In computer science, a continuation is an abstract representation of the control state of a computer program. A continuation implements (reifies) the program control state, i.e. the continuation is a data structure that represents the computational process at a given point in the process's execution; the created data structure can be accessed by the programming language, instead of being hidden in the runtime environment. Continuations are useful for encoding other control mechanisms in programming languages such as exceptions, generators, coroutines, and so on.
The "current continuation" or "continuation of the computation step" is the continuation that, from the perspective of running code, would be derived from the current point in a program's execution. The term continuations can also be used to refer to first-class continuations, which are constructs that give a programming language the ability to save the execution state at any point and return to that point at a later point in the program, possibly multiple times.
The earliest description of continuations was made by Adriaan van Wijngaarden in September 1964. Wijngaarden spoke at the IFIP Working Conference on Formal Language Description Languages held in Baden bei Wien, Austria. As part of a formulation for an Algol 60 preprocessor, he called for a transformation of proper procedures into continuation-passing style, though he did not use this name, and his intention was to simplify a program and thus make its result more clear.
Christopher Strachey, Christopher P. Wadsworth and John C. Reynolds brought the term continuation into prominence in their work in the field of denotational semantics that makes extensive use of continuations to allow sequential programs to be analysed in terms of functional programming semantics.
Reynolds (1993) gives a complete history of the discovery of continuations.
First-class continuations are a language's ability to completely control the execution order of instructions. They can be used to jump to a function that produced the call to the current function, or to a function that has previously exited. One can think of a first-class continuation as saving the execution state of the program. It is important to note that true first-class continuations do not save program data – unlike a process image – only the execution context. This is illustrated by the "continuation sandwich" description:
In this description, the sandwich is part of the program data (e.g., an object on the heap), and rather than calling a "make sandwich" routine and then returning, the person called a "make sandwich with current continuation" routine, which creates the sandwich and then continues where execution left off.
Continuations are also used in models of computation including denotational semantics, the actor model, process calculi, and lambda calculus. These models rely on programmers or semantics engineers to write mathematical functions in the so-called continuation-passing style. This means that each function consumes a function that represents the rest of the computation relative to this function call. To return a value, the function calls this "continuation function" with a return value; to abort the computation it returns a value.
Functional programmers who write their programs in continuation-passing style gain the expressive power to manipulate the flow of control in arbitrary ways. The cost is that they must maintain the invariants of control and continuations by hand, which can be a highly complex undertaking (but see 'continuation-passing style' below).
Continuations simplify and clarify the implementation of several common design patterns, including coroutines/green threads and exception handling, by providing the basic, low-level primitive which unifies these seemingly unconnected patterns. Continuations can provide elegant solutions to some difficult high-level problems, like programming a web server that supports multiple pages, accessed by the use of the forward and back buttons and by following links. The Smalltalk Seaside web framework uses continuations to great effect, allowing one to program the web server in procedural style, by switching continuations when switching pages.
More complex constructs for which "continuations provide an elegant description" also exist. For example, in C, longjmp can be used to jump from the middle of one function to another, provided the second function lies deeper in the stack (if it is waiting for the first function to return, possibly among others). Other more complex examples include coroutines in Simula 67, Lua, and Perl; tasklets in Stackless Python; generators in Icon and Python; continuations in Scala (starting in 2.8); fibers in Ruby (starting in 1.9.1); the backtracking mechanism in Prolog; monads in functional programming; and threads.
Using the above, the following code block defines a function
test that sets
the-continuation to the future execution state of itself:
For a gentler introduction to this mechanism, see call-with-current-continuation.
The functions defined above allow for defining and executing threads through cooperative multitasking, i.e. threads that yield control to the next one in a queue:
This is AAA 0 Hello from BBB 0 This is AAA 1 Hello from BBB 1 This is AAA 2 Hello from BBB 2 ...
A program must allocate space in memory for the variables its functions use. Most programming languages use a call stack for storing the variables needed because it allows for fast and simple allocating and automatic deallocation of memory. Other programming languages use a heap for this, which allows for flexibility at a higher cost for allocating and deallocating memory. Both of these implementations have benefits and drawbacks in the context of continuations.
Many programming languages exhibit first-class continuations under various names; specifically:
In any language which supports closures and proper tail calls, it is possible to write programs in continuation-passing style and manually implement call/cc. (In continuation-passing style, call/cc becomes a simple function that can be written with lambda.) This is a particularly common strategy in Haskell, where it is easy to construct a "continuation-passing monad" (for example, the
Cont monad and
ContT monad transformer in the
mtl library). The support for proper tail calls is needed because in continuation-passing style no function ever returns; all calls are tail calls.
One area that has seen practical use of continuations is in Web programming. The use of continuations shields the programmer from the stateless nature of the HTTP protocol. In the traditional model of web programming, the lack of state is reflected in the program's structure, leading to code constructed around a model that lends itself very poorly to expressing computational problems. Thus continuations enable code that has the useful properties associated with inversion of control, while avoiding its problems. is a paper that provides a good introduction to continuations applied to web programming.
Some of the more popular continuation-aware Web servers are the Racket , the and for Common Lisp, the Seaside framework for Smalltalk, Ocsigen/Eliom for OCaml, for Perl, for Ruby, for Fantom and the for Python, for C++, for Haskell. The Apache Cocoon Web application framework also provides continuations (see the ).
Support for continuations varies widely. A programming language supports re-invocable continuations if a continuation may be invoked repeatedly (even after it has already returned). Re-invocable continuations were introduced by Peter J. Landin using his J (for Jump) operator that could transfer the flow of control back into the middle of a procedure invocation. Re-invocable continuations have also been called "re-entrant" in the Racket language. However this use of the term "re-entrant" can be easily confused with its use in discussions of multithreading.
A more limited kind is the escape continuation that may be used to escape the current context to a surrounding one. Many languages which do not explicitly support continuations support exception handling, which is equivalent to escape continuations and can be used for the same purposes. C's
setjmp/longjmp are also equivalent: they can only be used to unwind the stack. Escape continuations can also be used to implement tail call elimination.
One generalization of continuations are delimited continuations. Continuation operators like
call/cc capture the entire remaining computation at a given point in the program and provide no way of delimiting this capture. Delimited continuation operators address this by providing two separate control mechanisms: a prompt that delimits a continuation operation and a reification operator such as
control. Continuations captured using delimited operators thus only represent a slice of the program context.
Continuations are the functional expression of the GOTO statement, and the same caveats apply. While they are a sensible option in some special cases such as web programming, use of continuations can result in code that is difficult to follow. In fact, the esoteric programming language Unlambda includes call-with-current-continuation as one of its features solely because expressions involving it "tend to be hopelessly difficult to track down." The external links below illustrate the concept in more detail.
In "Continuations and the nature of quantification", Chris Barker introduced the "continuation hypothesis", that
some linguistic expressions (in particular, QNPs [quantificational noun phrases]) have denotations that manipulate their own continuations.
The extent to which continuations can be used to explain other general phenomena in natural language is a topic of current research.