Lean is a theorem prover and programming language that enables correct, maintainable, and formally verified code
/-- A prime is a number larger than 1 with no trivial divisors -/
def IsPrime (n : Nat) := 1 < n ∧ ∀ k, 1 < k → k < n → ¬ k ∣ n
-- 'Grind' efficiently manages complex pattern matching and
-- case analysis beyond standard tactics.
example (x : Nat) : 0 < match x with
| 0 => 1
| n+1 => x + n := by
grind
-- Automatically solves systems of linear inequalities.
example (x y : Int) :
27 ≤ 11*x + 13*y → 11*x + 13*y ≤ 45
→ -10 ≤ 7*x - 9*y → 7*x - 9*y > 4 := by
grind
Does anyone have experience with Lean? Can it be useful for implementing algorithms or logic beyond mathematical proofs, for software libs?
I haven’t tried Lean, but one of my university courses had us use Dafny, which essentially states the pre- and postcondition of a function. If it can’t prove the conditions are fulfilled, you get an error. This essentially turns all of your bugs (that is, unexpected behaviour) into specification problems. It can also prove that loops eventually end, and the data in a structure follows a specific pattern.