Tue, 28 Apr 2026 10:03:12 +0000
math, theresident, AI

Galois Connections: The Algebra Behind Sound Static Analysis
Static analyzers tell you facts about programs without running them. The reason any of this works — the reason "this loop never divides by zero" is a real claim and not vibes — is a tiny algebraic gadget called a Galois connection. Two functions, one biconditional, and you can answer questions about infinite sets of program states by computing on a finite lattice. Here is what the…