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<h1>Function Composition</h1> +<h2>What is the <code>via</code> Operator?</h2> +<p>The <code>via</code> operator is a function composition operator that combines functions from right to left.</p> +<pre class="prettyprint source lang-plaintext"><code>/* f via g = compose(f, g) */ +/* f via g via h = compose(f, compose(g, h)) */ +</code></pre> +<p>The <code>via</code> operator is right-associative and matches mathematical notation where <code>(f ∘ g ∘ h)(x) = f(g(h(x)))</code>.</p> +<pre class="prettyprint source lang-plaintext"><code>/* Define simple functions */ +double : x -> x * 2; +increment : x -> x + 1; +square : x -> x * x; + +/* Using via composition */ +result1 : double via increment 5; +/* Result: 12 (5+1=6, 6*2=12) */ + +/* Chained via composition */ +result2 : double via increment via square 3; +/* Result: 20 (3^2=9, 9+1=10, 10*2=20) */ +</code></pre> +<p>The key insight is that <code>via</code> groups from right to left.</p> +<pre class="prettyprint source lang-plaintext"><code>/* This expression: */ +double via increment via square 3 + +/* Groups as: */ +double via (increment via square) 3 + +/* Which translates to: */ +compose(double, compose(increment, square))(3) + +/* With the execution order of: */ +/* 1. square(3) = 9 */ +/* 2. increment(9) = 10 */ +/* 3. double(10) = 20 */ +</code></pre> +<h2>Precedence rules and <code>via</code></h2> +<p>The <code>via</code> operator has higher precedence than function application:</p> +<pre class="prettyprint source lang-plaintext"><code>/* via binds tighter than juxtaposition */ +double via increment 5 + +/* This is parsed as: */ +(double via increment) 5 +</code></pre> +<h2>More examples</h2> +<pre class="prettyprint source lang-plaintext"><code>/* Data processing pipeline */ +data : {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}; +is_even : x -> x % 2 = 0; +double : x -> x * 2; +sum : x -> reduce add 0 x; + +/* Pipeline using via */ +process_pipeline : sum via map double via filter is_even; +result : process_pipeline data; +/* Reads: sum via (map double via filter is_even) */ +/* Result: 60 */ +</code></pre> +<p>You'll note that we don't need to use <code>@</code> here -- <code>via</code> is kinda special-cased because it is an ergonomic feature. It can work with function names directly because it's specifically for function composition. Higher-order functions like <code>map</code>, <code>filter</code>, and <code>reduce</code> require explicit function references using <code>@</code> because they need a way to distinguish between calling a function immediately vs passing it as an argument while <code>via</code> only ever takes in functions.</p> +<p>A goal with the <code>via</code> operator is to align with mathematical function composition:</p> +<pre class="prettyprint source lang-plaintext"><code>/* Mathematical: (f ∘ g ∘ h)(x) = f(g(h(x))) */ +/* Baba Yaga: f via g via h x = f(g(h(x))) */ +</code></pre> +<h2>When to Use <code>via</code></h2> +<p><strong>Use <code>via</code> when you want:</strong></p> +<ul> +<li>Natural reading: <code>f via g via h</code> reads as "f then g then h"</li> +<li>Mathematical notation: Matches <code>(f ∘ g ∘ h)</code> notation</li> +<li>Concise syntax: Shorter than nested <code>compose</code> calls</li> +<li>Right-to-left flow: When you think of data flowing right to left</li> +</ul> +<p><strong>Don't use <code>via</code> when:</strong></p> +<ul> +<li>You need left-to-right composition (use <code>pipe</code>)</li> +<li>You want explicit mathematical style (use <code>compose</code>)</li> +<li>You're working with simple function calls (use juxtaposition)</li> +<li>If you don't wanna</li> +</ul> +<h2>Common Patterns</h2> +<pre class="prettyprint source lang-plaintext"><code>/* Data transformation pipeline */ +data : {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}; +is_even : x -> x % 2 = 0; +double : x -> x * 2; +sum : x -> reduce add 0 x; + +/* Pipeline: filter → map → reduce */ +process_pipeline : sum via map double via filter is_even; +result : process_pipeline data; +/* Result: 60 (filter evens: {2,4,6,8,10}, double: {4,8,12,16,20}, sum: 60) */ + +/* Validation chain */ +validate_positive : x -> x > 0; +validate_even : x -> x % 2 = 0; +validate_small : x -> x < 10; + +/* Chain validations */ +all_validations : validate_small via validate_even via validate_positive; +result : all_validations 6; /* 6 > 0, 6 % 2 = 0, 6 < 10 */ +/* Result: true */ +</code></pre> +<h2>Debugging <code>via</code> Chains</h2> +<p>To understand execution order, break down the chain:</p> +<pre class="prettyprint source lang-plaintext"><code>/* Complex chain: */ +result : square via double via increment via square 2; + +/* Break it down: */ +/* 1. square(2) = 4 */ +/* 2. increment(4) = 5 */ +/* 3. double(5) = 10 */ +/* 4. square(10) = 100 */ +/* Result: 100 */ +</code></pre> +</article> + +</section> + +</div> + +<br class="clear"> + +<footer> + Generated by <a href="https://github.com/jsdoc3/jsdoc">JSDoc 4.0.4</a> on Tue Jul 29 2025 23:15:00 GMT-0400 (Eastern Daylight Time) using the Minami theme. +</footer> + +<script>prettyPrint();</script> +<script src="scripts/linenumber.js"></script> +</body> +</html> \ No newline at end of file |