Aspect-oriented programming (AOP) is a new programming paradigm whose goal is to more cleanly modularize crosscutting concerns such as logging, synchronization, and event notification which would otherwise be scattered throughout the system and tangled with functional code. However, while AOP languages provide promising ways to separate crosscutting concerns, they can also break conventional encapsulation mechanisms, making it difficult to reason about code without the aid of external tools.

We investigate modular reasoning in the presence of aspects through TinyAspect, a small functional language that directly models aspect-oriented programming constructs. We define Open Modules, a module system for TinyAspect that enforces Reynolds' abstraction theorem, a strong encapsulation property. Open Modules are ``open'' in that external aspects can advise functions and pointcuts in their interface, providing significant aspect-oriented expressiveness that is missing in non-AOP systems. In order to guarantee modular reasoning, however, our system places limits on advice: external aspects may not advise function calls internal to a module, except for calls explicitly exposed through pointcuts in the module's interface. The abstraction property of our system ensures that a module's implementation can be changed without affecting clients, and provides insight into formal reasoning, modular analysis, and tool support for aspect-oriented programming.

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