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We introduce ArcPro, a novel learning framework built on architectural programs to recover structured 3D abstractions from highly sparse and low-quality point clouds. Specifically, we design a domain-specific language (DSL) to hierarchically represent building structures as a program, which can be efficiently converted into a mesh. We bridge feedforward and inverse procedural modeling by using a feedforward process for training data synthesis, allowing the network to make reverse predictions. We train an encoder-decoder on the points-program pairs to establish a mapping from unstructured point clouds to architectural programs, where a 3D convolutional encoder extracts point cloud features and a transformer decoder autoregressively predicts the programs in a tokenized form. Inference by our method is highly efficient and produces plausible and faithful 3D abstractions. Comprehensive experiments demonstrate that ArcPro outperforms both traditional architectural proxy reconstruction and learning-based abstraction methods. We further explore its potential when working with multi-view image and natural language inputs.