Lambda Calculus - Logic

Thu, 06 Feb 2025 00:00:00 +0000

Logic

If, Else

Let’s build some boolean login out of power of pure combinations. Unlike usual logic, we won’t get true/false as values. Here true and false are lambda abstractions itself.

$\text{True} \stackrel{\beta}{=} \lambda xy.x$ - Meaning, take two values, and evaluate to only the first one.
$\text{False}\stackrel{\beta}{=} \lambda xy.y$ - Take two, and evaluate to only the second one, discarding the first.

These are often called $\text{First}$ and $\text{Second}$ correspondingly for these reasons. So we can write $\text{First} \equiv \text{True}$ and $\text{Second} \equiv \text{False}$.

Logic on Siddharth Mishra

Lambda Calculus - Logic

Logic

If, Else