"Why not just use Lean?"
7 hours ago
- #proof assistants
- #formal mathematics
- #history of formalization
- Lean is a modern formal proof assistant with strong tools and community, but the history of formalizing mathematics began much earlier with AUTOMATH in 1968.
- Key systems before Lean include AUTOMATH, LCF, HOL, Isabelle, and Coq, each contributing to formalization with different approaches like proof automation and hardware verification.
- Lean's popularity surged in mathematics due to efforts to formalize advanced concepts like Grothendieck schemes, and it moved away from the constructive proof focus seen in Coq.
- Isabelle offers advantages such as powerful automation (e.g., sledgehammer), readability, and absence of dependent types, which can simplify type checking and avoid universe level issues.
- The 'propositions as types' approach is not universal; systems like LCF use abstract data types for proof checking without massive proof objects, emphasizing efficiency and legibility.
- AI integration is enhancing proof assistants by generating and tidying proofs, and enabling translation between systems, reducing dependency on a single tool choice.