continuations

Continuations are an abstraction used in computer science to represent the future of a computation from a given point. A continuation captures the control state and the remaining steps required to complete a computation, after a value is produced. In a programming language, a continuation can be thought of as a function that, given the result of the current computation, computes the final answer.

Continuations enable non-linear control flow and can be manipulated directly. A common approach is continuation-passing style (CPS), in which every function receives an extra argument, the continuation, and instead of returning a value, it applies the continuation to that value. CPS is used both as a compilation target and as a theoretical model of control flow.

A primary control operator is call-with-current-continuation (call/cc), which captures the current continuation as a first-class value. The captured continuation can be stored, invoked later, or discarded, enabling patterns such as early exits, backtracking, coroutines, generators, and lightweight threading. Delimited continuations, with operators such as shift and reset, capture only a portion of the continuation, allowing modular control effects.

Continuations have broad applications in programming language design and implementation. They underpin advanced control features, such as exceptions, backtracking, and asynchronous I/O, and are used to implement features in Scheme, Lisp, and other languages. In functional programming, the continuation monad provides a principled way to compose computations that depend on future results.

From a theoretical perspective, continuations are studied in the theory of programming languages and category theory, and they relate to concepts such as monads and algebraic effects. They provide a formal framework for modeling non-linear control and for transforming programs into explicit representations of control flow.