Explanatory Denotational Semantics for Complex Event Patterns

Recent years brought popularity and importance of complex event processing (CEP) and associated query languages. CEP systems can be hard to understand. It is often non-trivial to determine streams of events matched by a query, and sometimes we may not notice important edge cases. Hence, the desirability of formal semantics permitting reasoning about resulting complex events and checking if actual matchings agree with our intentions follows. In the paper we introduce a pattern language \({\sl PatLang} \) with some unique syntactic features related to variable binding. We provide two distinct denotational semantics for \({\sl PatLang} \): Minimal semantics, sufficient to describe when patterns match, and tree semantics, which provides detailed information about subpatterns with which the matched events actually match, i.e., information about interpretation of matched events induced by the pattern matching. The tree semantics is unnecessary for verifying correctness of pattern matching execution. However, we show that neither minimal semantics, nor semantics from the prior work suffices to effectively locate errors in patterns with respect to their intended meaning, and that the additional information provided by the tree semantics is crucial for that purpose. We prove that tree semantics can be mapped to minimal semantics. Finally, we provide some practical evaluation.