We study the problem of parametric parallel complexity analysis of concurrent, message-passing programs. To make the analysis local and compositional, it is based on a conservative extension of binary session types, which structure the type and direction of communication between processes and stand in a Curry-Howard correspondence with intuitionistic linear logic. The main innovation is to enrich session types with the temporal modalities next (◯ A ), always (□ A ), and eventually (◇ A ), to additionally prescribe the timing of the exchanged messages in a way that is precise yet flexible. The resulting temporal session types uniformly express properties such as the message rate of a stream, the latency of a pipeline, the response time of a concurrent queue, or the span of a fork/join parallel program. The analysis is parametric in the cost model and the presentation focuses on communication cost as a concrete example. The soundness of the analysis is established by proofs of progress and type preservation using a timed multiset rewriting semantics. Representative examples illustrate the scope and usability of the approach.

@article{paperbot275,
  title = {Parallel complexity analysis with temporal session types},
  author = {Ankush Das and Jan Hoffmann and Frank Pfenning},
  journal = {Proceedings of the ACM on Programming Languages},
  volume = {2},
  number = {ICFP},
  year = {2018},
  doi = {10.1145/3236786}
}