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Reasoning over streams of input data is an essential part of human intelligence. During the last decade {\em stream reasoning} has emerged as a research area within the AI-community with many potential applications. In fact, the increased availability of streaming data via services like Google and Facebook has raised the need for reasoning engines coping with data that changes at high rate. Recently, the rule-based formalism {\em LARS} for non-monotonic stream reasoning under the answer set semantics has been introduced. Syntactically, LARS programs are logic programs with negation incorporating operators for temporal reasoning, most notably {\em window operators} for selecting relevant time points. Unfortunately, by preselecting {\em fixed} intervals for the semantic evaluation of programs, the rigid semantics of LARS programs is not flexible enough to {\em constructively} cope with rapidly changing data dependencies. Moreover, we show that defining the answer set semantics of LARS in terms of FLP reducts leads to undesirable circular justifications similar to other ASP extensions. This paper fixes all of the aforementioned shortcomings of LARS. More precisely, we contribute to the foundations of stream reasoning by providing an operational fixed point semantics for a fully flexible variant of LARS and we show that our semantics is sound and constructive in the sense that answer sets are derivable bottom-up and free of circular justifications.