Ubiquitous computing applications or widespread robots interactions execute in unforeseen environments and need to adapt to changeful available services, user needs, and variations of the environment. Context-awareness ability addresses such a need, enabling, through adaptation rules, applications to react to the perceived dynamic variations. Responses to adaptation have to be quick enough to maximize the time during which the application is coherent with its environment. Adaptation rules, associating variations of the environment to application reactions, are usually established at design time. However, in unforeseen and partially anticipated environments, we claim that adaptation rules have to be dynamically extensible to match previously unexpected variations. Our approach enables rule composition and ensures a deterministic result. We propose to use parameter adaptation to quickly respond to environmental variations and dynamic compositional adaptation to provide extensibility to the parameter adaptation. To foster even lower response times, we internalize context-awareness processing and decision into the application.