First-class 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 state of the program. However, it is important to note that true first-class continuations do not save program data, only the execution context. This is illustrated by the "continuation sandwich" description:
Say you're in the kitchen in front of the refrigerator, thinking about a sandwich. You take a continuation right there and stick it in your pocket. Then you get some turkey and bread out of the refrigerator and make yourself a sandwich, which is now sitting on the counter. You invoke the continuation in your pocket, and you find yourself standing in front of the refrigerator again, thinking about a sandwich. But fortunately, there's a sandwich on the counter, and all the materials used to make it are gone. So you eat it. :-)
Scheme was the first full production system, providing first "catch" and then call/cc. Bruce Duba introduced call/cc into SML.
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 is a highly complex undertaking.
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