Algebraic Tiny Compiler

[u/jonas1ara]

https://github.com/jonas1ara/ATC

Algebraic Tiny Compiler in F#

A from‑scratch compiler that uses algebra as the lens to understand how real compilers work — no abstractions for the sake of abstractions, no academic overhead, just a clean, inspectable pipeline built in F#.

By treating expressions as algebraic structures, the project walks through every stage of a compiler with concrete, mathematical transformations:
- Tokenizer → turns raw text into meaningful tokens
- Parser → recursive‑descent parsing with operator precedence
- AST → algebraic expression trees representing structure and intent
- Polynomial Expansion → distributive expansion and normalization
- Term Combination → merging like terms into canonical form
- Equation Solving → linear and quadratic solvers using discriminants
- Code Generation → assembly‑style output to show how machines evaluate expressions
- Execution Modes → JIT on .NET or AoT with NativeAOT for ultra‑fast startup

A practical, algebra‑driven walkthrough of how compilers read, understand, transform, and execute code.

Blog posts:

• Understanding Compilers Through an Algebraic Expression Compiler
• Building a Better Algebraic Compiler - Advanced Techniques
• F# Weekly #19, 2026 – Understanding Compilers Through an Algebraic Expression Compiler