Zola 2025-09-13T00:00:00+00:00 https://blog.kyleandzoebarton.com/posts/atom.xml 2025-09-13T00:00:00+00:00 2025-09-13T00:00:00+00:00 Unknown https://blog.kyleandzoebarton.com/posts/functional-for-loop/ <p>Let's look at a few use-cases which highlight the big three higher order functions for handling lists:</p> <ol> <li>Given a list of numbers, increase all of the numbers by one</li> <li>Given a list of numbers, return all the even numbered elements</li> <li>Given a list of numbers, return the sum of all the elements in the list</li> </ol> <h1 id="loops">Loops<a class="zola-anchor" href="#loops" aria-label="Anchor link for: loops" style="visibility: hidden;"></a> </h1> <p>In a procedural context, these can all be solved with <code>for</code> loops. Let's implement in Java.</p> <h4 id="add-one-to-elements">Add one to elements<a class="zola-anchor" href="#add-one-to-elements" aria-label="Anchor link for: add-one-to-elements" style="visibility: hidden;"></a> </h4> <pre data-lang="java" class="language-java z-code"><code class="language-java" data-lang="java"><span class="z-source z-java"><span class="z-storage z-modifier z-java">public</span> <span class="z-storage z-modifier z-java">static</span> <span class="z-support z-class z-java">List</span><span class="z-meta z-generic z-java"><span class="z-punctuation z-definition z-generic z-begin z-java">&lt;</span><span class="z-support z-class z-java">Integer</span><span class="z-punctuation z-definition z-generic z-end z-java">&gt;</span></span> <span class="z-meta z-function-call z-java"><span class="z-variable z-function z-java">addOne</span><span class="z-punctuation z-section z-parens z-begin z-java">(</span><span class="z-support z-class z-java">List</span><span class="z-meta z-generic z-java"><span class="z-punctuation z-definition z-generic z-begin z-java">&lt;</span><span class="z-support z-class z-java">Integer</span><span class="z-punctuation z-definition z-generic z-end z-java">&gt;</span></span> givenValues<span class="z-punctuation z-section z-parens z-end z-java">)</span></span> <span class="z-meta z-block z-java"><span class="z-punctuation z-section z-block z-begin z-java">{</span> </span></span><span class="z-source z-java"><span class="z-meta z-block z-java"> <span class="z-storage z-type z-var z-java">var</span> returnValues <span class="z-meta z-assignment z-rhs z-java"><span class="z-keyword z-operator z-assignment z-java">=</span> <span class="z-meta z-instantiation z-java"><span class="z-keyword z-other z-storage z-new z-java">new</span> <span class="z-support z-class z-java">ArrayList</span><span class="z-meta z-generic z-java"><span class="z-punctuation z-definition z-generic z-begin z-java">&lt;</span><span class="z-support z-class z-java">Integer</span><span class="z-punctuation z-definition z-generic z-end z-java">&gt;</span></span><span class="z-meta z-parens z-constructor-arguments z-java"><span class="z-punctuation z-section z-parens z-begin z-java">(</span><span class="z-punctuation z-section z-parens z-end z-java">)</span></span></span></span><span class="z-punctuation z-terminator z-java">;</span> </span></span><span class="z-source z-java"><span class="z-meta z-block z-java"> <span class="z-keyword z-control z-loop z-for z-java">for</span> <span class="z-meta z-parens z-java"><span class="z-punctuation z-section z-parens z-begin z-java">(</span><span class="z-storage z-type z-var z-java">var</span> currentValue <span class="z-keyword z-operator z-ternary z-java">:</span> givenValues<span class="z-punctuation z-section z-parens z-end z-java">)</span></span> <span class="z-meta z-block z-java"><span class="z-punctuation z-section z-block z-begin z-java">{</span> </span></span></span><span class="z-source z-java"><span class="z-meta z-block z-java"><span class="z-meta z-block z-java"> returnValues<span class="z-punctuation z-accessor z-dot z-java">.</span><span class="z-meta z-function-call z-java"><span class="z-variable z-function z-java">add</span><span class="z-punctuation z-section z-parens z-begin z-java">(</span>currentValue <span class="z-keyword z-operator z-arithmetic z-java">+</span> <span class="z-constant z-numeric z-integer z-decimal z-java">1</span><span class="z-punctuation z-section z-parens z-end z-java">)</span></span><span class="z-punctuation z-terminator z-java">;</span> </span></span></span><span class="z-source z-java"><span class="z-meta z-block z-java"><span class="z-meta z-block z-java"> <span class="z-punctuation z-section z-block z-end z-java">}</span></span> </span></span><span class="z-source z-java"><span class="z-meta z-block z-java"> <span class="z-keyword z-control z-flow z-return z-java">return</span> returnValues<span class="z-punctuation z-terminator z-java">;</span> </span></span><span class="z-source z-java"><span class="z-meta z-block z-java"><span class="z-punctuation z-section z-block z-end z-java">}</span></span> </span></code></pre> <h4 id="return-all-the-even-numbered-elements">Return all the even numbered elements<a class="zola-anchor" href="#return-all-the-even-numbered-elements" aria-label="Anchor link for: return-all-the-even-numbered-elements" style="visibility: hidden;"></a> </h4> <pre data-lang="java" class="language-java z-code"><code class="language-java" data-lang="java"><span class="z-source z-java"><span class="z-storage z-modifier z-java">public</span> <span class="z-storage z-modifier z-java">static</span> <span class="z-support z-class z-java">List</span><span class="z-meta z-generic z-java"><span class="z-punctuation z-definition z-generic z-begin z-java">&lt;</span><span class="z-support z-class z-java">Integer</span><span class="z-punctuation z-definition z-generic z-end z-java">&gt;</span></span> <span class="z-meta z-function-call z-java"><span class="z-variable z-function z-java">evenNumbers</span><span class="z-punctuation z-section z-parens z-begin z-java">(</span><span class="z-support z-class z-java">List</span><span class="z-meta z-generic z-java"><span class="z-punctuation z-definition z-generic z-begin z-java">&lt;</span><span class="z-support z-class z-java">Integer</span><span class="z-punctuation z-definition z-generic z-end z-java">&gt;</span></span> givenValues<span class="z-punctuation z-section z-parens z-end z-java">)</span></span> <span class="z-meta z-block z-java"><span class="z-punctuation z-section z-block z-begin z-java">{</span> </span></span><span class="z-source z-java"><span class="z-meta z-block z-java"> <span class="z-storage z-type z-var z-java">var</span> returnValues <span class="z-meta z-assignment z-rhs z-java"><span class="z-keyword z-operator z-assignment z-java">=</span> <span class="z-meta z-instantiation z-java"><span class="z-keyword z-other z-storage z-new z-java">new</span> <span class="z-support z-class z-java">ArrayList</span><span class="z-meta z-generic z-java"><span class="z-punctuation z-definition z-generic z-begin z-java">&lt;</span><span class="z-support z-class z-java">Integer</span><span class="z-punctuation z-definition z-generic z-end z-java">&gt;</span></span><span class="z-meta z-parens z-constructor-arguments z-java"><span class="z-punctuation z-section z-parens z-begin z-java">(</span><span class="z-punctuation z-section z-parens z-end z-java">)</span></span></span></span><span class="z-punctuation z-terminator z-java">;</span> </span></span><span class="z-source z-java"><span class="z-meta z-block z-java"> <span class="z-keyword z-control z-loop z-for z-java">for</span> <span class="z-meta z-parens z-java"><span class="z-punctuation z-section z-parens z-begin z-java">(</span><span class="z-storage z-type z-var z-java">var</span> currentValue <span class="z-keyword z-operator z-ternary z-java">:</span> givenValues<span class="z-punctuation z-section z-parens z-end z-java">)</span></span> <span class="z-meta z-block z-java"><span class="z-punctuation z-section z-block z-begin z-java">{</span> </span></span></span><span class="z-source z-java"><span class="z-meta z-block z-java"><span class="z-meta z-block z-java"> <span class="z-keyword z-control z-conditional z-if z-java">if</span> <span class="z-meta z-parens z-java"><span class="z-punctuation z-section z-parens z-begin z-java">(</span>currentValue <span class="z-keyword z-operator z-arithmetic z-java">%</span> <span class="z-constant z-numeric z-integer z-decimal z-java">2</span> <span class="z-keyword z-operator z-comparison z-java">==</span> <span class="z-constant z-numeric z-integer z-decimal z-java">0</span><span class="z-punctuation z-section z-parens z-end z-java">)</span></span> <span class="z-meta z-block z-java"><span class="z-punctuation z-section z-block z-begin z-java">{</span> </span></span></span></span><span class="z-source z-java"><span class="z-meta z-block z-java"><span class="z-meta z-block z-java"><span class="z-meta z-block z-java"> returnValues<span class="z-punctuation z-accessor z-dot z-java">.</span><span class="z-meta z-function-call z-java"><span class="z-variable z-function z-java">add</span><span class="z-punctuation z-section z-parens z-begin z-java">(</span>currentValue<span class="z-punctuation z-section z-parens z-end z-java">)</span></span><span class="z-punctuation z-terminator z-java">;</span> </span></span></span></span><span class="z-source z-java"><span class="z-meta z-block z-java"><span class="z-meta z-block z-java"><span class="z-meta z-block z-java"> <span class="z-punctuation z-section z-block z-end z-java">}</span></span> </span></span></span><span class="z-source z-java"><span class="z-meta z-block z-java"><span class="z-meta z-block z-java"> <span class="z-punctuation z-section z-block z-end z-java">}</span></span> </span></span><span class="z-source z-java"><span class="z-meta z-block z-java"> <span class="z-keyword z-control z-flow z-return z-java">return</span> returnValues<span class="z-punctuation z-terminator z-java">;</span> </span></span><span class="z-source z-java"><span class="z-meta z-block z-java"><span class="z-punctuation z-section z-block z-end z-java">}</span></span> </span></code></pre> <h4 id="return-the-sum-of-the-values-in-the-list">Return the sum of the values in the list<a class="zola-anchor" href="#return-the-sum-of-the-values-in-the-list" aria-label="Anchor link for: return-the-sum-of-the-values-in-the-list" style="visibility: hidden;"></a> </h4> <pre data-lang="java" class="language-java z-code"><code class="language-java" data-lang="java"><span class="z-source z-java"><span class="z-storage z-modifier z-java">public</span> <span class="z-storage z-modifier z-java">static</span> <span class="z-support z-class z-java">Integer</span> <span class="z-meta z-function-call z-java"><span class="z-variable z-function z-java">sumNumbers</span><span class="z-punctuation z-section z-parens z-begin z-java">(</span><span class="z-support z-class z-java">List</span><span class="z-meta z-generic z-java"><span class="z-punctuation z-definition z-generic z-begin z-java">&lt;</span><span class="z-support z-class z-java">Integer</span><span class="z-punctuation z-definition z-generic z-end z-java">&gt;</span></span> givenValues<span class="z-punctuation z-section z-parens z-end z-java">)</span></span> <span class="z-meta z-block z-java"><span class="z-punctuation z-section z-block z-begin z-java">{</span> </span></span><span class="z-source z-java"><span class="z-meta z-block z-java"> <span class="z-storage z-type z-var z-java">var</span> returnValue <span class="z-meta z-assignment z-rhs z-java"><span class="z-keyword z-operator z-assignment z-java">=</span> <span class="z-constant z-numeric z-integer z-decimal z-java">0</span></span><span class="z-punctuation z-terminator z-java">;</span> </span></span><span class="z-source z-java"><span class="z-meta z-block z-java"> <span class="z-keyword z-control z-loop z-for z-java">for</span> <span class="z-meta z-parens z-java"><span class="z-punctuation z-section z-parens z-begin z-java">(</span><span class="z-storage z-type z-var z-java">var</span> currentValue <span class="z-keyword z-operator z-ternary z-java">:</span> givenValues<span class="z-punctuation z-section z-parens z-end z-java">)</span></span> <span class="z-meta z-block z-java"><span class="z-punctuation z-section z-block z-begin z-java">{</span> </span></span></span><span class="z-source z-java"><span class="z-meta z-block z-java"><span class="z-meta z-block z-java"> returnValue <span class="z-meta z-assignment z-rhs z-java"><span class="z-keyword z-operator z-assignment z-java">+=</span> currentValue</span><span class="z-punctuation z-terminator z-java">;</span> </span></span></span><span class="z-source z-java"><span class="z-meta z-block z-java"><span class="z-meta z-block z-java"> <span class="z-punctuation z-section z-block z-end z-java">}</span></span> </span></span><span class="z-source z-java"><span class="z-meta z-block z-java"> <span class="z-keyword z-control z-flow z-return z-java">return</span> returnValue<span class="z-punctuation z-terminator z-java">;</span> </span></span><span class="z-source z-java"><span class="z-meta z-block z-java"><span class="z-punctuation z-section z-block z-end z-java">}</span></span> </span></code></pre> <h1 id="the-functional-approach-recursion">The functional approach - recursion<a class="zola-anchor" href="#the-functional-approach-recursion" aria-label="Anchor link for: the-functional-approach-recursion" style="visibility: hidden;"></a> </h1> <p>In pure functional languages, these problems are generally solved with a recursive approach, since this maps more to a declarative, function-oriented syntax. Let's demonstrate in Erlang.