Context-oriented programming (COP) is a new technique for programming that allows changing the context in which commands execute as a program executes. Compared to object-oriented programming (aspect-oriented programming), COP is more flexible (modular and structured). This paper presents a precise syntax-directed operational semantics for context-oriented programming with layers, as realized by COP languages like ContextJ* and ContextL. Our language model is built on Java enriched with layer concepts and activation and deactivation of layer scopes. The paper also presents a static type system that guarantees that typed programs do not get stuck. Using the means of the proposed semantics, the mathematical correctness of the type system is presented in the paper.