Delimited continuation
In programming languages, a delimited continuation, composable continuation or partial continuation, is a "slice" of a continuation frame that has been reified into a function. Unlike regular continuations, delimited continuations return a value, and thus may be reused and composed. Control delimiters, the basis of delimited continuations, were introduced by Matthias Felleisen in 1988[1] though early allusions to composable and delimited continuations can be found in Carolyn Talcott's Stanford 1984 dissertation, Felleisen et al.,[2] Felleisen's 1987 dissertation,[3] and algorithms for functional backtracking, e.g., for pattern matching, for parsing, in the Algebraic Logic Functional programming language, and in the functional implementations of Prolog where the failure continuation is often kept implicit and the reason of being for the success continuation is that it is composable.
History
Delimited continuations were first introduced by Felleisen in 1988[1] with an operator called [math]\displaystyle{ \mathcal{F} }[/math], first introduced in a tech report in 1987,[2] along with a prompt construct [math]\displaystyle{ \# }[/math]. The operator was designed to be a generalization of control operators that had been described in the literature such as call/cc
from Scheme, ISWIM's J operator, John C. Reynolds' escape
operator, and others. Subsequently, many competing delimited control operators were invented by the programming languages research community such as prompt
and control
,[4] shift
and reset
,[5][6]cupto
,[7] fcontrol
, and others.
Examples
Various operators for delimited continuations have been proposed in the research literature.[8]
One independent proposal[5] is based on continuation-passing style (CPS) -- i.e., not on continuation frames—and offers two control operators, shift
and reset
, that give rise to static rather than to dynamic delimited continuations.[9]
The reset
operator sets the limit for the continuation while the shift
operator captures or reifies the current continuation up to the innermost enclosing reset
. For example, consider the following snippet in Scheme:
(* 2 (reset (+ 1 (shift k (k 5)))))
The reset
delimits the continuation that shift
captures (named by k
in this example). When this snippet is executed, the use of shift
will bind k
to the continuation (+ 1 [])
where []
represents the part of the computation that is to be filled with a value. This continuation directly corresponds to the code that surrounds the shift
up to the reset
. Because the body of shift (i.e., (k 5)
) immediately invokes the continuation, this code is equivalent to the following:
(* 2 (+ 1 5))
In general, these operators can encode more interesting behavior by, for example, returning the captured continuation k
as a value or invoking k
multiple times. The shift
operator passes the captured continuation k
to the code in its body, which can either invoke it, produce it as a result, or ignore it entirely. Whatever result that shift
produces is provided to the innermost reset
, discarding the continuation in between the reset
and shift
. However, if the continuation is invoked, then it effectively re-installs the continuation after returning to the reset
. When the entire computation within reset
is completed, the result is returned by the delimited continuation.[10] For example, in this Scheme code:
(reset (* 2 (shift k CODE)))
whenever CODE
invokes (k N)
, (* 2 N)
is evaluated and returned.
This is equivalent to the following:
(let ((k (lambda (x) (* 2 x)))) CODE)
Furthermore, once the entire computation within shift
is completed, the continuation is discarded, and execution restarts outside reset
. Therefore,
(reset (* 2 (shift k (k (k 4)))))
invokes (k 4)
first (which returns 8), and then (k 8)
(which returns 16). At this point, the shift
expression has terminated, and the rest of the reset
expression is discarded. Therefore, the final result is 16.
Everything that happens outside the reset
expression is hidden, i.e. not influenced by the control transfer. For example, this returns 17:
(+ 1 (reset (* 2 (shift k (k (k 4))))))
Delimited continuations were first described independently by Felleisen et al.[2] and Johnson.[11] They have since been used in a large number of domains, particularly in defining new control operators; see Queinnec[12] for a survey.
Let's take a look at a more complicated example. Let null
be the empty list:
(reset (begin (shift k (cons 1 (k (void)))) ;; (1) null))
The context captured by shift
is (begin [*] null)
, where [*]
is the hole where k
's parameter will be injected. The first call of k
inside shift
evaluates to this context with (void)
= #<void>
replacing the hole, so the value of (k (void))
is (begin #<void> null)
= null
. The body of shift
, namely (cons 1 null)
= (1)
, becomes the overall value of the reset
expression as the final result.
