Control-flow analysis of functional programs

Midtgaard, Jan

doi:10.1145/2187671.2187672

Cited by 65 publications

(46 citation statements)

References 149 publications

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“…0CFA [20] is a popular form of Control Flow Analysis. It is flow insensitive and context insensitive, but precise enough to be useful for many applications, including guiding compiler optimisations [17,2], providing autocompletion hints in IDEs and noninterference analysis [14]. It is perhaps the simplest static analysis that handles higher order functions, which are a staple of functional programming.…”

Section: Cfa For Lambda Calculusmentioning

confidence: 99%

“…A term t l can be analysed by finding a Γ and ϕ such that Γ, ϕ |= t l . This is done by solving the 6 2 , @ (7,2) } Γ(11) = {F 10 1 , @ (10,9) , @ (17,8) , @ (7,2) } ϕ(13) = true ϕ(15) = true Γ, ϕ |= (S 15 @ 16 (F 13 @ 14 F 12 )@ 17 (F 10 @ 11 F 9 ))@ 18 (S 6 @ 7 (F 4 @ 5 F 3 )@ 8 (F 1 @ 2 F 0 )) Figure 8: Solution of the analysis for application of identity to itself in SF-calculus.…”

Section: Analysis Rulesmentioning

confidence: 99%

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Control Flow Analysis for SF Combinator Calculus

Lester

2015

Electron. Proc. Theor. Comput. Sci.

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Programs that transform other programs often require access to the internal structure of the program to be transformed. This is at odds with the usual extensional view of functional programming, as embodied by the lambda calculus and SK combinator calculus. The recently-developed SF combinator calculus offers an alternative, intensional model of computation that may serve as a foundation for developing principled languages in which to express intensional computation, including program transformation. Until now there have been no static analyses for reasoning about or verifying programs written in SF-calculus. We take the first step towards remedying this by developing a formulation of the popular control flow analysis 0CFA for SK-calculus and extending it to support SF-calculus. We prove its correctness and demonstrate that the analysis is invariant under the usual translation from SK-calculus into SF-calculus.

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Section: Cfa For Lambda Calculusmentioning

confidence: 99%

Section: Analysis Rulesmentioning

confidence: 99%

Control Flow Analysis for SF Combinator Calculus

Lester

2015

Electron. Proc. Theor. Comput. Sci.

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“…Midtgaard's survey [12] and the book by Nielson et al [13]). The aim of CFA is to approximate the flow of control within a program phrase in the course of a computation.…”

Section: Control Flow Analysismentioning

confidence: 99%

Verifying higher-order functional programs with pattern-matching algebraic data types

Ong¹,

Ramsay²

2011

Proceedings of the 38th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

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Type-based model checking algorithms for higher-order recursion schemes have recently emerged as a promising approach to the verification of functional programs. We introduce pattern-matching recursion schemes (PMRS) as an accurate model of computation for functional programs that manipulate algebraic data-types. PMRS are a natural extension of higher-order recursion schemes that incorporate pattern-matching in the defining rules.This paper is concerned with the following (undecidable) verification problem: given a correctness property ϕ, a functional program P (qua PMRS) and a regular input set I, does every term that is reachable from I under rewriting by P satisfy ϕ? To solve the PMRS verification problem, we present a sound semi-algorithm which is based on model-checking and counterexample guided abstraction refinement. Given a no-instance of the verification problem, the method is guaranteed to terminate.From an order-n PMRS and an input set generated by a regular tree grammar, our method constructs an order-n weak PMRS which over-approximates only the first-order pattern-matching behaviour, whilst remaining completely faithful to the higher-order control flow. Using a variation of Kobayashi's type-based approach, we show that the (trivial automaton) model-checking problem for weak PMRS is decidable. When a violation of the property is detected in the abstraction which does not correspond to a violation in the model, the abstraction is automatically refined by 'unfolding' the pattern-matching rules in the program to give successively more and more accurate weak PMRS models.

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“…Static analysis by abstract interpretation proves properties of a program by running its code through an interpreter powered by an abstract semantics that approximates the behavior of a concrete semantics. This process is a general method for analyzing programs and serves applications such as program verification, malware/vulnerability detection, and compiler optimization, among others [1][2][3]10] The abstracting abstract machines (AAM) approach uses abstract interpretation of abstract machines for controlflow analysis (CFA) of functional (higher-order) programming languages [9,12,15]. The AAM methodology allows a high degree of control over how program states are represented and is easy to instrument.…”

Section: Introductionmentioning

confidence: 99%

Pushdown control-flow analysis for free

Gilray

Lyde

Adams

et al. 2016

Proceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

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Traditional control-flow analysis (CFA) for higher-order languages introduces spurious connections between callers and callees, and different invocations of a function may pollute each other's return flows. Recently, three distinct approaches have been published that provide perfect call-stack precision in a computable manner: CFA2, PDCFA, and AAC. Unfortunately, implementing CFA2 and PDCFA requires significant engineering effort. Furthermore, all three are computationally expensive. For a monovariant analysis, CFA2 is in O(2 n ), PDCFA is in O(n 6 ), and AAC is in O(n 8 ).In this paper, we describe a new technique that builds on these but is both straightforward to implement and computationally inexpensive. The crucial insight is an unusual state-dependent allocation strategy for the addresses of continuations. Our technique imposes only a constant-factor overhead on the underlying analysis and costs only O(n 3 ) in the monovariant case. We present the intuitions behind this development, benchmarks demonstrating its efficacy, and a proof of the precision of this analysis.

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Control-flow analysis of functional programs

Cited by 65 publications

References 149 publications

Control Flow Analysis for SF Combinator Calculus

Control Flow Analysis for SF Combinator Calculus

Verifying higher-order functional programs with pattern-matching algebraic data types

Pushdown control-flow analysis for free

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