http://brightprogrammer.in/tags/free-variables/Recent content in Free-Variables on Siddharth MishraHugoenSun, 14 Jun 2026 21:53:10 -0700http://brightprogrammer.in/posts/3-lambda-calculus-free-and-bound-variables/Thu, 06 Feb 2025 00:00:00 +0000http://brightprogrammer.in/posts/3-lambda-calculus-free-and-bound-variables/<h1 id="free--bound-variables">Free &amp; Bound Variables</h1> <p>A variable occurrence is <strong>bound</strong> if it lies inside the scope of some $\lambda$ that binds it. Otherwise it&rsquo;s <strong>free</strong>. Free variables are just the &ldquo;inputs&rdquo; a term still depends on.</p> <div class="notice notice-info"> <p class="notice-title">Info</p> <div class="notice-body">When I say a variable is free/bound, I mean the <strong>occurrence</strong>. The same symbol can be both free and bound inside the same expression.</div> </div> <h2 id="definitions">Definitions</h2> <p>We can define the set of free variables $\text{FV}(M)$ and bound variables $\text{BV}(M)$ inductively:</p>