In a previous blog post, we showed an implementation of a subset formal system of Peano’s axioms that could represent numbers and the addition operator. In a blog post before that, we showed and implemented a formal system that could represent numbers and the addition operator at a more basic level.

This blog post will show yet another way to represent numbers and arithmetic operations such as addition, subtraction, multiplication, and division. Finally, we’ll extend this system to also support complex arithmetic operations (combining the previous basic operations).

For last year’s AoC, I decided to use 20 different programming languages. For the year before that, I used Haskell. This year I decided to not participate as I’m already busy with other stuff, but I thought I could try something different.

So the first task of AoC day 1 is essentially giving you a list of lists, and you need to sum each element and find the max. Here’s a one-liner in Python:

max([ sum(x) for x in L ])

But I thought to myself, why write code in a “normal” programming language to solve an easy problem? Why not complicate things a little bit and write a code that generates mathematical proof in Budge-TP? In this post, we will write a Python script that will solve AoC 1-1 by generating Budge-TP code.