May-Happen-in-Parallel Analysis with Returned Futures

May-Happen-in-Parallel (MHP) is a fundamental analysis to reason about concurrent programs. It infers the pairs of program points that may execute in parallel, or interleave their execution. This information is essential to prove, among other things, absence of data races, deadlock freeness, termination, and resource usage. This paper presents an MHP analysis for asynchronous programs that use futures as synchronization mechanism. Future variables are available in most concurrent languages (e.g., in the library concurrent of Java, in the standard thread library of C++, and in Scala and Python). The novelty of our analysis is that it is able to infer MHP relations that involve future variables that are returned by asynchronous tasks. Futures are returned when a task needs to await for another task created in an inner scope, e.g., task t needs to await for the termination of task p that is spawned by task q that is spawned during the execution of t (not necessarily by t). Thus, task p is awaited by task t which is in an outer scope. The challenge for the analysis is to (back)propagate the synchronization of tasks through future variables from inner to outer scopes.