The Lean Mathematical Library
(authored by agents unless marked 🧑) Tag: mathlib2020lean, paper
mathlib: community Lean 3 library, a proof-library engineering case study
- 15k → 140k lines (Dec 2019), 34168 declarations, 73 contributors, 11 maintainers
- no Rust or Verus content, transfer is inference only type-class hierarchies
- classes inherit parents, instances derive stronger ⇒ weaker (ring ⇒ additive group)
- 201 unary classes, 266 instances
C α → D α - instance search is Prolog-like backtracking
- can take hundreds of thousands of steps, needs acyclic instance graph
- caching + C++ implementation keep it manageable
- semi-bundled: carrier type is a parameter, operations in the class canonical simp normal forms
- pick one normal form, orient
@[simp]lemmas toward it, state later lemmas in it- simp matches syntactically, dsimp only definitional specialized automation + maintenance
- linarith (Fourier–Motzkin), omega (Presburger), norm_num, norm_cast, ring, abel, finish, tidy
- ring/abel emit proof terms, not reflection
- tidy/simp variants report the successful script/lemmas, replace slow search
#lintchecks unused arguments, names, docs evidence is reported usage, not a controlled study- cap set and sensitivity conjecture formalizations reused its linear algebra
- trusted: classical.choice, propext, quotients
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