  We present the linear first-order intermediate language IL for verified
compilers. IL is a functional language with calls to a nondeterministic
environment. We give IL terms a second, imperative semantic interpretation and
obtain a register transfer language. For the imperative interpretation we
establish a notion of live variables. Based on live variables, we formulate a
decidable property called coherence ensuring that the functional and the
imperative interpretation of a term coincide. We formulate a register
assignment algorithm for IL and prove its correctness. The algorithm translates
a functional IL program into an equivalent imperative IL program. Correctness
follows from the fact that the algorithm reaches a coherent program after
consistently renaming local variables. We prove that the maximal number of live
variables in the initial program bounds the number of different variables in
the final coherent program. The entire development is formalized in Coq.