</p> <h4 id="add-one-to-elements-1">Add one to elements<a class="zola-anchor" href="#add-one-to-elements-1" aria-label="Anchor link for: add-one-to-elements-1" style="visibility: hidden;"></a> </h4> <pre data-lang="erlang" class="language-erlang z-code"><code class="language-erlang" data-lang="erlang"><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-entity z-name z-function z-erlang">add_one</span></span></span><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-function z-parameters z-erlang"><span class="z-meta z-sequence z-list z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">[</span><span class="z-punctuation z-section z-sequence z-end z-erlang">]</span></span><span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-function z-name z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-meta z-sequence z-list z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">[</span><span class="z-punctuation z-section z-sequence z-end z-erlang">]</span></span><span class="z-punctuation z-separator z-clauses z-erlang">;</span></span> </span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-entity z-name z-function z-erlang">add_one</span></span></span><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-function z-parameters z-erlang"><span class="z-meta z-sequence z-list z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">[</span><span class="z-variable z-parameter z-erlang">Head</span><span class="z-punctuation z-separator z-sequence z-erlang">|</span><span class="z-variable z-parameter z-erlang">Tail</span><span class="z-punctuation z-section z-sequence z-end z-erlang">]</span></span><span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-function z-name z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-meta z-sequence z-list z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">[</span><span class="z-variable z-other z-erlang">Head</span><span class="z-keyword z-operator z-arithmetic z-erlang">+</span><span class="z-constant z-numeric z-integer z-decimal z-erlang">1</span><span class="z-punctuation z-separator z-sequence z-erlang">|</span><span class="z-meta z-function-call z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-variable z-function z-erlang">add_one</span></span></span><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-punctuation z-section z-arguments z-begin z-erlang">(</span><span class="z-variable z-other z-erlang">Tail</span><span class="z-punctuation z-section z-arguments z-end z-erlang">)</span></span><span class="z-punctuation z-section z-sequence z-end z-erlang">]</span></span><span class="z-punctuation z-terminator z-clause z-erlang">.</span></span> </span></code></pre> <h4 id="return-all-the-even-numbered-elements-1">Return all the even numbered elements<a class="zola-anchor" href="#return-all-the-even-numbered-elements-1" aria-label="Anchor link for: return-all-the-even-numbered-elements-1" style="visibility: hidden;"></a> </h4> <pre data-lang="erlang" class="language-erlang z-code"><code class="language-erlang" data-lang="erlang"><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-entity z-name z-function z-erlang">get_evens</span></span></span><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-function z-parameters z-erlang"><span class="z-meta z-sequence z-list z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">[</span><span class="z-punctuation z-section z-sequence z-end z-erlang">]</span></span><span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-function z-name z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-meta z-sequence z-list z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">[</span><span class="z-punctuation z-section z-sequence z-end z-erlang">]</span></span><span class="z-punctuation z-separator z-clauses z-erlang">;</span></span> </span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-entity z-name z-function z-erlang">get_evens</span></span></span><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-function z-parameters z-erlang"><span class="z-meta z-sequence z-list z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">[</span><span class="z-variable z-parameter z-erlang">Head</span><span class="z-punctuation z-separator z-sequence z-erlang">|</span><span class="z-variable z-parameter z-erlang">Tail</span><span class="z-punctuation z-section z-sequence z-end z-erlang">]</span></span><span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-function z-name z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> </span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"> <span class="z-meta z-case z-erlang"><span class="z-keyword z-control z-conditional z-case z-erlang">case</span> <span class="z-variable z-other z-erlang">Head</span> <span class="z-keyword z-operator z-arithmetic z-erlang">rem</span> <span class="z-constant z-numeric z-integer z-decimal z-erlang">2</span> <span class="z-keyword z-control z-flow z-erlang">of</span> </span></span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-case z-erlang"> <span class="z-constant z-numeric z-integer z-decimal z-erlang">0</span> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-meta z-sequence z-list z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">[</span><span class="z-variable z-other z-erlang">Head</span><span class="z-punctuation z-separator z-sequence z-erlang">|</span><span class="z-meta z-function-call z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-variable z-function z-erlang">get_evens</span></span></span><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-punctuation z-section z-arguments z-begin z-erlang">(</span><span class="z-variable z-other z-erlang">Tail</span><span class="z-punctuation z-section z-arguments z-end z-erlang">)</span></span><span class="z-punctuation z-section z-sequence z-end z-erlang">]</span></span><span class="z-punctuation z-separator z-clauses z-erlang">;</span> </span></span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-case z-erlang"> <span class="z-variable z-language z-anonymous z-erlang">_</span> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-meta z-function-call z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-variable z-function z-erlang">get_evens</span></span></span><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-punctuation z-section z-arguments z-begin z-erlang">(</span><span class="z-variable z-other z-erlang">Tail</span><span class="z-punctuation z-section z-arguments z-end z-erlang">)</span></span> </span></span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-case z-erlang"> <span class="z-keyword z-control z-conditional z-end z-erlang">end</span></span><span class="z-punctuation z-terminator z-clause z-erlang">.</span></span> </span></code></pre> <h4 id="return-the-sum-of-the-values-in-the-list-1">Return the sum of the values in the list<a class="zola-anchor" href="#return-the-sum-of-the-values-in-the-list-1" aria-label="Anchor link for: return-the-sum-of-the-values-in-the-list-1" style="visibility: hidden;"></a> </h4> <pre data-lang="erlang" class="language-erlang z-code"><code class="language-erlang" data-lang="erlang"><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-entity z-name z-function z-erlang">sum_values</span></span></span><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-function z-parameters z-erlang"><span class="z-meta z-sequence z-list z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">[</span><span class="z-punctuation z-section z-sequence z-end z-erlang">]</span></span><span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-function z-name z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-constant z-numeric z-integer z-decimal z-erlang">0</span><span class="z-punctuation z-separator z-clauses z-erlang">;</span></span> </span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-entity z-name z-function z-erlang">sum_values</span></span></span><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-function z-parameters z-erlang"><span class="z-meta z-sequence z-list z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">[</span><span class="z-variable z-parameter z-erlang">Head</span><span class="z-punctuation z-separator z-sequence z-erlang">|</span><span class="z-variable z-parameter z-erlang">Tail</span><span class="z-punctuation z-section z-sequence z-end z-erlang">]</span></span><span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-function z-name z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-variable z-other z-erlang">Head</span> <span class="z-keyword z-operator z-arithmetic z-erlang">+</span> <span class="z-meta z-function-call z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-variable z-function z-erlang">sum_values</span></span></span><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-punctuation z-section z-arguments z-begin z-erlang">(</span><span class="z-variable z-other z-erlang">Tail</span><span class="z-punctuation z-section z-arguments z-end z-erlang">)</span></span><span class="z-punctuation z-terminator z-clause z-erlang">.</span></span> </span></code></pre> <h1 id="generalizing-to-map-filter-fold">Generalizing to <code>map</code>, <code>filter</code>, <code>fold</code><a class="zola-anchor" href="#generalizing-to-map-filter-fold" aria-label="Anchor link for: generalizing-to-map-filter-fold" style="visibility: hidden;"></a> </h1> <p>These three examples are concrete use-cases for the "Big Three" higher order functions: <code>map</code>, <code>filter</code>, and <code>fold</code>. So, let's abstract out to these functions. Note that Erlang provides these functions out of the box, but for illustrative purposes, let's implement them anyway.</p> <h4 id="add-one-to-elements-2">Add one to elements<a class="zola-anchor" href="#add-one-to-elements-2" aria-label="Anchor link for: add-one-to-elements-2" style="visibility: hidden;"></a> </h4> <pre data-lang="erlang" class="language-erlang z-code"><code class="language-erlang" data-lang="erlang"><span class="z-source z-erlang"><span class="z-comment z-line z-percentage z-erlang"><span class="z-punctuation z-definition z-comment z-percentage z-erlang">%</span> abstract out to map </span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-entity z-name z-function z-erlang">add_one</span></span></span><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-function z-parameters z-erlang"><span class="z-variable z-parameter z-erlang">List</span><span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-function z-name z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-meta z-function-call z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-variable z-function z-erlang">map</span></span></span><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-punctuation z-section z-arguments z-begin z-erlang">(</span><span class="z-meta z-fun z-erlang"><span class="z-keyword z-declaration z-function z-erlang">fun</span></span><span class="z-meta z-fun z-erlang"><span class="z-meta z-fun z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-fun z-parameters z-erlang"><span class="z-variable z-parameter z-erlang">X</span><span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-fun z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-variable z-other z-erlang">X</span> <span class="z-keyword z-operator z-arithmetic z-erlang">+</span> <span class="z-constant z-numeric z-integer z-decimal z-erlang">1</span> <span class="z-keyword z-declaration z-end z-erlang">end</span></span><span class="z-punctuation z-separator z-arguments z-erlang">,</span> <span class="z-variable z-other z-erlang">List</span><span class="z-punctuation z-section z-arguments z-end z-erlang">)</span></span><span class="z-punctuation z-terminator z-clause z-erlang">.