Context-sensitivity is essential for achieving good precision in inter-procedural static analysis. To be context-sensitive, top-down analysis needs to fully inline all the statements in
a callee at all its callsites, leading to statement explosion. Compositional analysis, which inlines summaries of all the callees, scales up but often loses precision, as it is not strictly context-sensitive. We propose a compositional and strictly context-sensitive framework for static analysis. This framework is based on a key observation: a compositional
analysis often loses precision only on some \emph{critical} statements that need to be analyzed context-sensitively. Our approach hybridly inlines the critical statements and the summaries of non-critical statements of each callee, thus avoiding re-analyzing non-critical ones.
In addition, our analysis lazily summarizes the critical statements, by stopping propagating the critical statements once the calling context accumulated is adequate.
We have designed and implemented several analyses (including a pointer analysis) based on this framework. Our evaluation on the pointer analysis shows that it can analyze large Java programs from the DaCapo benchmark suite and industry in minutes. Compared to context-insensitive analysis, Hybrid Inlining introduces only 65% and 1% additional time overheads on DaCapo and industrial applications, respectively.