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AI Engineering
Lobsters·Jun 30·5 min read
Proving the Fundamental Theorem of Arithmetic in Agda
TL;DR
A gap existed in providing a comprehensive, hands-on proof of the Fundamental Theorem of Arithmetic (FTA) using Agda, a dependently typed programming language. The author created a detailed, commentated proof from scratch, relying solely on personal experience and knowledge of Agda.
✦ Why It Matters
Engineers and researchers can use this proof as a learning tool for formal verification in dependently typed programming languages.
Key Takeaways
- Explore the Fundamental Theorem of Arithmetic in Agda for formal proof techniques.
- Utilize the provided proof as a learning resource for intermediate Agda users.
- Understand the relationship between programming and mathematical proofs through Agda.
- Apply insights from this proof to enhance skills in formal verification.
Full Summary
The Fundamental Theorem of Arithmetic states that every integer greater than 1 can be uniquely factored into prime numbers. While this theorem is included in the Agda standard library, the author sought to create a complete proof from scratch to aid students and others learning Agda.
The methodology involved using personal experience with Agda and informal knowledge of the theorem, without referencing existing materials. The resulting proof is extensive and serves as a practical example for intermediate learners.
By publishing this work, the author aims to bridge the gap between basic Agda knowledge and more complex formal proofs. This resource can help engineers and researchers understand the application of dependently typed programming in formal verification.