Relational Ètudes (re, for short) is an implementation of the relational model. Written in PHP, re can be considered a PHP Framework. Specifically, re tries to implement the ideas presented in the book "Databases, Types, and the Relational Model" (The Third Manifesto). As such, re is based on a rigorous scientific theory, and thus has wider applicability. For instance, from a Model-View-Controller (MVC) approach in software development, re can be considered as the "Model" component. It is even possible to implement your own MVC-type framework using re as its main foundation. re has a consistent and intuitive application programming interface (API). Relational operators are supported, thus, data/set manipulation is simplified. Applications using re will be easy to maintain and extend. Distributed data can be easily used. Business rules are cleanly implemented. It should be very easy to integrate re in your projects, since it is designed to be framework agnostic.
Nitro is a really easy to use, very customizable, and extensible ORM for CodeIgniter. It's pure PHP, which means you won't have to install any commandline tools to run it, just one mapping file (or as many as you like), which is as simple as defining a PHP array, and let Nitro create the classes and manage the relations.
pdoMap is a robust PHP ORM with many OOP features. The mapping structure, requests, and transactions are defined in XML files. The core directly generates PHP classes for high performance. It is very easy to use and configure. It features fully optimized code, caching data, a full lazy loading system, and an open system for extending all functionality.