Continuation

Continuation refers to the act or instance of continuing or resuming something after an interruption. In technical contexts, a continuation is an object or concept that encodes the remaining computation, narrative, or process to be performed from a given point. The term is used across mathematics, computer science, linguistics, and philosophy to describe how a sequence, extension, or state persists or proceeds.

In complex analysis, analytic continuation extends a function defined on a region to a larger region where the function remains analytic. Such extensions, when they exist, agree on overlaps and are unique on connected regions. Analytic continuation often encounters singularities that bound the domain but can lead to multivalued functions via monodromy.

In programming, a continuation is an abstract representation of the future steps of a computation. It captures the rest of the program after a given point and enables non-linear control flow, such as early exits, exceptions, or asynchronous execution. Continuations are central to continuation-passing style and to features like call-with-current-continuation in some languages.

In linguistics and formal semantics, continuations provide a way to model how the rest of a discourse or a sentence affects the meaning of a constituent. Continuation semantics uses the idea that expressions can carry a continuation representing how their content will be evaluated in broader contexts, aiding analyses of quantification, scope and focus.

Other uses include general discussions of temporal persistence and process continuity in philosophy, as well as narrative and media where a continuation signals a sequel or the ongoing development of a storyline. Across domains, the core notion is that a current state points toward or determines subsequent states.