</span></span> </span><span class="z-source z-erlang"> </span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-entity z-name z-function z-erlang">map</span></span></span><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-function z-parameters z-erlang"><span class="z-variable z-language z-anonymous z-erlang">_</span><span class="z-punctuation z-separator z-parameters z-erlang">,</span> <span class="z-meta z-sequence z-list z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">[</span><span class="z-punctuation z-section z-sequence z-end z-erlang">]</span></span><span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-function z-name z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-meta z-sequence z-list z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">[</span><span class="z-punctuation z-section z-sequence z-end z-erlang">]</span></span><span class="z-punctuation z-separator z-clauses z-erlang">;</span></span> </span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-entity z-name z-function z-erlang">map</span></span></span><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-function z-parameters z-erlang"><span class="z-variable z-parameter z-erlang">Fun</span><span class="z-punctuation z-separator z-parameters z-erlang">,</span> <span class="z-meta z-sequence z-list z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">[</span><span class="z-variable z-parameter z-erlang">Head</span><span class="z-punctuation z-separator z-sequence z-erlang">|</span><span class="z-variable z-parameter z-erlang">Tail</span><span class="z-punctuation z-section z-sequence z-end z-erlang">]</span></span><span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-function z-name z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-meta z-sequence z-list z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">[</span><span class="z-meta z-function-call z-name z-erlang"><span class="z-variable z-other z-erlang">Fun</span></span><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-punctuation z-section z-arguments z-begin z-erlang">(</span><span class="z-variable z-other z-erlang">Head</span><span class="z-punctuation z-section z-arguments z-end z-erlang">)</span></span><span class="z-punctuation z-separator z-sequence z-erlang">|</span><span class="z-meta z-function-call z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-variable z-function z-erlang">map</span></span></span><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-punctuation z-section z-arguments z-begin z-erlang">(</span><span class="z-variable z-other z-erlang">Fun</span><span class="z-punctuation z-separator z-arguments z-erlang">,</span> <span class="z-variable z-other z-erlang">Tail</span><span class="z-punctuation z-section z-arguments z-end z-erlang">)</span></span><span class="z-punctuation z-section z-sequence z-end z-erlang">]</span></span><span class="z-punctuation z-terminator z-clause z-erlang">.</span></span> </span></code></pre> <h4 id="return-all-the-even-numbered-elements-2">Return all the even numbered elements<a class="zola-anchor" href="#return-all-the-even-numbered-elements-2" aria-label="Anchor link for: return-all-the-even-numbered-elements-2" style="visibility: hidden;"></a> </h4> <pre data-lang="erlang" class="language-erlang z-code"><code class="language-erlang" data-lang="erlang"><span class="z-source z-erlang"><span class="z-comment z-line z-percentage z-erlang"><span class="z-punctuation z-definition z-comment z-percentage z-erlang">%</span> abstract out to filter </span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-entity z-name z-function z-erlang">get_evens</span></span></span><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-function z-parameters z-erlang"><span class="z-variable z-parameter z-erlang">List</span><span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-function z-name z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-meta z-function-call z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-variable z-function z-erlang">filter</span></span></span><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-punctuation z-section z-arguments z-begin z-erlang">(</span><span class="z-meta z-fun z-erlang"><span class="z-keyword z-declaration z-function z-erlang">fun</span></span><span class="z-meta z-fun z-erlang"><span class="z-meta z-fun z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-fun z-parameters z-erlang"><span class="z-variable z-parameter z-erlang">X</span><span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-fun z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-variable z-other z-erlang">X</span> <span class="z-keyword z-operator z-arithmetic z-erlang">rem</span> <span class="z-constant z-numeric z-integer z-decimal z-erlang">2</span> <span class="z-keyword z-operator z-logical z-erlang">=:=</span> <span class="z-constant z-numeric z-integer z-decimal z-erlang">0</span> <span class="z-keyword z-declaration z-end z-erlang">end</span></span><span class="z-punctuation z-separator z-arguments z-erlang">,</span> <span class="z-variable z-other z-erlang">List</span><span class="z-punctuation z-section z-arguments z-end z-erlang">)</span></span><span class="z-punctuation z-terminator z-clause z-erlang">.</span></span> </span><span class="z-source z-erlang"> </span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-entity z-name z-function z-erlang">filter</span></span></span><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-function z-parameters z-erlang"><span class="z-variable z-language z-anonymous z-erlang">_</span><span class="z-punctuation z-separator z-parameters z-erlang">,</span> <span class="z-meta z-sequence z-list z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">[</span><span class="z-punctuation z-section z-sequence z-end z-erlang">]</span></span><span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-function z-name z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-meta z-sequence z-list z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">[</span><span class="z-punctuation z-section z-sequence z-end z-erlang">]</span></span><span class="z-punctuation z-separator z-clauses z-erlang">;</span></span> </span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-entity z-name z-function z-erlang">filter</span></span></span><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-function z-parameters z-erlang"><span class="z-variable z-parameter z-erlang">Pred</span><span class="z-punctuation z-separator z-parameters z-erlang">,</span> <span class="z-meta z-sequence z-list z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">[</span><span class="z-variable z-parameter z-erlang">Head</span><span class="z-punctuation z-separator z-sequence z-erlang">|</span><span class="z-variable z-parameter z-erlang">Tail</span><span class="z-punctuation z-section z-sequence z-end z-erlang">]</span></span><span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-function z-name z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> </span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"> <span class="z-meta z-case z-erlang"><span class="z-keyword z-control z-conditional z-case z-erlang">case</span> <span class="z-meta z-function-call z-name z-erlang"><span class="z-variable z-other z-erlang">Pred</span></span><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-punctuation z-section z-arguments z-begin z-erlang">(</span><span class="z-variable z-other z-erlang">Head</span><span class="z-punctuation z-section z-arguments z-end z-erlang">)</span></span> <span class="z-keyword z-control z-flow z-erlang">of</span> </span></span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-case z-erlang"> <span class="z-constant z-language z-boolean z-erlang">true</span> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-meta z-sequence z-list z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">[</span><span class="z-variable z-other z-erlang">Head</span><span class="z-punctuation z-separator z-sequence z-erlang">|</span><span class="z-meta z-function-call z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-variable z-function z-erlang">filter</span></span></span><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-punctuation z-section z-arguments z-begin z-erlang">(</span><span class="z-variable z-other z-erlang">Pred</span><span class="z-punctuation z-separator z-arguments z-erlang">,</span> <span class="z-variable z-other z-erlang">Tail</span><span class="z-punctuation z-section z-arguments z-end z-erlang">)</span></span><span class="z-punctuation z-section z-sequence z-end z-erlang">]</span></span><span class="z-punctuation z-separator z-clauses z-erlang">;</span> </span></span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-case z-erlang"> <span class="z-constant z-language z-boolean z-erlang">false</span> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-meta z-function-call z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-variable z-function z-erlang">filter</span></span></span><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-punctuation z-section z-arguments z-begin z-erlang">(</span><span class="z-variable z-other z-erlang">Pred</span><span class="z-punctuation z-separator z-arguments z-erlang">,</span> <span class="z-variable z-other z-erlang">Tail</span><span class="z-punctuation z-section z-arguments z-end z-erlang">)</span></span> </span></span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-case z-erlang"> <span class="z-keyword z-control z-conditional z-end z-erlang">end</span></span><span class="z-punctuation z-terminator z-clause z-erlang">.</span></span> </span></code></pre> <h4 id="return-the-sum-of-the-values-in-the-list-2">Return the sum of the values in the list<a class="zola-anchor" href="#return-the-sum-of-the-values-in-the-list-2" aria-label="Anchor link for: return-the-sum-of-the-values-in-the-list-2" style="visibility: hidden;"></a> </h4> <p>Note that in this case, we have to provide a "starting" value upon which to fold for this to work.</p> <pre data-lang="erlang" class="language-erlang z-code"><code class="language-erlang" data-lang="erlang"><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-entity z-name z-function z-erlang">sum_values</span></span></span><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-function z-parameters z-erlang"><span class="z-variable z-parameter z-erlang">List</span><span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-function z-name z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-meta z-function-call z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-variable z-function z-erlang">fold</span></span></span><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-punctuation z-section z-arguments z-begin z-erlang">(</span><span class="z-meta z-fun z-erlang"><span class="z-keyword z-declaration z-function z-erlang">fun</span></span><span class="z-meta z-fun z-erlang"><span class="z-meta z-fun z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-fun z-parameters z-erlang"><span class="z-variable z-parameter z-erlang">X</span><span class="z-punctuation z-separator z-parameters z-erlang">,</span> <span class="z-variable z-parameter z-erlang">SumSoFar</span><span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-fun z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-variable z-other z-erlang">X</span> <span class="z-keyword z-operator z-arithmetic z-erlang">+</span> <span class="z-variable z-other z-erlang">SumSoFar</span> <span class="z-keyword z-declaration z-end z-erlang">end</span></span><span class="z-punctuation z-separator z-arguments z-erlang">,</span> <span class="z-variable z-other z-erlang">List</span><span class="z-punctuation z-separator z-arguments z-erlang">,</span> <span class="z-constant z-numeric z-integer z-decimal z-erlang">0</span><span class="z-punctuation z-section z-arguments z-end z-erlang">)</span></span><span class="z-punctuation z-terminator z-clause z-erlang">.</span></span> </span><span class="z-source z-erlang"> </span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-entity z-name z-function z-erlang">fold</span></span></span><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-function z-parameters z-erlang"><span class="z-meta z-sequence z-list z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">[</span><span class="z-punctuation z-section z-sequence z-end z-erlang">]</span></span><span class="z-punctuation z-separator z-parameters z-erlang">,</span> <span class="z-variable z-language z-anonymous z-erlang">_</span><span class="z-punctuation z-separator z-parameters z-erlang">,</span> <span class="z-variable z-parameter z-erlang">Accumulated</span><span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-function z-name z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-variable z-other z-erlang">Accumulated</span><span class="z-punctuation z-separator z-clauses z-erlang">;</span></span> </span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-entity z-name z-function z-erlang">fold</span></span></span><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-function z-parameters z-erlang"><span class="z-meta z-sequence z-list z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">[</span><span class="z-variable z-parameter z-erlang">Head</span><span class="z-punctuation z-separator z-sequence z-erlang">|</span><span class="z-variable z-parameter z-erlang">Tail</span><span class="z-punctuation z-section z-sequence z-end z-erlang">]</span></span><span class="z-punctuation z-separator z-parameters z-erlang">,</span> <span class="z-variable z-parameter z-erlang">Fun</span><span class="z-punctuation z-separator z-parameters z-erlang">,</span> <span class="z-variable z-parameter z-erlang">Accumulated</span><span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-function z-name z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-meta z-function-call z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-variable z-function z-erlang">fold</span></span></span><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-punctuation z-section z-arguments z-begin z-erlang">(</span><span class="z-variable z-other z-erlang">Tail</span><span class="z-punctuation z-separator z-arguments z-erlang">,</span> <span class="z-variable z-other z-erlang">Fun</span><span class="z-punctuation z-separator z-arguments z-erlang">,</span> <span class="z-meta z-function-call z-name z-erlang"><span class="z-variable z-other z-erlang">Fun</span></span><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-punctuation z-section z-arguments z-begin z-erlang">(</span><span class="z-variable z-other z-erlang">Head</span><span class="z-punctuation z-separator z-arguments z-erlang">,</span> <span class="z-variable z-other z-erlang">Accumulated</span><span class="z-punctuation z-section z-arguments z-end z-erlang">)</span></span><span class="z-punctuation z-section z-arguments z-end z-erlang">)</span></span><span class="z-punctuation z-terminator z-clause z-erlang">.