2013/11/17 by Matthew Might, Yannis Smaragdakis, Might, Matthew +3
Computer Science · #FOS: Computer and information sciences #Formal Methods in Verification #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #Programming Languages (cs.PL)
paper · pdf · doi:10.48550/arxiv.1311.4231
openalex publication_date 2013/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Low-level program analysis is a fundamental problem, taking the shape of "flow analysis" in functional languages and "points-to" analysis in imperative and object-oriented languages. Despite the similarities, the vocabulary and results in the two communities remain largely distinct, with limited cross-understanding. One of the few links is Shivers's k-CFA work, which has advanced the concept of "context-sensitive analysis" and is widely known in both communities. Recent results indicate that the relationship between the functional and object-oriented incarnations of k-CFA is not as well understood as thought. Van Horn and Mairson proved k-CFA for k ≥ 1 to be EXPTIME-complete; hence, no polynomial-time algorithm can exist. Yet, there are several polynomial-time formulations of context-sensitive points-to analyses in object-oriented languages. Thus, it seems that functional k-CFA may actually be a profoundly different analysis from object-oriented k-CFA. We resolve this paradox by showing that the exact same specification of k-CFA is polynomial-time for object-oriented languages yet exponential- time for functional ones: objects and closures are subtly different, in a way that interacts crucially with context-sensitivity and complexity. This illumination leads to an immediate payoff: by projecting the object-oriented treatment of objects onto closures, we derive a polynomial-time hierarchy of context-sensitive CFAs for functional programs.