Stable relations and abstract interpretation of higher-order programs

Montagu, Benoît; Jensen, Thomas

doi:10.1145/3409001

Cited by 5 publications

(4 citation statements)

References 56 publications

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“…This idea could be pushed further, to analyse other intentional properties of programs, such as effect analysis, or complexity analysis. Moreover, we could also enrich the traces with the inputs of the programÐan approach similar to the analysis of input-output relations [30]. This would result in a relational control-flow analysis that detects which functions are called at a given program point, depending on the inputs of the program.…”

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%

“…Exploring ways to recover more precision is left for future work. We could for instance perform a narrowing pass, or design a more expressive domain for closures, that keeps information about the results of functionsÐa sort of function summaryÐor use a relational domain such as the one of [30], that keeps relations between inputs and outputs of functions.…”

mentioning

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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“…This challenging extension will require to define an adapted widening, and will greatly expand the range of programs we can analyze. Finally, combining NPRs with the recent extension of correlations to higher-order functions [14] is yet to be studied.…”

Section: Discussionmentioning

confidence: 99%

Numeric domains meet algebraic data types

Bautista

Jensen

Montagu

2020

Proceedings of the 9th ACM SIGPLAN International Workshop on Numerical and Symbolic Abstract Domains

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We report on the design and formalization of a novel abstract domain, called numeric path relations (NPRs), that combines numeric relational domains with algebraic data types. This domain expresses relations between algebraic values that can contain scalar data. The construction of the domain is parameterized by the choice of a relational domain on scalar values. The construction employs projection paths on algebraic values, and in particular projections on variant cases, whose sound treatment is subtle due to mutual exclusiveness.CCS Concepts: • Theory of computation → Program analysis; • Software and its engineering → Automated static analysis.

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“…Finally, we hope that our abstract interpreter can be extended to perform other kinds of static analyses for OCaml programs, such as a purity analysis, or the detection of whether the behaviour of a program might depend on the order of evaluation. We would also like our implementation to serve as a basis for experimenting with recent relational domains for trees and scalars [29,61,2], and with relational analyses of functional programs [49].…”

Section: Conclusive Remarks and Future Workmentioning

confidence: 99%

Detection of Uncaught Exceptions in Functional Programs by Abstract Interpretation

Lermusiaux,

Montagu

2024

Lecture Notes in Computer Science

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Exception handling is a key feature in modern programming languages. Exceptions can be used to deal with errors, or as a means to control the flow of execution of a program. Since they might unexpectedly terminate a program, unhandled exceptions are a serious safety concern. We propose a static analysis to detect uncaught exceptions in functional programs, that is defined as an abstract interpreter. It computes a description of the values potentially returned by a program using a novel abstract domain, that can express inductively defined sets of values. Simultaneously, the analysis infers the possibly raised exceptions, by computing in the abstract exception monad. This abstract interpreter has been implemented as an effective static analyser for a large subset of programs, that supports mutable data types, the module system, and dynamically extensible data types such as the exception type. The analyser has been evaluated on several hundreds of programs.

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Stable relations and abstract interpretation of higher-order programs

Cited by 5 publications

References 56 publications

Trace-based control-flow analysis

Trace-based control-flow analysis

Numeric domains meet algebraic data types

Detection of Uncaught Exceptions in Functional Programs by Abstract Interpretation

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