</span></span> </span></code></pre> <h1 id="making-them-tail-recursive">Making them tail recursive<a class="zola-anchor" href="#making-them-tail-recursive" aria-label="Anchor link for: making-them-tail-recursive" style="visibility: hidden;"></a> </h1> <p>For most of these implementations, we run into the scaling problem of recursive approaches: since the frames of the previous recursive calls have to be preserved, memory usage scales linearly with the size of the given list. Languages like Erlang solve for this with <a href="https://beta.erlang.org/doc/system/ref_man_functions.html#tail-recursion">Tail Call Optimization</a>. As such, we can avoid the inefficiency as long as we make these implementations tail recursive:</p> <h4 id="map">Map<a class="zola-anchor" href="#map" aria-label="Anchor link for: map" style="visibility: hidden;"></a> </h4> <pre data-lang="erlang" class="language-erlang z-code"><code class="language-erlang" data-lang="erlang"><span class="z-source z-erlang"><span class="z-comment z-line z-percentage z-erlang"><span class="z-punctuation z-definition z-comment z-percentage z-erlang">%</span> Start with a 2-arity function which performs the list reverse, and provides a default starting value for the accumulator </span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-entity z-name z-function z-erlang">map_tco</span></span></span><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-function z-parameters z-erlang"><span class="z-variable z-parameter z-erlang">List</span><span class="z-punctuation z-separator z-parameters z-erlang">,</span> <span class="z-variable z-parameter z-erlang">Fun</span> <span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-function z-name z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> </span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"> <span class="z-meta z-function-call z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-variable z-function z-erlang">map_tco</span></span></span><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-punctuation z-section z-arguments z-begin z-erlang">(</span><span class="z-meta z-path z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-variable z-namespace z-erlang">lists</span></span><span class="z-punctuation z-accessor z-double-colon z-erlang">:</span><span class="z-meta z-path z-erlang"></span></span><span class="z-meta z-path z-erlang"><span class="z-meta z-function-call z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-variable z-function z-erlang">reverse</span></span></span></span><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-punctuation z-section z-arguments z-begin z-erlang">(</span><span class="z-variable z-other z-erlang">List</span><span class="z-punctuation z-section z-arguments z-end z-erlang">)</span></span><span class="z-punctuation z-separator z-arguments z-erlang">,</span> <span class="z-variable z-other z-erlang">Fun</span><span class="z-punctuation z-separator z-arguments z-erlang">,</span> <span class="z-meta z-sequence z-list z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">[</span><span class="z-punctuation z-section z-sequence z-end z-erlang">]</span></span><span class="z-punctuation z-section z-arguments z-end z-erlang">)</span></span><span class="z-punctuation z-terminator z-clause z-erlang">.</span></span> </span><span class="z-source z-erlang"> </span><span class="z-source z-erlang"><span class="z-comment z-line z-percentage z-erlang"><span class="z-punctuation z-definition z-comment z-percentage z-erlang">%</span> Use the 3-arity function with the accumulator for TCO </span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-entity z-name z-function z-erlang">map_tco</span></span></span><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-function z-parameters z-erlang"><span class="z-meta z-sequence z-list z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">[</span><span class="z-punctuation z-section z-sequence z-end z-erlang">]</span></span><span class="z-punctuation z-separator z-parameters z-erlang">,</span> <span class="z-variable z-language z-anonymous z-erlang">_</span><span class="z-punctuation z-separator z-parameters z-erlang">,</span> <span class="z-variable z-parameter z-erlang">Acc</span><span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-function z-name z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-variable z-other z-erlang">Acc</span><span class="z-punctuation z-separator z-clauses z-erlang">;</span></span> </span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-entity z-name z-function z-erlang">map_tco</span></span></span><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-function z-parameters z-erlang"><span class="z-meta z-sequence z-list z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">[</span><span class="z-variable z-parameter z-erlang">Head</span><span class="z-punctuation z-separator z-sequence z-erlang">|</span><span class="z-variable z-parameter z-erlang">Tail</span><span class="z-punctuation z-section z-sequence z-end z-erlang">]</span></span><span class="z-punctuation z-separator z-parameters z-erlang">,</span> <span class="z-variable z-parameter z-erlang">Fun</span><span class="z-punctuation z-separator z-parameters z-erlang">,</span> <span class="z-variable z-parameter z-erlang">Acc</span><span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-function z-name z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-meta z-function-call z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-variable z-function z-erlang">map_tco</span></span></span><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-punctuation z-section z-arguments z-begin z-erlang">(</span><span class="z-variable z-other z-erlang">Tail</span><span class="z-punctuation z-separator z-arguments z-erlang">,</span> <span class="z-variable z-other z-erlang">Fun</span><span class="z-punctuation z-separator z-arguments z-erlang">,</span> <span class="z-meta z-sequence z-list z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">[</span><span class="z-meta z-function-call z-name z-erlang"><span class="z-variable z-other z-erlang">Fun</span></span><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-punctuation z-section z-arguments z-begin z-erlang">(</span><span class="z-variable z-other z-erlang">Head</span><span class="z-punctuation z-section z-arguments z-end z-erlang">)</span></span><span class="z-punctuation z-separator z-sequence z-erlang">|</span><span class="z-variable z-other z-erlang">Acc</span><span class="z-punctuation z-section z-sequence z-end z-erlang">]</span></span><span class="z-punctuation z-section z-arguments z-end z-erlang">)</span></span><span class="z-punctuation z-terminator z-clause z-erlang">.</span></span> </span></code></pre> <h4 id="filter">Filter<a class="zola-anchor" href="#filter" aria-label="Anchor link for: filter" style="visibility: hidden;"></a> </h4> <pre data-lang="erlang" class="language-erlang z-code"><code class="language-erlang" data-lang="erlang"><span class="z-source z-erlang"><span class="z-comment z-line z-percentage z-erlang"><span class="z-punctuation z-definition z-comment z-percentage z-erlang">%</span> Again, a 2-arity proxy for convenience </span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-entity z-name z-function z-erlang">filter_tco</span></span></span><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-function z-parameters z-erlang"><span class="z-variable z-parameter z-erlang">List</span><span class="z-punctuation z-separator z-parameters z-erlang">,</span> <span class="z-variable z-parameter z-erlang">Pred</span><span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-function z-name z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> </span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"> <span class="z-meta z-function-call z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-variable z-function z-erlang">filter_tco</span></span></span><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-punctuation z-section z-arguments z-begin z-erlang">(</span><span class="z-meta z-path z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-variable z-namespace z-erlang">lists</span></span><span class="z-punctuation z-accessor z-double-colon z-erlang">:</span><span class="z-meta z-path z-erlang"></span></span><span class="z-meta z-path z-erlang"><span class="z-meta z-function-call z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-variable z-function z-erlang">reverse</span></span></span></span><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-punctuation z-section z-arguments z-begin z-erlang">(</span><span class="z-variable z-other z-erlang">List</span><span class="z-punctuation z-section z-arguments z-end z-erlang">)</span></span><span class="z-punctuation z-separator z-arguments z-erlang">,</span> <span class="z-variable z-other z-erlang">Pred</span><span class="z-punctuation z-separator z-arguments z-erlang">,</span> <span class="z-meta z-sequence z-list z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">[</span><span class="z-punctuation z-section z-sequence z-end z-erlang">]</span></span><span class="z-punctuation z-section z-arguments z-end z-erlang">)</span></span><span class="z-punctuation z-terminator z-clause z-erlang">.</span></span> </span><span class="z-source z-erlang"> </span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-entity z-name z-function z-erlang">filter_tco</span></span></span><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-function z-parameters z-erlang"><span class="z-meta z-sequence z-list z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">[</span><span class="z-punctuation z-section z-sequence z-end z-erlang">]</span></span><span class="z-punctuation z-separator z-parameters z-erlang">,</span> <span class="z-variable z-language z-anonymous z-erlang">_</span><span class="z-punctuation z-separator z-parameters z-erlang">,</span> <span class="z-variable z-parameter z-erlang">Acc</span><span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-function z-name z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-variable z-other z-erlang">Acc</span><span class="z-punctuation z-separator z-clauses z-erlang">;</span></span> </span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-entity z-name z-function z-erlang">filter_tco</span></span></span><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-function z-parameters z-erlang"><span class="z-meta z-sequence z-list z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">[</span><span class="z-variable z-parameter z-erlang">Head</span><span class="z-punctuation z-separator z-sequence z-erlang">|</span><span class="z-variable z-parameter z-erlang">Tail</span><span class="z-punctuation z-section z-sequence z-end z-erlang">]</span></span><span class="z-punctuation z-separator z-parameters z-erlang">,</span> <span class="z-variable z-parameter z-erlang">Pred</span><span class="z-punctuation z-separator z-parameters z-erlang">,</span> <span class="z-variable z-parameter z-erlang">Acc</span><span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-function z-name z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> </span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"> <span class="z-meta z-case z-erlang"><span class="z-keyword z-control z-conditional z-case z-erlang">case</span> <span class="z-meta z-function-call z-name z-erlang"><span class="z-variable z-other z-erlang">Pred</span></span><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-punctuation z-section z-arguments z-begin z-erlang">(</span><span class="z-variable z-other z-erlang">Head</span><span class="z-punctuation z-section z-arguments z-end