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diff --git a/docs/doc/map.html b/docs/doc/map.html index f84421cf..396b0a48 100644 --- a/docs/doc/map.html +++ b/docs/doc/map.html @@ -6,7 +6,7 @@ <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="mapping-modifiers"><a class="header" href="#mapping-modifiers">Mapping modifiers</a></h1> <p>Mapping a function over an array means to call it on each element of that array, creating an array of results. It's also possible to map over two arrays, applying the function to various choices of one element from each, but there's no longer a single correct way to iterate over these elements.</p> -<p>BQN has two 1-modifiers to map over arrays: Each (<code><span class='Modifier'>¨</span></code>) and Table (<code><span class='Modifier'>⌜</span></code>). On two arguments, Table applies its operand to all combinations of elements while Each creates a one-to-one or one-to-many matching. Since they apply to elements, these modifiers are different from Cells (<code><span class='Modifier'>˘</span></code>) or its generalization Rank (<code><span class='Modifier2'>⎉</span></code>), which apply the function to array cells. The modifier <a href="depth.html#the-depth-modifier">Depth</a> (<code><span class='Modifier2'>⚇</span></code>) is a generalization of Each, so that <code><span class='Modifier'>¨</span></code> is <code><span class='Modifier2'>⚇</span><span class='Number'>¯1</span></code>; however, it can't be used to implement Table without some additional array operations.</p> +<p>As a result, BQN has two 1-modifiers to map over arrays: Each (<code><span class='Modifier'>¨</span></code>) and Table (<code><span class='Modifier'>⌜</span></code>). On two arguments, Table applies its operand to all combinations of elements while Each creates a one-to-one or one-to-many matching. Since they apply to elements, these modifiers are different from <a href="rank.html#cells">Cells</a> (<code><span class='Modifier'>˘</span></code>) or its generalization <a href="rank.html#rank">Rank</a> (<code><span class='Modifier2'>⎉</span></code>), which apply the function to array cells. The modifier <a href="depth.html#the-depth-modifier">Depth</a> (<code><span class='Modifier2'>⚇</span></code>) is a generalization of Each, so that <code><span class='Modifier'>¨</span></code> is <code><span class='Modifier2'>⚇</span><span class='Number'>¯1</span></code>; however, it can't be used to implement Table without some additional array operations.</p> <h2 id="one-argument-mapping"><a class="header" href="#one-argument-mapping">One-argument mapping</a></h2> <svg viewBox='-224 -21.6 680 187.2'> <g fill='currentColor' font-family='BQN,monospace'> @@ -133,7 +133,7 @@ "C0" "C1" "C2" "C3" "C4" ┘ </pre> -<p>Its name comes from the "multiplication table" or "times table" often used to teach arithmetic, and with it you can easily make such a table, by repeating the same argument with Self (<code><span class='Modifier'>˜</span></code>):</p> +<p>Its name comes from the "multiplication table" or "times table" often used to teach arithmetic, and with it you can easily make such a table, by repeating the same argument with <a href="swap.html">Self</a> (<code><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=w5fijJzLnCAxK+KGlTY=">↗️</a><pre> <span class='Function'>×</span><span class='Modifier'>⌜˜</span> <span class='Number'>1</span><span class='Function'>+↕</span><span class='Number'>6</span> ┌─ ╵ 1 2 3 4 5 6 @@ -213,11 +213,11 @@ <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> ⟨ "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">Transpose</a>.</p> +<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> ⟨ "A0" "B1" "C2" "D3" ⟩ </pre> -<p>If the argument lengths don't match then Each gives an error. This contrasts with 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> +<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> <span class='Error'>Error: Mapping: Expected equal shape prefix (⟨3⟩ ≡ ≢𝕨, ⟨5⟩ ≡ ≢𝕩)</span> </pre> @@ -228,12 +228,13 @@ ⟨ 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 according to the <a href="leading.html">leading axis convention</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/MeKlijAgICMgVG9vIHNtYWxsCuKJoiAoMOKAvzLigL824qWKQCkg4omNwqggMOKAvzLipYowICAjIEp1c3QgcmlnaHQK4omiICgw4oC/MuKAvzbipYpAKSDiiY3CqCAw4oC/M+KlijAgICMgVG9vIGxhcmdl">↗️</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 +<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 </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'>2</span><span class='Function'>⥊</span><span class='Number'>0</span> <span class='Comment'># Just right -</span>⟨ 0 2 6 ⟩ + <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>⟨ 0 2 6 ⟩ </pre> -<p>Leading axis agreement is described further <a href="leading.html#leading-axis-agreement">here</a>.</p> |