Lambda the Ultimate

Witnessing Side-Effects, Tachio Terauchi and Alex Aiken. ICFP 2005.

We present a new approach to the old problem of adding side effects 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 static checking algorithm that makes use of a network flow property equivalent to the semantic condition.

If I understand the idea in this paper correctly, you take a functional language with a possibly non-deterministic or parallel execution model, and then add references to it. To keep this from being impossible to reason about, you add dataflow tokens to each reference operation (assignment, allocation, reading) to ensure that they don't happen until each op's predecessors have happened -- and you make the tokens first class, so that the programmer can directly specify the amount of serial execution needed. Then you can do an analysis to ensure that the reduction is confluent, which means that you have no races.