Object-oriented scripting languages like JavaScript and Python are popular partly because of their dynamic features. These include the runtime modification of objects and classes through addition of fields or updating of methods. These features make static typing difficult and so usually dynamic typing is used. Consequently, errors such as access to non-existent members are not detected until runtime. We first develop a formalism for an object based language, JS0, with features from JavaScript, including dynamic addition of fields and updating of methods. We give an operational semantics and static type system for JS0 using structural types. Our types allow objects to evolve in a controlled manner by classifying members as definite or potential. We define a type inference algorithm for JS0 that is sound with respect to the type system. If the type inference algorithm succeeds, then the program is typeable. Therefore, programmers can benefit from the safety offered by the type ...