mimium (https://mimium.org) is a functional programming language designed for audio processing with syntax similar to Rust. It runs on both native and web platforms, and allows oscillators and signal processing to be defined from a very low level. It also features a proprietary live coding capability based on differential analysis of source code, enabling hot-swapping of signal processing code without resetting the internal state of the audio. This presentation will explain the details of its design and implementation.