A Concurrent Lambda Calculus with Futures

We introduce a new concurrent lambda calculus with futures, λ(fut), to model the operational semantics of Alice, a concurrent extension of ML. λ(fut) is a minimalist extension of the call-by-value λ-calculus that yields the full expressiveness to define, combine, and implement a variety of standard concurrency constructs such as channels, semaphores, and ports. We present a linear type system for λ(fut) by which the safety of such definitions and their combinations can be proved: Well-typed implementations cannot be corrupted in any well-typed context.