Abstract continuations: a mathematical semantics for handling full jumps

Continuation semantics is the traditional mathematical formalism for specifying the semantics of non-local control operations. Modern Lisp-style languages, however, contain advanced control structures like full functional jumps and control delimiters for which continuation semantics is insufficient. We solve this problem by introducing an abstract domain of rests of computations with appropriate operations. Beyond being useful for the problem at hand, these abstract continuations turn out to have applications in a much broader context, e.g., the explication of parallelism, the modeling of control facilities in parallel languages, and the design of new control structures.