z-erlang">)</span></span> <span class="z-keyword z-control z-flow z-erlang">of</span> </span></span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-case z-erlang"> <span class="z-constant z-language z-boolean z-erlang">true</span> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-meta z-function-call z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-variable z-function z-erlang">filter_tco</span></span></span><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-punctuation z-section z-arguments z-begin z-erlang">(</span><span class="z-variable z-other z-erlang">Tail</span><span class="z-punctuation z-separator z-arguments z-erlang">,</span> <span class="z-variable z-other z-erlang">Pred</span><span class="z-punctuation z-separator z-arguments z-erlang">,</span> <span class="z-meta z-sequence z-list z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">[</span><span class="z-variable z-other z-erlang">Head</span><span class="z-punctuation z-separator z-sequence z-erlang">|</span><span class="z-variable z-other z-erlang">Acc</span><span class="z-punctuation z-section z-sequence z-end z-erlang">]</span></span><span class="z-punctuation z-section z-arguments z-end z-erlang">)</span></span><span class="z-punctuation z-separator z-clauses z-erlang">;</span> </span></span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-case z-erlang"> <span class="z-constant z-language z-boolean z-erlang">false</span> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-meta z-function-call z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-variable z-function z-erlang">filter_tco</span></span></span><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-punctuation z-section z-arguments z-begin z-erlang">(</span><span class="z-variable z-other z-erlang">Tail</span><span class="z-punctuation z-separator z-arguments z-erlang">,</span> <span class="z-variable z-other z-erlang">Pred</span><span class="z-punctuation z-separator z-arguments z-erlang">,</span> <span class="z-variable z-other z-erlang">Acc</span><span class="z-punctuation z-section z-arguments z-end z-erlang">)</span></span> </span></span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-case z-erlang"> <span class="z-keyword z-control z-conditional z-end z-erlang">end</span></span><span class="z-punctuation z-terminator z-clause z-erlang">.</span></span> </span></code></pre> <h4 id="fold">Fold<a class="zola-anchor" href="#fold" aria-label="Anchor link for: fold" style="visibility: hidden;"></a> </h4> <p>Notice that fold is already tail recursive! The last call in <code>fold</code> is of a call to <code>fold</code>, so it already enjoys tail call optimization. We can rename it to <code>fold_tco</code>, to match our other functions, but the syntax doesn't change at all.</p> <pre data-lang="erlang" class="language-erlang z-code"><code class="language-erlang" data-lang="erlang"><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-entity z-name z-function z-erlang">fold_tco</span></span></span><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-function z-parameters z-erlang"><span class="z-meta z-sequence z-list z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">[</span><span class="z-punctuation z-section z-sequence z-end z-erlang">]</span></span><span class="z-punctuation z-separator z-parameters z-erlang">,</span> <span class="z-variable z-language z-anonymous z-erlang">_</span><span class="z-punctuation z-separator z-parameters z-erlang">,</span> <span class="z-variable z-parameter z-erlang">Accumulated</span><span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-function z-name z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-variable z-other z-erlang">Accumulated</span><span class="z-punctuation z-separator z-clauses z-erlang">;</span></span> </span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-entity z-name z-function z-erlang">fold_tco</span></span></span><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-function z-parameters z-erlang"><span class="z-meta z-sequence z-list z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">[</span><span class="z-variable z-parameter z-erlang">Head</span><span class="z-punctuation z-separator z-sequence z-erlang">|</span><span class="z-variable z-parameter z-erlang">Tail</span><span class="z-punctuation z-section z-sequence z-end z-erlang">]</span></span><span class="z-punctuation z-separator z-parameters z-erlang">,</span> <span class="z-variable z-parameter z-erlang">Fun</span><span class="z-punctuation z-separator z-parameters z-erlang">,</span> <span class="z-variable z-parameter z-erlang">Accumulated</span><span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-function z-name z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-meta z-function-call z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-variable z-function z-erlang">fold_tco</span></span></span><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-punctuation z-section z-arguments z-begin z-erlang">(</span><span class="z-variable z-other z-erlang">Tail</span><span class="z-punctuation z-separator z-arguments z-erlang">,</span> <span class="z-variable z-other z-erlang">Fun</span><span class="z-punctuation z-separator z-arguments z-erlang">,</span> <span class="z-meta z-function-call z-name z-erlang"><span class="z-variable z-other z-erlang">Fun</span></span><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-punctuation z-section z-arguments z-begin z-erlang">(</span><span class="z-variable z-other z-erlang">Head</span><span class="z-punctuation z-separator z-arguments z-erlang">,</span> <span class="z-variable z-other z-erlang">Accumulated</span><span class="z-punctuation z-section z-arguments z-end z-erlang">)</span></span><span class="z-punctuation z-section z-arguments z-end z-erlang">)</span></span><span class="z-punctuation z-terminator z-clause z-erlang">.</span></span> </span></code></pre> <h1 id="wait-don-t-these-all-look-similar">Wait - don't these all look similar?<a class="zola-anchor" href="#wait-don-t-these-all-look-similar" aria-label="Anchor link for: wait-don-t-these-all-look-similar" style="visibility: hidden;"></a> </h1> <p>Notice that all of these tail-recursive functions follow the same form:</p> <ol> <li>They are a function of the form <code>function_name(List, Function, Accumulator)</code></li> <li>In the recursive calls they make to themselves, they set the accumulator by composing the function, the head of the list, and the accumulator.</li> </ol> <p>The last bit is important to see how we can refactor further.</p> <ul> <li>In tail-recursive map: <code>map_tco(Tail, Fun, [Fun(Head)|Acc])</code> uses the expression <code>[Fun(Head)|Acc]</code></li> <li>In tail-recursive filter: <code>filter_tco(Tail ,Pred, [Head|Acc])</code> uses the expression <code>[Head|Acc]</code> (and just <code>Acc</code> in the other tree case)</li> <li>In fold: <code>fold_tco(Fun, Tail, Fun(Head, Accumulated))</code> uses the expression <code>Fun(Head, Accumulated)</code></li> </ul> <p>Recall that <code>fold</code> as we originally wrote it was already tail-recursive. And in fact, if we look at the pattern we've identified, we can see that <code>fold</code> is in fact <em>more abstract</em> than <code>map</code> and <code>filter</code>. In other words, <code>map</code> and <code>filter</code> can be written to use <code>fold</code>! Let's try:</p> <p>First <code>map</code>. Notice that we must reverse the list up front so that elements get ordered correctly after the fold. This can be done as a post-processing operation as well.</p> <pre data-lang="erlang" class="language-erlang z-code"><code class="language-erlang" data-lang="erlang"><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-entity z-name z-function z-erlang">map</span></span></span><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-function z-parameters z-erlang"><span class="z-variable z-parameter z-erlang">List</span><span class="z-punctuation z-separator z-parameters z-erlang">,</span> <span class="z-variable z-parameter z-erlang">Fun</span><span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-function z-name z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> </span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"> <span class="z-meta z-function-call z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-variable z-function z-erlang">fold</span></span></span><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-punctuation z-section z-arguments z-begin z-erlang">(</span><span class="z-meta z-path z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-variable z-namespace z-erlang">lists</span></span><span class="z-punctuation z-accessor z-double-colon z-erlang">:</span><span class="z-meta z-path z-erlang"></span></span><span class="z-meta z-path z-erlang"><span class="z-meta z-function-call z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-variable z-function z-erlang">reverse</span></span></span></span><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-punctuation z-section z-arguments z-begin z-erlang">(</span><span class="z-variable z-other z-erlang">List</span><span class="z-punctuation z-section z-arguments z-end z-erlang">)</span></span><span class="z-punctuation z-separator z-arguments z-erlang">,</span> <span class="z-meta z-fun z-erlang"><span class="z-keyword z-declaration z-function z-erlang">fun</span></span><span class="z-meta z-fun z-erlang"><span class="z-meta z-fun z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-fun z-parameters z-erlang"><span class="z-variable z-parameter z-erlang">Head</span><span class="z-punctuation z-separator z-parameters z-erlang">,</span> <span class="z-variable z-parameter z-erlang">Acc</span><span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-fun z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-meta z-sequence z-list z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">[</span><span class="z-meta z-function-call z-name z-erlang"><span class="z-variable z-other z-erlang">Fun</span></span><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-punctuation z-section z-arguments z-begin z-erlang">(</span><span class="z-variable z-other z-erlang">Head</span><span class="z-punctuation z-section z-arguments z-end z-erlang">)</span></span> <span class="z-punctuation z-separator z-sequence z-erlang">|</span> <span class="z-variable z-other z-erlang">Acc</span><span class="z-punctuation z-section z-sequence z-end z-erlang">]</span></span> <span class="z-keyword z-declaration z-end z-erlang">end</span></span><span class="z-punctuation z-separator z-arguments z-erlang">,</span> <span class="z-meta z-sequence z-list z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">[</span><span class="z-punctuation z-section z-sequence z-end z-erlang">]</span></span><span class="z-punctuation z-section z-arguments z-end z-erlang">)</span></span><span class="z-punctuation z-terminator z-clause z-erlang">.</span></span> </span></code></pre> <p><code>filter</code> can be written this way too:</p> <pre data-lang="erlang" class="language-erlang z-code"><code class="language-erlang" data-lang="erlang"><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-entity z-name z-function z-erlang">filter</span></span></span><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-function z-parameters z-erlang"><span class="z-variable z-parameter z-erlang">List</span><span class="z-punctuation z-separator z-parameters z-erlang">,</span> <span class="z-variable z-parameter z-erlang">Fun</span><span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-function z-name z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> </span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"> <span class="z-meta z-function-call z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-variable z-function z-erlang">fold</span></span></span><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-punctuation z-section z-arguments z-begin z-erlang">(</span><span class="z-meta z-path z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-variable z-namespace z-erlang">lists</span></span><span class="z-punctuation z-accessor z-double-colon z-erlang">:</span><span class="z-meta z-path z-erlang"></span></span><span class="z-meta z-path z-erlang"><span class="z-meta z-function-call z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-variable z-function z-erlang">reverse</span></span></span></span><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-punctuation z-section z-arguments z-begin z-erlang">(</span><span class="z-variable z-other z-erlang">List</span><span class="z-punctuation z-section z-arguments z-end z-erlang">)</span></span><span class="z-punctuation z-separator z-arguments z-erlang">,</span> </span></span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function-call z-arguments z-erlang"> <span class="z-meta z-fun z-erlang"><span class="z-keyword z-declaration z-function z-erlang">fun</span></span><span class="z-meta z-fun z-erlang"><span class="z-meta z-fun