Continuation passing style

From Academic Kids

Continuation passing style (CPS) is a term used within functional programming to describe a means of composing functions. Instead of "returning" values, functions written in CPS take an explicit "continuation" argument which receives the result of the computation performed within the function. Functions written in CPS return the value returned when the continuation argument is applied to this result.

Here is an example in Scheme:

Normal programming style
Continuation passing style
(define (mysqrt x) (sqrt x))
(display (mysqrt 4))
(define (mysqrt x k) (k (sqrt x)))
(mysqrt 4 display)
(+ (mysqrt 4) 2)
(mysqrt 4 (lambda (x k) (k (+ x 2))))

Continuation passing style can be used to implement continuations in a functional language that does not feature first class continuations but has first class functions.

As continuation passing style renders return values virtually useless, it can also be used to eliminate the need for a stack and return values entirely. Several interpreters for functional programming languages use this concept internally.

Outside of computer science, CPS is of more general interest as an alternative to the conventional method of composing simple expressions into complex expressions. For example, within linguistic semantics, Rober Barker has suggested that specifying the truth conditions of sentences using CPS might explain certain ambiguities found in natural language [1] (http://www.semanticsarchive.net/Archive/902ad5f7/barker.continuations.pdf).

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