Improvements for Concurrent Haskell with Futures

We propose a model for measuring the runtime of concurrent programs by the minimal number of evaluation steps. The focus of this paper are improvements, which are program transformations that improve this number in every context, where we distinguish between sequential and parallel improvements, for one or more processors, respectively. We apply the methods to CHF, a model of Concurrent Haskell extended by futures. The language CHF is a typed higher-order functional language with concurrent threads, monadic IO and MVars as synchronizing variables. We show that all deterministic reduction rules and 15 further program transformations are sequential and parallel improvements. We also show that introduction of deterministic parallelism is a parallel improvement, and its inverse a sequential improvement, provided it is applicable. This is a step towards more automated precomputation of concurrent programs during compile time, which is also formally proven to be correctly optimizing