigL8xMCw1MOKAvzQw4oC/NjBdICvin5zihpXCqCBbMuKAvzHigL8wLDPigL8y4oC/MV0=">↗️</a><pre> <span class='Bracket'>[</span><span class='Number'>20</span><span class='Ligature'>‿</span><span class='Number'>30</span><span class='Ligature'>‿</span><span class='Number'>10</span><span class='Separator'>,</span><span class='Number'>50</span><span class='Ligature'>‿</span><span class='Number'>40</span><span class='Ligature'>‿</span><span class='Number'>60</span><span class='Bracket'>]</span> <span class='Function'>+</span><span class='Modifier2'>⟜</span><span class='Function'>↕</span><span class='Modifier'>¨</span> <span class='Bracket'>[</span><span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>1</span><span class='Ligature'>‿</span><span class='Number'>0</span><span class='Separator'>,</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='Bracket'>]</span> ┌─ ╵ ⟨ 20 21 ⟩ ⟨ 30 ⟩ ⟨⟩ ⟨ 50 51 52 ⟩ ⟨ 40 41 ⟩ ⟨ 60 ⟩ ┘ </pre> <p>But arguments don't have to have exactly the same shape: just the same length along corresponding axes. These axes are matched up by <a href="leading.html#leading-axis-agreement">leading axis agreement</a>, so that one argument's shape has to be a prefix of the other's. With equal ranks, the shapes do have to match as we've seen above.</p> -<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4omiICgw4oC/MuKAvzbipYpAKSDiiY3CqCAw4oC/MeKlijAgICMgVG9vIHNtYWxsCgriiaIgKDDigL8y4oC/NuKlikApIOKJjcKoIDDigL8z4qWKMCAgIyBUb28gbGFyZ2UKCuKJoiAoMOKAvzLigL824qWKQCkg4omNwqggMOKAvzLipYowICAjIEp1c3QgcmlnaHQ=">↗️</a><pre> <span class='Function'>≢</span> <span class='Paren'>(</span><span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>6</span><span class='Function'>⥊</span><span class='String'>@</span><span class='Paren'>)</span> <span class='Function'>≍</span><span class='Modifier'>¨</span> <span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>1</span><span class='Function'>⥊</span><span class='Number'>0</span> <span class='Comment'># Too small +<a class="replLink" title="Open in the REPL" target="_blank" href="https://mlochbaum.github.io/BQN/try.html#code=4omiICgw4oC/MuKAvzbipYpAKSDii4jCqCAw4oC/MeKlijAgICMgVG9vIHNtYWxsCgriiaIgKDDigL8y4oC/NuKlikApIOKLiMKoIDDigL8z4qWKMCAgIyBUb28gbGFyZ2UKCuKJoiAoMOKAvzLigL824qWKQCkg4ouIwqggMOKAvzLipYowICAjIEp1c3QgcmlnaHQ=">↗️</a><pre> <span class='Function'>≢</span> <span class='Paren'>(</span><span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>6</span><span class='Function'>⥊</span><span class='String'>@</span><span class='Paren'>)</span> <span class='Function'>⋈</span><span class='Modifier'>¨</span> <span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>1</span><span class='Function'>⥊</span><span class='Number'>0</span> <span class='Comment'># Too small </span><span class='Error'>Error: Mapping: Expected equal shape prefix (0‿2‿6 ≡ ≢𝕨, 0‿1 ≡ ≢𝕩)</span> - <span class='Function'>≢</span> <span class='Paren'>(</span><span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>6</span><span class='Function'>⥊</span><span class='String'>@</span><span class='Paren'>)</span> <span class='Function'>≍</span><span class='Modifier'>¨</span> <span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>3</span><span class='Function'>⥊</span><span class='Number'>0</span> <span class='Comment'># Too large + <span class='Function'>≢</span> <span class='Paren'>(</span><span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>6</span><span class='Function'>⥊</span><span class='String'>@</span><span class='Paren'>)</span> <span class='Function'>⋈</span><span class='Modifier'>¨</span> <span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>3</span><span class='Function'>⥊</span><span class='Number'>0</span> <span class='Comment'># Too large </span><span class='Error'>Error: Mapping: Expected equal shape prefix (0‿2‿6 ≡ ≢𝕨, 0‿3 ≡ ≢𝕩)</span> - <span class='Function'>≢</span> <span class='Paren'>(</span><span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>6</span><span class='Function'>⥊</span><span class='String'>@</span><span class='Paren'>)</span> <span class='Function'>≍</span><span class='Modifier'>¨</span> <span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>2</span><span class='Function'>⥊</span><span class='Number'>0</span> <span class='Comment'># Just right + <span class='Function'>≢</span> <span class='Paren'>(</span><span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>2</span><span class='Ligature'>‿</span><span class='Number'>6</span><span class='Function'>⥊</span><span class='String'>@</span><span class='Paren'>)</span> <span class='Function'>⋈</span><span class='Modifier'>¨</span> <span class='Number'>0</span><span class='Ligature'>‿</span><span class='Number'>2</span><span class='Function'>⥊</span><span class='Number'>0</span> <span class='Comment'># Just right </span>⟨ 0 2 6 ⟩ </pre> |