The notion of event constitutes the general basis of the target program behavior model. This model, called H-space (History-space), is formally defined through a set of general axioms (event grammar) for two basic relations, which may or may not hold between two arbitrary events: these events may be sequentially ordered or one of them might be included in another composite event. Target program execution history is represented as a set of nested events.

A language for the description of computations over execution histories of target programs provides convenient means for assertion checking, debugging queries, profiles, and performance measurement. Event patterns and aggregate operations over event traces, can be used in order to describe typical bugs and debugging rules.

The knowledge about typical bugs and debugging rules can be formalized in the libraries of assertions and libraries of debugging rules and can be used for run-time detecting of bugs and bug localization. Examples of assertions and debugging rules are presented and prototype implementation issues are briefly discussed.

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