Real Fake DOMs: Verified Browser Rendering

In this writeup we present Real Fake DOMs, the first Coq development to our knowledge to model Document Object Models or the graphics primitives necessary to model browser rendering algorithms in a shallow embedding. As a first foray into verifying algorithms in this area, we model simplified DOMs with representative backgroundcolor, width, height, position, top, left, and overflow attributes. Additional features could in theory be implemented in terms of these, though it would be impractical to support a richer set of features in an exploratory development. Building on these models, we define and verify a series of renderers inspired by basic optimiations used in web browsers. We prove correctness by showing functional equivalence to an unoptimized reference renderer. Perhaps our biggest takeaway is a reminder that straightforward facts can require immense effort to prove if algorithms are not designed with verification in mind.