From 69a6187804aff44f48fe9047895e8c027ad5bf3f Mon Sep 17 00:00:00 2001
From: kitty piapiac <kcp@bsd.computer>
Date: Thu, 3 Oct 2024 06:13:41 +0100
Subject: init

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+---
+title: lambda calculus
+published: 2024-09-26T00:54:15+0100
+---
+
+:::::{.notice}
+**Lambda calculus** is a turing-complete system for expressing computations using only **[functions]** and **[application]**. Expressions can be one of a few elements:
+
+Syntax              Description   Example
+----------------    ------------  --------
+VAR                 Variable      `x`
+(λVAR.expr)         Function      `λx.x`
+(FUNCTION expr)     [Application] `(λx.x)a`
+
+Parentheses can be removed when it doesn't introduce ambiguity.
+:::::
+
+### Application
+Evaluation is done via substitution.
+
+When the expression `(λx.x)a` is evaluated, all occurences of **x** in the function's body are replaced with **a**. So, `(λx.x)a` evaluates to **a**.
+
+### Functions
+<details>
+<summary>The most basic function is the **identity function**, `λx.x`.</summary>
+<p>The function `λx.x` binds the variable "x" in the definition `λx` to the body `.x`. You can think of it like the function `f(x) = x`.</p>
+</details>
+
+
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