Human cognition has compositionality. We understand a scene by decomposing the scene into different concepts (e.g., shape and position of an object) and learning the respective laws of these concepts, which may be either natural (e.g., laws of motion) or man-made (e.g., laws of a game). The automatic parsing of these laws indicates the model's ability to understand the scene, which makes law parsing play a central role in many visual tasks. This paper proposes a deep latent variable model for Compositional LAw Parsing (CLAP), which achieves the human-like compositionality ability through an encoding-decoding architecture to represent concepts in the scene as latent variables. CLAP employs concept-specific latent random functions instantiated with Neural Processes to capture the law of concepts. Our experimental results demonstrate that CLAP outperforms the baseline methods in multiple visual tasks such as intuitive physics, abstract visual reasoning, and scene representation. The law manipulation experiments illustrate CLAP's interpretability by modifying specific latent random functions on samples. For example, CLAP learns the laws of position-changing and appearance constancy from the moving balls in a scene, making it possible to exchange laws between samples or compose existing laws into novel laws.