continuationstyle

Continuationstyle, sometimes written as continuation style, is a term used in programming to describe a style of constructing computations in which the future of the computation—the continuation—is made explicit. In this approach, functions do not return values in the usual sense. Instead, they take an extra argument, the continuation, which represents the rest of the computation and is invoked with the function’s result. This makes control flow a first-class entity that can be created, stored, passed around, and composed.

The concept is most closely associated with continuation-passing style (CPS). CPS is a formalization in which every function takes a continuation as an argument and ends by calling that continuation with the result. This contrasts with direct style, where functions return and the call stack determines the remaining steps. CPS enables precise modeling of control effects such as early exits, exceptions, non-local transfers of control, and advanced features like coroutines or backtracking. It also provides a foundation for certain compiler optimizations and transformations, since control flow becomes explicit and manipulable.

Example (very small): in direct style, a function f(x) might return x + 1. In CPS, f(x, k) would compute x + 1 and then call k(x + 1). Chaining multiple operations involves nesting continuations, so the thread of control is explicit in the code.

Applications and considerations: continuationstyle is a core technique in compiler design, program analysis, and language design. It supports modeling complex control structures, implementing features like non-blocking I/O and asynchronous programming, and enabling transformations such as defunctionalization. However, CPS-style code can become verbose and harder to read, so it is usually used as an intermediate representation within tools rather than as a hand-written programming style for everyday use.

Related concepts include continuation-passing style, call-with-current-continuation (call/cc), and defunctionalization.