## Exact Flow Analysis (1997)

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Venue: | In Proceedings of SAS’97, International Static Analysis Symposium |

Citations: | 9 - 0 self |

### BibTeX

@INPROCEEDINGS{Mossin97exactflow,

author = {Christian Mossin},

title = {Exact Flow Analysis},

booktitle = {In Proceedings of SAS’97, International Static Analysis Symposium},

year = {1997},

pages = {250--264},

publisher = {Springer-Verlag (LNCS}

}

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### Abstract

We present a type-based ow analysis for simply typed lambda calculus with booleans, data-structures and recursion. The analysis is exact in the following sense: if the analysis predicts a redex, then there exists a reduction sequence (using standard reduction plus context propagation rules) such that this redex will be reduced. The precision is accomplished using intersection typing. It follows that the analysis is non-elementary recursive | more surprisingly, the analysis is decidable. We argue that the specication of such an analysis provides a good starting point for developing new ow analyses and an important benchmark against which other ow analyses can be compared. Furthermore, we believe that the techniques employed for stating and proving exactness are of independent interest: they provide methods for reasoning about the precision of program analyses. 1

### Citations

220 |
A filter lambda model and the completeness of type-assignment
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(Show Context)
Citation Context ... each component has a certainsxed structure. We use a version of intersection types that includes a subtype ordering. This formulation originates from work by Barendregt, Coppo and Dezani-Ciancaglini =-=-=-[2]. The set of formulae presented insgure 2 denes properties. If e is the analysed expression, a property is a standard type where we add a set of labels Formulae: Bool Bool L 2 K(Bool) ! 2 K(t) 0 ... |

56 | A modular, polyvariant, and type-based closure analysis
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- 1997
(Show Context)
Citation Context ...r choice of abstractions and thus provide good starting points for the development of practical analyses. Independently of the present work, Banerjee has studied rank 2 intersection basedsow analysis =-=[1]-=-. The goal of his work is practical (modularity and increased precision compared to closure analysis), but an assessment of the practicality (in particular complexity) of his analysis is made dicult b... |

54 |
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- 1981
(Show Context)
Citation Context ... an even (odd) number of times then ` is said to occur positively (negatively) in . 4 Decidability We will give a syntax directed version of our inference system. Coppo, DezaniCiancaglini and Veneri [=-=4-=-] and van Bakel [32] have used a similar technique of integrating the the non-structural rules in the elimination rules. Thesrst step is to combine the two non-syntax-directed rules into one. Dene the... |

53 |
Dynamic typing: syntax and proof theory
- Henglein
- 1994
(Show Context)
Citation Context ...ructure. This often makes the analysis applicable to untyped languages but fails to exploit the structural information of the underlying types. Examples are: binding-time analysis [7], dynamic typing =-=[10]-=- andsow analysis [1,9] 13 Conclusion We have presented asow analysis for a higher-order typed language with recursion. The analysis is proven to be exact: if the analysis predicts a redex, then there ... |

49 | Control-flow analysis and type systems
- Heintze
- 1995
(Show Context)
Citation Context ...ent 2 . Palsberg and O'Keefe showed that the type information derived using closure analysis corresponds to Amadio-Cardelli typing [25]. Independently, Heintze showed the same result and the converse =-=[8]-=-: by annotating Amadio-Cardelli typings, closure analysis is derived. 2 The notion of evaluation-order dependency is well-known in the imperative data- ow community, but has received little attention ... |

44 | Linear-time subtransitive control flow analysis
- Heintze, McAllester
- 1997
(Show Context)
Citation Context ...erative data-flow community, but has received little attention for higher-order programming languages. Heintze and McAllester define a variant of Palsberg’s constraint formulation of closure analysis =-=[9]-=-. Termination of the analysis relies on the fact that the analysed program is well-typed — if the the size of types is bounded the analysis will run in quadratic time (in contrast to Palsberg’s cubic ... |