z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-fun z-parameters z-erlang"><span class="z-variable z-parameter z-erlang">Head</span><span class="z-punctuation z-separator z-parameters z-erlang">,</span> <span class="z-variable z-parameter z-erlang">Acc</span><span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-fun z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> </span></span></span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-meta z-fun z-erlang"> <span class="z-meta z-case z-erlang"><span class="z-keyword z-control z-conditional z-case z-erlang">case</span> <span class="z-meta z-function-call z-name z-erlang"><span class="z-variable z-other z-erlang">Fun</span></span><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-punctuation z-section z-arguments z-begin z-erlang">(</span><span class="z-variable z-other z-erlang">Head</span><span class="z-punctuation z-section z-arguments z-end z-erlang">)</span></span> <span class="z-keyword z-control z-flow z-erlang">of</span> </span></span></span></span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-meta z-fun z-erlang"><span class="z-meta z-case z-erlang"> <span class="z-constant z-language z-boolean z-erlang">true</span> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-meta z-sequence z-list z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">[</span><span class="z-variable z-other z-erlang">Head</span> <span class="z-punctuation z-separator z-sequence z-erlang">|</span> <span class="z-variable z-other z-erlang">Acc</span><span class="z-punctuation z-section z-sequence z-end z-erlang">]</span></span><span class="z-punctuation z-separator z-clauses z-erlang">;</span> </span></span></span></span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-meta z-fun z-erlang"><span class="z-meta z-case z-erlang"> <span class="z-variable z-language z-anonymous z-erlang">_</span> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-variable z-other z-erlang">Acc</span> </span></span></span></span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-meta z-fun z-erlang"><span class="z-meta z-case z-erlang"> <span class="z-keyword z-control z-conditional z-end z-erlang">end</span></span> </span></span></span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-meta z-fun z-erlang"> <span class="z-keyword z-declaration z-end z-erlang">end</span></span><span class="z-punctuation z-separator z-arguments z-erlang">,</span> </span></span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function-call z-arguments z-erlang"> <span class="z-meta z-sequence z-list z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">[</span><span class="z-punctuation z-section z-sequence z-end z-erlang">]</span></span><span class="z-punctuation z-section z-arguments z-end z-erlang">)</span></span><span class="z-punctuation z-terminator z-clause z-erlang">.</span></span> </span></code></pre> <h4 id="folds-and-for-loops">Folds and <code>for</code> loops<a class="zola-anchor" href="#folds-and-for-loops" aria-label="Anchor link for: folds-and-for-loops" style="visibility: hidden;"></a> </h4> <p><code>map</code> and <code>filter</code> can be written in terms of <code>fold</code> because, conceptually, <code>fold</code> is doing the same work as a <code>for</code> loop: we start with a list, we have a "current" element in the list (we refer to it as <code>Head</code> since we are pattern matching against the front of the list), and we operate on we've collected so far from our previous steps through the loop, in composition with the current element. We can write a sort of <code>fold</code> as a for loop using the same variable names in <code>java</code> to demonstrate:</p> <pre data-lang="java" class="language-java z-code"><code class="language-java" data-lang="java"><span class="z-source z-java"><span class="z-meta z-class z-java"><span class="z-storage z-modifier z-java">public</span> <span class="z-meta z-class z-identifier z-java"><span class="z-storage z-type z-java">interface</span> <span class="z-entity z-name z-class z-java">Accumulator</span></span><span class="z-meta z-generic z-declaration z-java"><span class="z-punctuation z-definition z-generic z-begin z-java">&lt;</span><span class="z-variable z-parameter z-type z-java">T</span><span class="z-punctuation z-separator z-comma z-java">,</span> <span class="z-variable z-parameter z-type z-java">E</span><span class="z-punctuation z-definition z-generic z-end z-java">&gt;</span></span> <span class="z-meta z-class z-body z-java"><span class="z-meta z-block z-java"><span class="z-punctuation z-section z-block z-begin z-java">{</span> </span></span></span></span><span class="z-source z-java"><span class="z-meta z-class z-java"><span class="z-meta z-class z-body z-java"><span class="z-meta z-block z-java"> <span class="z-support z-class z-java">E</span> <span class="z-meta z-method z-java"><span class="z-meta z-method z-identifier z-java"><span class="z-entity z-name z-function z-java">accumulate</span></span><span class="z-meta z-method z-parameters z-java"><span class="z-meta z-parens z-java"><span class="z-punctuation z-section z-parens z-begin z-java">(</span><span class="z-support z-class z-java">T</span> <span class="z-variable z-parameter z-java">first</span><span class="z-punctuation z-separator z-comma z-java">,</span> <span class="z-support z-class z-java">E</span> <span class="z-variable z-parameter z-java">second</span><span class="z-punctuation z-section z-parens z-end z-java">)</span></span></span></span><span class="z-punctuation z-terminator z-java">;</span> </span></span></span></span><span class="z-source z-java"><span class="z-meta z-class z-java"><span class="z-meta z-class z-body z-java"><span class="z-meta z-block z-java"><span class="z-punctuation z-section z-block z-end z-java">}</span></span></span></span> </span><span class="z-source z-java"> </span><span class="z-source z-java"><span class="z-storage z-modifier z-java">public</span> <span class="z-storage z-modifier z-java">static</span> <span class="z-keyword z-operator z-comparison z-java">&lt;</span><span class="z-support z-class z-java">T</span><span class="z-punctuation z-separator z-comma z-java">,</span><span class="z-support z-class z-java">E</span><span class="z-keyword z-operator z-comparison z-java">&gt;</span> <span class="z-support z-class z-java">E</span> <span class="z-meta z-function-call z-java"><span class="z-variable z-function z-java">fold</span><span class="z-punctuation z-section z-parens z-begin z-java">(</span><span class="z-support z-class z-java">List</span><span class="z-meta z-generic z-java"><span class="z-punctuation z-definition z-generic z-begin z-java">&lt;</span><span class="z-support z-class z-java">T</span><span class="z-punctuation z-definition z-generic z-end z-java">&gt;</span></span> list<span class="z-punctuation z-separator z-comma z-java">,</span> <span class="z-support z-class z-java">E</span> initialAccumulated<span class="z-punctuation z-separator z-comma z-java">,</span> <span class="z-support z-class z-java">Accumulator</span><span class="z-meta z-generic z-java"><span class="z-punctuation z-definition z-generic z-begin z-java">&lt;</span><span class="z-support z-class z-java">T</span><span class="z-punctuation z-separator z-comma z-java">,</span> <span class="z-support z-class z-java">E</span><span class="z-punctuation z-definition z-generic z-end z-java">&gt;</span></span> accumulator<span class="z-punctuation z-section z-parens z-end z-java">)</span></span> <span class="z-meta z-block z-java"><span class="z-punctuation z-section z-block z-begin z-java">{</span> </span></span><span class="z-source z-java"><span class="z-meta z-block z-java"> <span class="z-storage z-type z-var z-java">var</span> accumulated <span class="z-meta z-assignment z-rhs z-java"><span class="z-keyword z-operator z-assignment z-java">=</span> initialAccumulated</span><span class="z-punctuation z-terminator z-java">;</span> </span></span><span class="z-source z-java"><span class="z-meta z-block z-java"> </span></span><span class="z-source z-java"><span class="z-meta z-block z-java"> <span class="z-keyword z-control z-loop z-for z-java">for</span> <span class="z-meta z-parens z-java"><span class="z-punctuation z-section z-parens z-begin z-java">(</span><span class="z-support z-class z-java">T</span> head <span class="z-keyword z-operator z-ternary z-java">:</span> list<span class="z-punctuation z-section z-parens z-end z-java">)</span></span> <span class="z-meta z-block z-java"><span class="z-punctuation z-section z-block z-begin z-java">{</span> </span></span></span><span class="z-source z-java"><span class="z-meta z-block z-java"><span class="z-meta z-block z-java"> accumulated <span class="z-meta z-assignment z-rhs z-java"><span class="z-keyword z-operator z-assignment z-java">=</span> accumulator<span class="z-punctuation z-accessor z-dot z-java">.</span><span class="z-meta z-function-call z-java"><span class="z-variable z-function z-java">accumulate</span><span class="z-punctuation z-section z-parens z-begin z-java">(</span>head<span class="z-punctuation z-separator z-comma z-java">,</span> accumulated<span class="z-punctuation z-section z-parens z-end z-java">)</span></span></span><span class="z-punctuation z-terminator z-java">;</span> </span></span></span><span class="z-source z-java"><span class="z-meta z-block z-java"><span class="z-meta z-block z-java"> <span class="z-punctuation z-section z-block z-end z-java">}</span></span> </span></span><span class="z-source z-java"><span class="z-meta z-block z-java"> </span></span><span class="z-source z-java"><span class="z-meta z-block z-java"> <span class="z-keyword z-control z-flow z-return z-java">return</span> accumulated<span class="z-punctuation z-terminator z-java">;</span> </span></span><span class="z-source z-java"><span class="z-meta z-block z-java"><span class="z-punctuation z-section z-block z-end z-java">}</span></span> </span></code></pre> <p>By that same token, we can use the language of <code>fold</code> to define a <code>for</code> loop, but in Erlang!</p> <pre data-lang="erlang" class="language-erlang z-code"><code class="language-erlang" data-lang="erlang"><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-entity z-name z-function z-erlang">for</span></span></span><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-function z-parameters z-erlang"><span class="z-meta z-sequence z-list z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">[</span><span class="z-punctuation z-section z-sequence z-end z-erlang">]</span></span><span class="z-punctuation z-separator z-parameters z-erlang">,</span> <span class="z-variable z-language z-anonymous z-erlang">_</span><span class="z-punctuation z-separator z-parameters z-erlang">,</span> <span class="z-variable z-parameter z-erlang">ReturnValue</span><span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-function z-name z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-variable z-other z-erlang">ReturnValue</span><span class="z-punctuation z-separator z-clauses z-erlang">;</span></span> </span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-entity z-name z-function z-erlang">for</span></span></span><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-function z-parameters z-erlang"><span class="z-meta z-sequence z-list z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">[</span><span class="z-variable z-parameter z-erlang">Head</span><span class="z-punctuation z-separator z-sequence z-erlang">|</span><span class="z-variable z-parameter z-erlang">Tail</span><span class="z-punctuation z-section z-sequence z-end z-erlang">]</span></span><span class="z-punctuation z-separator z-parameters z-erlang">,</span> <span class="z-variable z-parameter z-erlang">Fun</span><span class="z-punctuation z-separator z-parameters z-erlang">,</span> <span class="z-variable z-parameter z-erlang">AccumulatedValue</span><span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-function z-name z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-meta z-function-call z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-variable z-function z-erlang">for</span></span></span><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-punctuation z-section z-arguments z-begin z-erlang">(</span><span class="z-variable z-other z-erlang">Tail</span><span class="z-punctuation z-separator z-arguments z-erlang">,</span> <span class="z-variable z-other z-erlang">Fun</span><span class="z-punctuation z-separator z-arguments z-erlang">,</span> <span class="z-meta z-function-call z-name z-erlang"><span class="z-variable z-other z-erlang">Fun</span></span><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-punctuation z-section z-arguments z-begin z-erlang">(</span><span class="z-variable z-other z-erlang">Head</span><span class="z-punctuation z-separator z-arguments z-erlang">,</span> <span class="z-variable z-other z-erlang">AccumulatedValue</span><span class="z-punctuation z-section z-arguments z-end z-erlang">)</span></span><span class="z-punctuation z-section z-arguments z-end z-erlang">)</span></span><span class="z-punctuation z-terminator z-clause z-erlang">.