Making this example more complicated, add a line:
(reset (begin (shift k (cons 1 (k (void)))) (shift k (cons 2 (k (void)))) null))
If we comment out the first shift
, we already know the result, it is (2)
; so we can as well rewrite the expression like this:
(reset (begin (shift k (cons 1 (k (void)))) (list 2)))
This is pretty familiar, and can be rewritten as (cons 1 (list 2))
, that is, (list 1 2)
.
We can define yield
using this trick:
(define (yield x) (shift k (cons x (k (void)))))
and use it in building lists:
(reset (begin (yield 1) (yield 2) (yield 3) null)) ;; (list 1 2 3)
If we replace cons
with stream-cons
, we can build lazy streams:
(define (stream-yield x) (shift k (stream-cons x (k (void))))) (define lazy-example (reset (begin (stream-yield 1) (stream-yield 2) (stream-yield 3) stream-null)))
We can generalize this and convert lists to stream, in one fell swoop:
(define (list->stream xs) (reset (begin (for-each stream-yield xs) stream-null)))
In a more complicated example below the continuation can be safely wrapped into a body of a lambda, and be used as such:
(define (for-each->stream-maker for-each) (lambda (collection) (reset (begin (for-each (lambda (element) (shift k (stream-cons element (k 'ignored)))) collection) stream-null))))
The part between reset
and shift
includes control functions like lambda
and for-each
; this is impossible to rephrase using lambdas[why?].
Delimited continuations are also useful in linguistics: see Continuations in linguistics for details.
References
- ↑ 1.0 1.1 Felleisen, Matthias (1988). "The theory and practice of first-class prompts". pp. 180–190. doi:10.1145/73560.73576. ISBN 0-89791-252-7.
- ↑ 2.0 2.1 2.2 Template:Cite tech report
- ↑ Felleisen, Matthias (1987). The Calculi of Lambda-v-CS Conversion: A Syntactic Theory of Control and State in Imperative Higher-Order Programming Languages (PDF) (Thesis).
- ↑ Sitaram, Dorai; Felleisen, Matthias (1990). "Control Delimiters and their Hierarchies". LISP and Symbolic Computation 3: 67–99. doi:10.1007/BF01806126. http://www.ccs.neu.edu/racket/pubs/lasc1990-sf.pdf.
- ↑ 5.0 5.1 Danvy, Olivier; Filinski, Andrzej (1990). "Abstracting Control". pp. 151–160. doi:10.1145/91556.91622. ISBN 0-89791-368-X.
- ↑ Danvy, Olivier (2006). An Analytical Approach to Programs as Data Objects (Thesis). doi:10.7146/aul.214.152.
- ↑ Rémy, Didier; Gunter, Carl; Riecke, Jon G. (1995). "A generalization of exceptions and control in ML-like languages".
- ↑ See for instance the operators offered by the
racket/control
Racket library [1]; the following examples can run in Racket using(require racket/control)
- ↑ Biernacki, Dariusz; Danvy, Olivier; Shan, Chung-chieh (2006). "On the Static and Dynamic Extents of Delimited Continuations". Science of Computer Programming 60 (3): 274–297. https://tidsskrift.dk/brics/article/download/21903/19329/.
- ↑ Gasbichler, Martin; Sperber, Michael (2002).
- ↑ Johnson, Gregory F. (June 1987). "GL: a denotational testbed with continuations and partial continuations". pp. 218–225.
- ↑ Queinnec, Christian (April 1994). "A library of high-level control operators". Lisp Pointers, ACM SIGPLAN Special Interest Publ. On Lisp (École Polytechnique and INRIA-Rocquencourt) 6: 11–26.
External links
- Composable continuations tutorial at SchemeWiki
- Delimited continuations in operating systems, by Oleg Kiselyov and Chung-chieh Shan
- Native delimited continuations in (byte-code and native-code) OCaml
- Shift/reset для самых маленьких (in Russian)
- Some nice papers on delimited continuations and first-class macros
Original source: https://en.wikipedia.org/wiki/Delimited continuation.
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