While existing automatic differentiation (AD) frameworks allow flexibly composing model architectures, they do not provide the same flexibility for composing learning algorithms---everything has to be implemented in terms of back propagation. To address this gap, we invent Automatic Propagation (AP) software, which generalizes AD, and allows custom and composable construction of complex learning algorithms. The framework allows packaging custom learning algorithms into propagators that automatically implement the necessary computations, and can be reused across different computation graphs. We implement Proppo, a prototype AP software package built on top of the Pytorch AD framework. To demonstrate the utility of Proppo, we use it to implement Monte Carlo gradient estimation techniques, such as reparameterization and likelihood ratio gradients, as well as the total propagation algorithm and Gaussian shaping gradients, which were previously used in model-based reinforcement learning, but do not have any publicly available implementation. Finally, in minimalistic experiments, we show that these methods allow increasing the gradient accuracy by orders of magnitude, particularly when the machine learning system is at the edge of chaos.