Call-with-current-continuation


In computer programming with the language Scheme, the subroutine or function call-with-current-continuation, abbreviated call/cc, is used as a control flow operator. It has been adopted by several other programming languages.
Taking a function f as its only argument, within an expression is applied to the current continuation of the expression.
For example is equivalent to applying f to the current continuation of the expression. The current continuation is given by replacing by a variable c bound by a lambda abstraction, so the current continuation is ). Applying the function f to it gives the final result )).
As a complementary example, in an expression , the continuation for the sub-expression is ), so the whole expression is equivalent to )).
In other words it takes a "snapshot" of the current control context or control state of the program as an object and applies f to it.
The continuation object is a first-class value and is represented as a function, with function application as its only operation. When a continuation object is applied to an argument, the existing continuation is eliminated and the applied continuation is restored in its place, so that the program flow will continue at the point at which the continuation was captured and the argument of the continuation then becomes the "return value" of the call/cc invocation. Continuations created with call/cc may be called more than once, and even from outside the dynamic extent of the call/cc application.
In computer science, making this type of implicit program state visible as an object is termed reification.
With call/cc a variety of complex control operators can be implemented from other languages via a few lines of code, e.g., McCarthy's amb operator for nondeterministic choice, Prolog-style backtracking, Simula 67-style coroutines and generalizations thereof, Icon-style generators, or engines and threads or even the obscure COMEFROM.

Examples

As shown by the next example, call/cc can be used to emulate the function of the return statement known from C-style languages, which is missing from Scheme:


3)
) ; displays 3
; displays 2

Calling f with a regular function argument first applies this function to the value 2, then returns 3. However, when f is passed to call/cc, applying the parameter to 2 forces execution of the program to jump to the point where call/cc was called, and causes call/cc to return the value 2. This is then printed by the display function.
In the next example, call/cc is used twice: once to generate a "return" continuation as in the first example and once to suspend an iteration through a list of items:

;; ->
;; Both internal functions are closures over lst
;; Internal variable/Function which passes the current element in a list
;; to its return argument, or passes an end-of-list marker
;; if no more elements are left. On each step the function name is
;; rebound to a continuation which points back into the function body,
;; while return is rebound to whatever continuation the caller specifies.



;; Grab the current continuation

)))) ;; evaluates to next return
lst)
)

;;
;; This is the actual generator, producing one item from a-list at a time.

)
;; Return the generator
generator)
;; 0
;; 1
;; 2
;; you-fell-off-the-end

Every time the loop is about to process another item from the list, the function grabs the current continuation, and assigns it to the variable 'control-state'. This variable initially is the closure that iterates through all elements of the list. As the computation progresses, it becomes a closure that iterates through a suffix of the given list. While the use of "call/cc" is unnecessary for a linear collection, such as , the code generalizes to any collection that can be traversed.
Call-with-current-continuation can also express other sophisticated primitives. For example, the next sample performs cooperative multitasking using continuations:

;; Cooperative multitasking using call-with-current-continuation
;; in 25 lines of scheme
;; The list of threads waiting to run. This is a list of one
;; argument non-returning functions
;; A continuation is a non-returning function, just like,
;; in that it never gives up control to whatever called it.
)
;; A non-returning function. If there is any other thread
;; waiting to be run, it causes the next thread to run if there
;; is any left to run, otherwise it calls the original exit
;; which exits the whole environment.
)
;; The overriding function.



;; Since the ready-list is only non-returning
;; functions, this will not return.
)
;; Nothing left to run.
;; The original is a non returning function,
;; so this is a non-returning function.
))))
;; Takes a one argument function with a given
;; argument and forks it off. The forked function's new
;; thread will exit if/when the function ever exits.


)))))
;; Gives up control for the next thread waiting to be run.
;; Although it will eventually return, it gives up control
;; and will only regain it when the continuation is called.

;; Stick it on the ready list

;; Get the next thread, and start it running.


;; Run it.
))))

In 1999, David Madore found a 12 characters term in callcc-enabled Unlambda that have the same effect of an over 600 characters term in Unlambda without call/cc. When converting this term into Scheme he obtained a scheme program that known as the yin-yang puzzle. It was then being customary to show while discussing call/cc:

))
)))
)

An illustration of the puzzle: Every statements between brackets are the states of yin and yang immediately before ; The number means whether the 1st continuation or the 2nd to jump. The statement after the number represents the context.

;@*
;@*
;*
;@*
;*
;*
;@*
;...
;...

Criticism

Oleg Kiselyov, author of a delimited continuation implementation for OCaml, and designer of an application programming interface for delimited stack manipulation to implement control operators, advocates the use of delimited continuations instead of the full-stack continuations that call/cc manipulates: "Offering call/cc as a core control feature in terms of which all other control facilities should be implemented turns out a bad idea. Performance, memory and resource leaks, ease of implementation, ease of use, ease of reasoning all argue against call/cc."

Relation to non-constructive logic

The Curry–Howard correspondence between proofs and programs relates call/cc to Peirce's law, which extends intuitionistic logic to non-constructive, classical logic: → α. Here, is the type of the function f, which can either return a value of type α directly or apply an argument to the continuation of type. Since the existing context is deleted when the continuation is applied, the type β is never used and may be taken to be ⊥, the empty type.
The principle of double negation elimination → α is comparable to a variant of call-cc which expects its argument f to always evaluate the current continuation without normally returning a value.
Embeddings of classical logic into intuitionistic logic are related to continuation passing style translation.

Languages implementing call/cc