Witnessing side effects

We present a new approach to the old problem of adding global mutable state to purely functional languages. Our idea is to extend the language with "witnesses," which is based on an arguably more pragmatic motivation than past approaches. We give a semantic condition for correctness and prove it is sufficient. We also give a somewhat surprising static checking algorithm that makes use of a network flow property equivalent to the semantic condition via reduction to a satisfaction problem for a system of linear inequalities.