The PINDESYM project aims to develop insightful program understanding via declarative static analysis. Such insightful understanding of program behavior captures the essence of the computation, at multiple levels of abstraction, some close to human reasoning. To address this grand challenge, the project will significantly advance the state of the art in program analysis with new concepts, algorithms, implementation techniques, and publicly available tools. The key component of the approach is declarative specifications of analysis algorithms—an already highly successful methodology. What promises to dramatically raise the impact of declarative program analysis is two innovations, matching emerging research and technology trends. The first is the idea of combining a declarative system (e.g. a Datalog fixpoint engine) and a symbolic reasoning system, such as an SMT solver or algebraic rewrite system. The second is the seamless integration of a machine learning approach, over large amounts of data (from past code bases), in the declarative inference process. The PINDESYM project leverages symbolic reasoning and learning approaches to greatly advance program analysis. The challenge is dual: not only to invent powerful new techniques and algorithms, but also to capture all the diversity in symbolic, value-flow, and learning-based reasoning in a single, unified, reusable, and extensible analysis framework—a true deep program understanding engine, far beyond current approaches.