A characteristic of aspect-oriented programming, as embodied in AspectJ, is the use of advice to incrementally modify the behavior of a program. An advice declaration specifies an action to be taken whenever some condition arises during the execution of the program. The condition is specified by a formula called a pointcut designator or pcd. The events during execution at which advice may be triggered are called join points. In this model of aspectoriented programming, join points are dynamic in that they refer to events during the execution of the program. We give a denotational semantics for a minilanguage that embodies the key features of dynamic join points, pointcut designators, and advice. This is the first semantics for aspect-oriented programming that handles dynamic join points and recursive procedures. It is intended as a baseline semantics against which future correctness results may be measured.

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Continuationsemantics 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 s,olve 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.

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