</span></span> </span></code></pre> <p>Because all of our use-cases are variants on a <code>for</code> loop in a procedural context, they can all be similarly solved with <code>fold</code>.</p> <h4 id="add-one">Add One<a class="zola-anchor" href="#add-one" aria-label="Anchor link for: add-one" style="visibility: hidden;"></a> </h4> <pre data-lang="erlang" class="language-erlang z-code"><code class="language-erlang" data-lang="erlang"><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-entity z-name z-function z-erlang">add_one</span></span></span><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-function z-parameters z-erlang"><span class="z-variable z-parameter z-erlang">List</span><span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-function z-name z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-meta z-function-call z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-variable z-function z-erlang">fold</span></span></span><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-punctuation z-section z-arguments z-begin z-erlang">(</span><span class="z-meta z-path z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-variable z-namespace z-erlang">lists</span></span><span class="z-punctuation z-accessor z-double-colon z-erlang">:</span><span class="z-meta z-path z-erlang"></span></span><span class="z-meta z-path z-erlang"><span class="z-meta z-function-call z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-variable z-function z-erlang">reverse</span></span></span></span><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-punctuation z-section z-arguments z-begin z-erlang">(</span><span class="z-variable z-other z-erlang">List</span><span class="z-punctuation z-section z-arguments z-end z-erlang">)</span></span><span class="z-punctuation z-separator z-arguments z-erlang">,</span> <span class="z-meta z-fun z-erlang"><span class="z-keyword z-declaration z-function z-erlang">fun</span></span><span class="z-meta z-fun z-erlang"><span class="z-meta z-fun z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-fun z-parameters z-erlang"><span class="z-variable z-parameter z-erlang">X</span><span class="z-punctuation z-separator z-parameters z-erlang">,</span> <span class="z-variable z-parameter z-erlang">Ls</span><span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-fun z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-meta z-sequence z-list z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">[</span><span class="z-variable z-other z-erlang">X</span> <span class="z-keyword z-operator z-arithmetic z-erlang">+</span> <span class="z-constant z-numeric z-integer z-decimal z-erlang">1</span><span class="z-punctuation z-separator z-sequence z-erlang">|</span><span class="z-variable z-other z-erlang">Ls</span><span class="z-punctuation z-section z-sequence z-end z-erlang">]</span></span> <span class="z-keyword z-declaration z-end z-erlang">end</span></span><span class="z-punctuation z-separator z-arguments z-erlang">,</span> <span class="z-meta z-sequence z-list z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">[</span><span class="z-punctuation z-section z-sequence z-end z-erlang">]</span></span><span class="z-punctuation z-section z-arguments z-end z-erlang">)</span></span><span class="z-punctuation z-terminator z-clause z-erlang">.</span></span> </span><span class="z-source z-erlang"> </span><span class="z-source z-erlang"><span class="z-comment z-line z-percentage z-erlang"><span class="z-punctuation z-definition z-comment z-percentage z-erlang">%</span> Or, if you&#39;d rather append the value (less efficient in erlang, but readable), you can avoid the list reverse: </span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-entity z-name z-function z-erlang">add_one</span></span></span><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-function z-parameters z-erlang"><span class="z-variable z-parameter z-erlang">List</span><span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-function z-name z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-meta z-function-call z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-variable z-function z-erlang">fold</span></span></span><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-punctuation z-section z-arguments z-begin z-erlang">(</span><span class="z-variable z-other z-erlang">List</span><span class="z-punctuation z-separator z-arguments z-erlang">,</span> <span class="z-meta z-fun z-erlang"><span class="z-keyword z-declaration z-function z-erlang">fun</span></span><span class="z-meta z-fun z-erlang"><span class="z-meta z-fun z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-fun z-parameters z-erlang"><span class="z-variable z-parameter z-erlang">X</span><span class="z-punctuation z-separator z-parameters z-erlang">,</span> <span class="z-variable z-parameter z-erlang">Ls</span><span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-fun z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-variable z-other z-erlang">Ls</span> <span class="z-keyword z-operator z-lists z-erlang">++</span> <span class="z-meta z-sequence z-list z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">[</span><span class="z-variable z-other z-erlang">X</span> <span class="z-keyword z-operator z-arithmetic z-erlang">+</span> <span class="z-constant z-numeric z-integer z-decimal z-erlang">1</span><span class="z-punctuation z-section z-sequence z-end z-erlang">]</span></span> <span class="z-keyword z-declaration z-end z-erlang">end</span></span><span class="z-punctuation z-separator z-arguments z-erlang">,</span> <span class="z-meta z-sequence z-list z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">[</span><span class="z-punctuation z-section z-sequence z-end z-erlang">]</span></span><span class="z-punctuation z-section z-arguments z-end z-erlang">)</span></span><span class="z-punctuation z-terminator z-clause z-erlang">.</span></span> </span></code></pre> <h4 id="get-evens">Get Evens<a class="zola-anchor" href="#get-evens" aria-label="Anchor link for: get-evens" style="visibility: hidden;"></a> </h4> <pre data-lang="erlang" class="language-erlang z-code"><code class="language-erlang" data-lang="erlang"><span class="z-source z-erlang"><span class="z-comment z-line z-percentage z-erlang"><span class="z-punctuation z-definition z-comment z-percentage z-erlang">%</span> again, swap append for reverse if you&#39;d prefer here </span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-entity z-name z-function z-erlang">get_evens</span></span></span><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-function z-parameters z-erlang"><span class="z-variable z-parameter z-erlang">List</span><span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-function z-name z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> </span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"> <span class="z-meta z-function-call z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-variable z-function z-erlang">fold</span></span></span><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-punctuation z-section z-arguments z-begin z-erlang">(</span> </span></span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function-call z-arguments z-erlang"> <span class="z-meta z-path z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-variable z-namespace z-erlang">lists</span></span><span class="z-punctuation z-accessor z-double-colon z-erlang">:</span><span class="z-meta z-path z-erlang"></span></span><span class="z-meta z-path z-erlang"><span class="z-meta z-function-call z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-variable z-function z-erlang">reverse</span></span></span></span><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-punctuation z-section z-arguments z-begin z-erlang">(</span><span class="z-variable z-other z-erlang">List</span><span class="z-punctuation z-section z-arguments z-end z-erlang">)</span></span><span class="z-punctuation z-separator z-arguments z-erlang">,</span> </span></span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function-call z-arguments z-erlang"> <span class="z-meta z-fun z-erlang"><span class="z-keyword z-declaration z-function z-erlang">fun</span></span><span class="z-meta z-fun z-erlang"><span class="z-meta z-fun z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-fun z-parameters z-erlang"><span class="z-variable z-parameter z-erlang">X</span><span class="z-punctuation z-separator z-parameters z-erlang">,</span> <span class="z-variable z-parameter z-erlang">Ls</span><span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-fun z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-meta z-if z-erlang"><span class="z-keyword z-control z-conditional z-if z-erlang">if</span> <span class="z-variable z-other z-erlang">X</span> <span class="z-keyword z-operator z-arithmetic z-erlang">rem</span> <span class="z-constant z-numeric z-integer z-decimal z-erlang">2</span> <span class="z-keyword z-operator z-logical z-erlang">=:=</span> <span class="z-constant z-numeric z-integer z-decimal z-erlang">0</span> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-meta z-sequence z-list z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">[</span><span class="z-variable z-other z-erlang">X</span><span class="z-punctuation z-separator z-sequence z-erlang">|</span><span class="z-variable z-other z-erlang">Ls</span><span class="z-punctuation z-section z-sequence z-end z-erlang">]</span></span><span class="z-punctuation z-separator z-clauses z-erlang">;</span> <span class="z-constant z-language z-boolean z-erlang">true</span> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-variable z-other z-erlang">Ls</span> <span class="z-keyword z-control z-conditional z-end z-erlang">end</span></span> <span class="z-keyword z-declaration z-end z-erlang">end</span></span><span class="z-punctuation z-separator z-arguments z-erlang">,</span> </span></span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function-call z-arguments z-erlang"> <span class="z-meta z-sequence z-list z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">[</span><span class="z-punctuation z-section z-sequence z-end z-erlang">]</span></span><span class="z-punctuation z-section z-arguments z-end z-erlang">)</span></span><span class="z-punctuation z-terminator z-clause z-erlang">.</span></span> </span></code></pre> <p>With this longer syntax, it even starts to look a little bit like a <code>for</code> loop - just replace the word <code>fold</code> with <code>for</code>.</p> <h4 id="sum">Sum<a class="zola-anchor" href="#sum" aria-label="Anchor link for: sum" style="visibility: hidden;"></a> </h4> <p>Since we're returning a single value in this case, we can avoid calling <code>lists:reverse</code>.</p> <pre data-lang="erlang" class="language-erlang z-code"><code class="language-erlang" data-lang="erlang"><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-entity z-name z-function z-erlang">sum_values</span></span></span><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-function z-parameters z-erlang"><span class="z-variable z-parameter z-erlang">List</span><span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-function z-name z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-meta z-function-call z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-variable z-function z-erlang">fold</span></span></span><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-punctuation z-section z-arguments z-begin z-erlang">(</span><span class="z-variable z-other z-erlang">List</span><span class="z-punctuation z-separator z-arguments z-erlang">,</span> <span class="z-meta z-fun z-erlang"><span class="z-keyword z-declaration z-function z-erlang">fun</span></span><span class="z-meta z-fun z-erlang"><span class="z-meta z-fun z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-fun z-parameters z-erlang"><span class="z-variable z-parameter z-erlang">X</span><span class="z-punctuation z-separator z-parameters z-erlang">,</span> <span class="z-variable z-parameter z-erlang">SumSoFar</span><span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-fun z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-variable z-other z-erlang">X</span> <span class="z-keyword z-operator z-arithmetic z-erlang">+</span> <span class="z-variable z-other z-erlang">SumSoFar</span> <span class="z-keyword z-declaration z-end z-erlang">end</span></span><span class="z-punctuation z-separator z-arguments z-erlang">,</span><span class="z-constant z-numeric z-integer z-decimal z-erlang">0</span><span class="z-punctuation z-section z-arguments z-end z-erlang">)</span></span><span class="z-punctuation z-terminator z-clause z-erlang">.