Typing Composable Coroutines

Coroutine, as a powerful programming construct, is widely used in asynchronous applications to replace thread-based programming or the callback hell. Using coroutines makes code more readable and maintainable, for its ability to transfer control while keeping the literal scope. However, reasoning about coroutine behavior can be challenging without proper typing. We propose a type notation and calculus for composing asymmetric, first-class, stackless coroutines. Given the types of a list of coroutines, we can compute a composed type matching the collective behavior of the coroutines, so that the input and output can be type-checked by a type system. Our coroutine types can model the data received by or yielded from a coroutine, which be of coroutine types as well. On top of our type calculus, we discuss its soundness and evaluation issues, then provide four application scenarios of our coroutine types. Not only can our types be used in modern programming languages, such as Python, but also model program behaviors in OCaml and even Prolog.