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Linear-Time Triangulation of Simple Polygons (Chazelle's Algorithm) in Lean 4

Robert D. Barish

Palomar Registrypalomar/PALOMAR-2026-10-05-000003Oct 5, 2026cs.CGscore 0

A formalization and provably correct implementation of a linear-time algorithm for triangulating a simple polygon. The implementation is a concrete program for an explicit exact real RAM. Lean proves that on every simple polygon with n vertices the program halts within C(n+1) steps, with natural-number words at most K(n+1), and outputs a conforming triangulation with exactly n - 2 triangles on the input vertices. No general-position assumption is made. The proofs use exactly Lean's three standard axioms (propext, Classical.choice, Quot.sound), with no sorry and no native_decide. They are…

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