A hyperfunction is a continuation-like construction that can be used to implement communication in the
context of concurrency. Though it has been reinvented many times, it remains somewhat obscure: since its
definition by Launchbury et al., hyperfunctions have been used to implement certain algebraic effect handlers,
coroutines, and breadth-first traversals; however, in each of these examples, the hyperfunction type went
unrecognised.
We identify the hyperfunctions hidden in all of these algorithms, and we exposit the common pattern
between them, building a framework for working with and reasoning about hyperfunctions. We use this
framework to solve a long-standing problem: giving a fully-abstract continuation-based semantics for a
concurrent calculus, the Calculus of Communicating Systems. Finally, we use hyperfunctions to build a
monadic Haskell library for efficient first-class coroutines.