Pushdown flow analysis of first-class control

Vardoulakis, Dimitris; Shivers, Olin

doi:10.1145/2034773.2034785

Cited by 14 publications

(7 citation statements)

References 18 publications

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“…Using the same approach, we think -CFA [10,29] could be obtained using a different abstraction on traces, that would keep frames instead of call sites. The question remains open whether we could also derive the more recent pushdown CFAs [6,7,11,44,45]. This could be achieved possibly by employing more precise abstractions.…”

Section: Discussionmentioning

confidence: 99%

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Trace-based control-flow analysis

Montagu

Jensen

2021

Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation

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We define a small-step semantics for the untyped λ-calculus, that traces the β-reductions that occur during evaluation. By abstracting the computation traces, we reconstruct -CFA using abstract interpretation, and justify constraint-based -CFA in a semantic way. The abstract interpretation of the trace semantics also paves the way for introducing widening operators in CFA that go beyond existing analyses, that are all based on exploring a finite state space. We define ∇CFA, a widening-based analysis that limits the cycles in call stacks, and can achieve better precision than -CFA at a similar cost.

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Section: Discussionmentioning

confidence: 99%

“…[4] demonstrate that the łabstracting abstract machinesž approach carry over to more high-level definitional interpreters that are not expressed as state machines. In particular, they show that this approach can reconstruct the CFA2 control flow analyses [44,45] based on push-down structures that also computes precise return information.…”

Section: Related Workmentioning

confidence: 99%

Trace-based control-flow analysis

Montagu

Jensen

2021

Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation

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“…We do not discuss call/cc in detail, since we believe there are no significant barriers to adapting the techniques of Vardoulakis and Shivers (2011) to the direct-style setting, given related work in Johnson and Van Horn (2013). Languages with exceptions fit within the pushdown model since a throw can be modeled as "pop until first catch.…”

Section: Contributionsmentioning

confidence: 99%

“…CFA2 has a follow-up that sacrifices its complete abstraction with the machine that only abstracts bindings in order to handle first-class control (Vardoulakis and Shivers, 2011). We do not have an analogous construction since loss of complete abstraction was an antigoal of this work.…”

Section: Related Workmentioning

confidence: 99%

Pushdown flow analysis with abstract garbage collection

et al. 2014

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In the static analysis of functional programs, pushdown flow analysis and abstract garbage collection push the boundaries of what we can learn about programs statically. This work illuminates and poses solutions to theoretical and practical challenges that stand in the way of combining the power of these techniques. Pushdown flow analysis grants unbounded yet computable polyvariance to the analysis of return-flow in higher-order programs. Abstract garbage collection grants unbounded polyvariance to abstract addresses which become unreachable between invocations of the abstract contexts in which they were created. Pushdown analysis solves the problem of precisely analyzing recursion in higherorder languages; abstract garbage collection is essential in solving the "stickiness" problem. Alone, our benchmarks demonstrate that each method can reduce analysis times and boost precision by orders of magnitude. We combine these methods. The challenge in marrying these techniques is not subtle: computing the reachable control states of a pushdown system relies on limiting access during transition to the top of the stack; abstract garbage collection, on the other hand, needs full access to the entire stack to compute a root set, just as concrete collection does. Conditional pushdown systems were developed for just such a conundrum, but existing methods are ill-suited for the dynamic nature of garbage collection. We show fully precise and approximate solutions to the feasible paths problem for pushdown garbage-collecting control-flow analysis. Experiments reveal synergistic interplay between garbage collection and pushdown techniques, and the fusion demonstrates "better-than-bothworlds" precision.

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“…This paper offers an automata-theoretic perspective on this challenge, providing a fresh set of tools that contrast with previous intersection-type approaches. Techniques based on pushdown automata have previously visited ICFP, such as the approximate higher-order controlflow analysis CFA2 [40], but our aims are a bit different in that we wish to match the expressivity of HORS. Consequently we require a more sophisticated notion of pushdown automaton.…”

Section: Introductionmentioning

confidence: 99%

C-SHORe

Broadbent

Carayol

Hague

et al. 2013

Proceedings of the 18th ACM SIGPLAN International Conference on Functional Programming

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Higher-order recursion schemes (HORS) have recently received much attention as a useful abstraction of higher-order functional programs with a number of new verification techniques employing HORS model-checking as their centrepiece. This paper contributes to the ongoing quest for a truly scalable model-checker for HORS by offering a different, automata theoretic perspective. We introduce the first practical model-checking algorithm that acts on a generalisation of pushdown automata equi-expressive with HORS called collapsible pushdown systems (CPDS). At its core is a substantial modification of a recently studied saturation algorithm for CPDS. In particular it is able to use information gathered from an approximate forward reachability analysis to guide its backward search. Moreover, we introduce an algorithm that prunes the CPDS prior to model-checking and a method for extracting counter-examples in negative instances. We compare our tool with the state-of-the-art verification tools for HORS and obtain encouraging results. In contrast to some of the main competition tackling the same problem, our algorithm is fixed-parameter tractable, and we also offer significantly improved performance over the only previously published tool of which we are aware that also enjoys this property. The tool and additional material are available from

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Pushdown flow analysis of first-class control

Cited by 14 publications

References 18 publications

Trace-based control-flow analysis

Trace-based control-flow analysis

Pushdown flow analysis with abstract garbage collection

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