Reference immutability ensures that a reference is not used to modify the referenced object, and enables the safe sharing of object structures. A pure method does not cause side-effects on the objects that existed in the pre-state of the method execution. Checking and inference of reference immutability and method purity enables a variety of program analyses and optimizations.We present ReIm, a type system for reference immutability, and ReImInfer, a corresponding type inference analysis. The type system is concise and context-sensitive. The type inference analysis is precise and scalable, and requires no manual annotations. In addition, we present a novel application of the reference immutability type system: method purity inference.To support our theoretical results, we implemented the type system and the type inference analysis for Java. We include a type checker to verify the correctness of the inference result. Empirical results on Java applications and libraries of up to 348kLOC show that our approach achieves both scalability and precision.