Compositional reasoning is critical for real-world problem solving: since training data is necessarily limited, models must generalize by composing learned skills in new ways. While post-training methods such as reinforcement learning (RL) have substantially improved the reasoning abilities of language models (LMs), their effects on compositional reasoning remain less well understood. We propose a dependency-graph framework to formalize compositional reasoning, yielding three levels of compositionality with increasing complexity. Empirically, we instantiate this framework with data-structure tasks, which provide deterministic reward computation and clear compositional structure. We find a consistent decomposed-to-composed asymmetry: decomposed-skill training does not reliably transfer to composed tasks, whereas composed-task training transfers more readily back to decomposed tasks. We provide theoretical explanation for this asymmetry, and further evaluate compositional generalization under length extrapolation, structural distribution shift, and transfer to tasks requiring unseen skills. Finally, we present a pilot study on real-world tool-calling benchmarks, showing preliminary evidence that the decomposed-to-composed asymmetry can extend to practical settings.

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