A run-time monitor is a program that runs in parallel with an untrusted application and examines actions from the application's instruction stream. If the sequence of program actions deviates from a specified security policy, the monitor transforms the sequence or terminates the program. We present the design and formal specification of a language for defining the policies enforced by program monitors. Our language provides a number of facilities for composing complex policies from simpler ones. We allow policies to be parameterized by values or other policies, and we define operators for forming the conjunction and disjunction of policies. Since the computations that implement these policies modify program behavior, naive composition of computations does not necessarily produce the conjunction (or disjunction) of the policies that the computations implement separately. We use a type and effect system to ensure that computations do not interfere with one another when they are composed.