The programming techniques used so far in the course have, for the most part, been "purely functional". Some problems, however, are more naturally addressed by keeping track of the "state" of an internal machine. Typically this requires the use of mutable storage. SML supports mutable cells, or references, that store values of a fixed type. The value in a mutable cell can be initialized, read, and changed (mutated), and these operations result in effects that change the store. Programming with references is often carried out with the help of imperative techniques. Imperative functions are used primarily for the way they change storage, rather than for their return values. References allow us to create data structures that are ephemeral, i.e., that change over time. Their main advantage is the ability to maintain state as a shared resource among many routines. Another advantage in some cases is the ability to write code that is more time-efficient than purely functional code. On the other hand, they are conceptually complex and therefore error-prone: our routines may accidentally and irreversibly change the contents of a data structure; variables may be aliases for each other. As a result it is much more difficult to prove the correctness of code involving ephemeral data structures.