Concrete Semantics for Pushdown Analysis: The Essence of Summarization

J. Ian Johnson and David Van Horn
Preprint, 2013

Pushdown analysis is better than finite-state analysis in precision and performance. Why then have we not seen total widespread adoption of these techniques? For one, the known techniques are technically burdened and difficult to understand or extend. Control structure of the programming language gets pulled into the model of computation, which makes extensions to non-pushdown control structures, such as call/cc or shift and reset, non-trivial. We show a derivational approach to abstract interpretation that yields transparently sound static analyses that can precisely match calls and returns when applied to well-known abstract machines. We show that adding memoization and segmenting the continuation into bounded pieces leads to machines that abstract to static analyses for context-free reachability by simply bounding the stores. This technique allows us to derive existing, more technically involved analyses, and a novel pushdown analysis for delimited, composable control.

Acknowledgements: We'd like to thank Stephen Chang for his in-depth reading and comments on the paper.