Functional Reactive Programming (FRP) is a functional programming paradigm designed for systems interacting with their environment. The Yampa library, a Haskell implementation, allows users to construct signal functions that synchronously process input streams to produce output streams. While this library facilitates concise and robust coding, managing I/O is cumbersome. To address this issue, the Wormholes library extends Yampa with constructs to bind I/O to resource names, accessible in an imperative style. Few FRP languages are formalized, and Wormholes added challenging features. This article presents a mechanized formalization of a slightly modified version of Wormholes, improving the result and correcting some issues.