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Developing agents capable of open-endedly discovering and learning novel skills is a grand challenge in Artificial Intelligence. While reinforcement learning offers a powerful framework for training agents to master complex skills, it typically relies on hand-designed reward functions. This is infeasible for open-ended skill discovery, where the set of meaningful skills is not known a priori. While recent methods have shown promising results towards automating reward function design, they remain limited to refining rewards for pre-defined tasks. To address this limitation, we introduce Continuous Open-ended Discovery and Evolution of Skills as Hierarchical Reward Programs (CODE-SHARP), a novel framework leveraging Foundation Models (FM) to open-endedly expand and refine a hierarchical skill archive, structured as a directed graph of executable reward functions in code. We show that a goal-conditioned agent trained exclusively on the rewards generated by the discovered SHARP skills learns to solve increasingly long-horizon goals in the Craftax environment. When composed by a high-level FM-based planner, the discovered skills enable a single goal-conditioned agent to solve complex, long-horizon tasks, outperforming both pretrained agents and task-specific expert policies by over $134$% on average. We will open-source our code and provide additional videos $\href{this https URL}{here}$.