</span></span> </span></code></pre> <h4 id="some-other-use-cases">Some other use-cases<a class="zola-anchor" href="#some-other-use-cases" aria-label="Anchor link for: some-other-use-cases" style="visibility: hidden;"></a> </h4> <ol> <li> <p>Find element in a list</p> <pre data-lang="erlang" class="language-erlang z-code"><code class="language-erlang" data-lang="erlang"><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-entity z-name z-function z-erlang">find_value</span></span></span><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-function z-parameters z-erlang"><span class="z-variable z-parameter z-erlang">List</span><span class="z-punctuation z-separator z-parameters z-erlang">,</span> <span class="z-variable z-parameter z-erlang">Value</span><span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-function z-name z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-meta z-function-call z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-variable z-function z-erlang">fold</span></span></span><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-punctuation z-section z-arguments z-begin z-erlang">(</span> </span></span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function-call z-arguments z-erlang"> <span class="z-variable z-other z-erlang">List</span><span class="z-punctuation z-separator z-arguments z-erlang">,</span> </span></span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function-call z-arguments z-erlang"> <span class="z-meta z-fun z-erlang"><span class="z-keyword z-declaration z-function z-erlang">fun</span></span><span class="z-meta z-fun z-erlang"><span class="z-meta z-fun z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-fun z-parameters z-erlang"><span class="z-variable z-parameter z-erlang">X</span><span class="z-punctuation z-separator z-parameters z-erlang">,</span> <span class="z-variable z-parameter z-erlang">Else</span><span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-fun z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> </span></span></span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-meta z-fun z-erlang"> <span class="z-meta z-if z-erlang"><span class="z-keyword z-control z-conditional z-if z-erlang">if</span> <span class="z-variable z-other z-erlang">X</span> <span class="z-keyword z-operator z-logical z-erlang">==</span> <span class="z-variable z-other z-erlang">Value</span> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-variable z-other z-erlang">Value</span><span class="z-punctuation z-separator z-clauses z-erlang">;</span> </span></span></span></span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-meta z-fun z-erlang"><span class="z-meta z-if z-erlang"> <span class="z-constant z-language z-boolean z-erlang">true</span> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-variable z-other z-erlang">Else</span> </span></span></span></span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-meta z-fun z-erlang"><span class="z-meta z-if z-erlang"> <span class="z-keyword z-control z-conditional z-end z-erlang">end</span></span> </span></span></span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-meta z-fun z-erlang"> <span class="z-keyword z-declaration z-end z-erlang">end</span></span><span class="z-punctuation z-separator z-arguments z-erlang">,</span> </span></span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function-call z-arguments z-erlang"> <span class="z-meta z-atom z-erlang"><span class="z-constant z-other z-symbol z-erlang">notfound</span></span> </span></span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-punctuation z-section z-arguments z-end z-erlang">)</span></span><span class="z-punctuation z-terminator z-clause z-erlang">.</span></span> </span></code></pre> </li> <li> <p>Index of an element in a list</p> <p>In cases like this, the accumulator doesn't really need to contain much information about the list at all. In this case, it's just a) the index to check next, and b) whether the element has been found.</p> <pre data-lang="erlang" class="language-erlang z-code"><code class="language-erlang" data-lang="erlang"><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-entity z-name z-function z-erlang">index_of</span></span></span><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-function z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-function z-parameters z-erlang"><span class="z-variable z-parameter z-erlang">List</span><span class="z-punctuation z-separator z-parameters z-erlang">,</span> <span class="z-variable z-parameter z-erlang">Value</span><span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-function z-name z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> </span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"> <span class="z-meta z-case z-erlang"><span class="z-keyword z-control z-conditional z-case z-erlang">case</span> <span class="z-meta z-function-call z-name z-erlang"><span class="z-meta z-atom z-erlang"><span class="z-variable z-function z-erlang">fold</span></span></span><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-punctuation z-section z-arguments z-begin z-erlang">(</span> </span></span></span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-case z-erlang"><span class="z-meta z-function-call z-arguments z-erlang"> <span class="z-variable z-other z-erlang">List</span><span class="z-punctuation z-separator z-arguments z-erlang">,</span> </span></span></span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-case z-erlang"><span class="z-meta z-function-call z-arguments z-erlang"> <span class="z-meta z-fun z-erlang"><span class="z-keyword z-declaration z-function z-erlang">fun</span></span><span class="z-meta z-fun z-erlang"><span class="z-meta z-fun z-parameters z-erlang"><span class="z-punctuation z-section z-parameters z-begin z-erlang">(</span></span></span><span class="z-meta z-fun z-parameters z-erlang"><span class="z-variable z-parameter z-erlang">CurrentValue</span><span class="z-punctuation z-separator z-parameters z-erlang">,</span> <span class="z-meta z-sequence z-tuple z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">{</span><span class="z-variable z-parameter z-erlang">FoundIndex</span><span class="z-punctuation z-separator z-sequence z-erlang">,</span> <span class="z-variable z-parameter z-erlang">IsFound</span><span class="z-punctuation z-section z-sequence z-end z-erlang">}</span></span><span class="z-punctuation z-section z-parameters z-end z-erlang">)</span></span><span class="z-meta z-fun z-erlang"> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> </span></span></span></span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-case z-erlang"><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-meta z-fun z-erlang"> <span class="z-meta z-if z-erlang"><span class="z-keyword z-control z-conditional z-if z-erlang">if</span> <span class="z-variable z-other z-erlang">IsFound</span> <span class="z-keyword z-operator z-logical z-erlang">==</span> <span class="z-meta z-atom z-erlang"><span class="z-constant z-other z-symbol z-erlang">found</span></span> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-meta z-sequence z-tuple z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">{</span><span class="z-variable z-other z-erlang">FoundIndex</span><span class="z-punctuation z-separator z-sequence z-erlang">,</span> <span class="z-meta z-atom z-erlang"><span class="z-constant z-other z-symbol z-erlang">found</span></span><span class="z-punctuation z-section z-sequence z-end z-erlang">}</span></span><span class="z-punctuation z-separator z-clauses z-erlang">;</span> </span></span></span></span></span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-case z-erlang"><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-meta z-fun z-erlang"><span class="z-meta z-if z-erlang"> <span class="z-variable z-other z-erlang">CurrentValue</span> <span class="z-keyword z-operator z-logical z-erlang">==</span> <span class="z-variable z-other z-erlang">Value</span> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-meta z-sequence z-tuple z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">{</span><span class="z-variable z-other z-erlang">FoundIndex</span><span class="z-keyword z-operator z-arithmetic z-erlang">+</span><span class="z-constant z-numeric z-integer z-decimal z-erlang">1</span><span class="z-punctuation z-separator z-sequence z-erlang">,</span> <span class="z-meta z-atom z-erlang"><span class="z-constant z-other z-symbol z-erlang">found</span></span><span class="z-punctuation z-section z-sequence z-end z-erlang">}</span></span><span class="z-punctuation z-separator z-clauses z-erlang">;</span> </span></span></span></span></span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-case z-erlang"><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-meta z-fun z-erlang"><span class="z-meta z-if z-erlang"> <span class="z-constant z-language z-boolean z-erlang">true</span> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-meta z-sequence z-tuple z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">{</span><span class="z-variable z-other z-erlang">FoundIndex</span><span class="z-keyword z-operator z-arithmetic z-erlang">+</span><span class="z-constant z-numeric z-integer z-decimal z-erlang">1</span><span class="z-punctuation z-separator z-sequence z-erlang">,</span> <span class="z-meta z-atom z-erlang"><span class="z-constant z-other z-symbol z-erlang">notfound</span></span><span class="z-punctuation z-section z-sequence z-end z-erlang">}</span></span> </span></span></span></span></span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-case z-erlang"><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-meta z-fun z-erlang"><span class="z-meta z-if z-erlang"> <span class="z-keyword z-control z-conditional z-end z-erlang">end</span></span> </span></span></span></span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-case z-erlang"><span class="z-meta z-function-call z-arguments z-erlang"><span class="z-meta z-fun z-erlang"> <span class="z-keyword z-declaration z-end z-erlang">end</span></span><span class="z-punctuation z-separator z-arguments z-erlang">,</span> </span></span></span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-case z-erlang"><span class="z-meta z-function-call z-arguments z-erlang"> <span class="z-meta z-sequence z-tuple z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">{</span><span class="z-keyword z-operator z-arithmetic z-erlang">-</span><span class="z-constant z-numeric z-integer z-decimal z-erlang">1</span><span class="z-punctuation z-separator z-sequence z-erlang">,</span> <span class="z-meta z-atom z-erlang"><span class="z-constant z-other z-symbol z-erlang">notfound</span></span><span class="z-punctuation z-section z-sequence z-end z-erlang">}</span></span> </span></span></span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-case z-erlang"><span class="z-meta z-function-call z-arguments z-erlang"> <span class="z-punctuation z-section z-arguments z-end z-erlang">)</span></span> <span class="z-keyword z-control z-flow z-erlang">of</span> </span></span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-case z-erlang"> <span class="z-meta z-sequence z-tuple z-erlang"><span class="z-punctuation z-section z-sequence z-begin z-erlang">{</span><span class="z-variable z-other z-erlang">Index</span><span class="z-punctuation z-separator z-sequence z-erlang">,</span> <span class="z-meta z-atom z-erlang"><span class="z-constant z-other z-symbol z-erlang">found</span></span><span class="z-punctuation z-section z-sequence z-end z-erlang">}</span></span> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-variable z-other z-erlang">Index</span><span class="z-punctuation z-separator z-clauses z-erlang">;</span> </span></span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-case z-erlang"> <span class="z-variable z-language z-anonymous z-erlang">_</span> <span class="z-punctuation z-separator z-clause-head-body z-erlang">-&gt;</span> <span class="z-meta z-atom z-erlang"><span class="z-constant z-other z-symbol z-erlang">notfound</span></span> </span></span></span><span class="z-source z-erlang"><span class="z-meta z-function z-name z-erlang"><span class="z-meta z-case z-erlang"> <span class="z-keyword z-control z-conditional z-end z-erlang">end</span></span><span class="z-punctuation z-terminator z-clause z-erlang">.</span></span> </span></code></pre> </li> </ol> <h1 id="wrapping-up">Wrapping up<a class="zola-anchor" href="#wrapping-up" aria-label="Anchor link for: wrapping-up" style="visibility: hidden;"></a> </h1> <p>Whether in a functional or a procedural paradigm, programmers frequently need to operate on lists of objects. It turns out, whether you're using an iterative loop (procedural paradigm) or a tail-recursive function (functional paradigm), you conceptually have to do the same work: "seek" through the list, and operate on the current element in composition with however you've accumlated values in the previous iterations (starting, of course, with a seed element). Whether you call it a <code>for</code> loop or a <code>fold</code>, it's a remarkably similar operation.</p>