In mathematical logic and proof verification, two main approaches are Lean formalization and human-style proofs.
Here’s a brief overview:
What is Lean? Lean is an open-source theorem prover and programming language used to formalize mathematical proofs, ensuring they are precise and verifiable by a computer.
Process:
- Logical Foundations: Based on dependent type theory.
- Lean Language: Combines logical statements with functional programming constructs.
- Tactics: Tools to automate the proof process.
Advantages:
- Verification: Proofs are mechanically verified, eliminating logical errors.
- Reusability: Formalized proofs can be reused and built upon.
- Precision: Ensures precise and unambiguous proofs.
Example:
theorem add_comm (a b : nat) : a + b = b + a :=
begin
exact nat.add_comm a b,
end
Latex render may look like this: $ A := {(a,b) : ℕ | a+b = b+a}$
Formalization of Human Proofs: Human-style proofs can be formalized in Lean to ensure correctness. Explanations for Formal Proofs: Formal proofs can be accompanied by human-readable explanations for better understanding.
Your project includes directories for different types of files:
- input/ and output/: Directories for input and output files, including markdown files.
- lean/: Contains .lean files for Lean formalizations and .human files for human-readable proofs.
- website/: Hosts the static files for the web interface to display the proofs.
node index.js
OR
npm start