The Purely Functional Linux Distribution – NixOS (by Dolstra, Eelco).

NixOS is a Linux distribution with a unique approach to package and configuration management. Built on top of the Nix package manager, it is completely declarative, makes upgrading systems reliable, and has many other advantages.

Research project

NixOS started as a research project (Dolstra, Eelco. "Integrating Software Construction and Software Deployment"), but it is a fully functional and usable operating system.

From its documentation:

NixOS is a GNU/Linux distribution that aims to improve the state of the art in system configuration management. In existing distributions, actions such as upgrades are dangerous: upgrading a package can cause other packages to break, upgrading an entire system is much less reliable than reinstalling from scratch, you can't safely test what the results of a configuration change will be, you cannot easily undo changes to the system, and so on. We want to change that. NixOS has many innovative features.