40 | Formally optimal boxing
- Henglein, Jorgensen
- 1994
(Show Context)
Citation Context ...ider our analysis an instance of annotated types due to the intersection). Examples of Church style analyses are: binding-time analysis [23,12,5], strictness analysis [16,17,33,14,3], boxing analysis =-=[18,11,15-=-], totality analysis [28,29] andsow analysis [8,21,6]. Eect systems also belong to this category [19,31]. In Curry style analysis, the analysis does not make use of the underlying type structure. This... |

38 |
Polymorphic binding-time analysis
- Henglein, Mossin
(Show Context)
Citation Context ...found by adding annotations to type constructors (we do not consider our analysis an instance of annotated types due to the intersection). Examples of Church style analyses are: binding-time analysis =-=[23,12,5-=-], strictness analysis [16,17,33,14,3], boxing analysis [18,11,15], totality analysis [28,29] andsow analysis [8,21,6]. Eect systems also belong to this category [19,31]. In Curry style analysis, the ... |

30 |
Strictness Analysis of Lazy Functional Programs
- Benton
- 1993
(Show Context)
Citation Context ...type constructors (we do not consider our analysis an instance of annotated types due to the intersection). Examples of Church style analyses are: binding-time analysis [23,12,5], strictness analysis =-=[16,17,33,14,3-=-], boxing analysis [18,11,15], totality analysis [28,29] andsow analysis [8,21,6]. Eect systems also belong to this category [19,31]. In Curry style analysis, the analysis does not make use of the und... |

28 | Polymorphic recursion and subtype qualifications: Polymorphic binding-time analysis in polynomial time
- Dussart, Henglein, et al.
- 1995
(Show Context)
Citation Context ...found by adding annotations to type constructors (we do not consider our analysis an instance of annotated types due to the intersection). Examples of Church style analyses are: binding-time analysis =-=[23,12,5]-=-, strictness analysis [16,17,33,14,3], boxing analysis [18,11,15], totality analysis [28,29] and flow analysis [8,21,6]. Effect systems also belong to this category [19,31]. In Curry style analysis, t... |

14 |
Higher order partial evaluation - hope for the lambda calculus
- Gomard
- 1989
(Show Context)
Citation Context ...e underlying type structure. This often makes the analysis applicable to untyped languages but fails to exploit the structural information of the underlying types. Examples are: binding-time analysis =-=[7]-=-, dynamic typing [10] andsow analysis [1,9] 13 Conclusion We have presented asow analysis for a higher-order typed language with recursion. The analysis is proven to be exact: if the analysis predicts... |

13 |
Polymorphic recursion and subtype quali Polymorphic binding-time analysis in polynomial time
- Dussart, Henglein, et al.
(Show Context)
Citation Context ...found by adding annotations to type constructors (we do not consider our analysis an instance of annotated types due to the intersection). Examples of Church style analyses are: binding-time analysis =-=[23,12,5-=-], strictness analysis [16,17,33,14,3], boxing analysis [18,11,15], totality analysis [28,29] andsow analysis [8,21,6]. Eect systems also belong to this category [19,31]. In Curry style analysis, the ... |

13 | Analysing, Transforming and Compiling Lazy Functional Programs
- Faxén
- 1997
(Show Context)
Citation Context ...closure analysis) , polymorphicsow analysis (with polymorphic recursion) and the intersectionsow analysis presented here. Independently, Faxen gives asow analysis with letpolymorphism in annotations [=-=6]-=-. 12.3 Type-Based Analysis Type-based analysis has received considerable attention over the last decade. The analyses can be divided into Church and Curry style. In Church style analysis, the language... |

10 |
Linear-time subtransitive control analysis
- Heintze, McAllester
(Show Context)
Citation Context ...mperative data- ow community, but has received little attention for higher-order programming languages. Heintze and McAllester dene a variant of Palsberg's constraint formulation of closure analysis [=-=9]-=-. Termination of the analysis relies on the fact that the analysed program is well-typed | if the the size of types is bounded the analysis will run in quadratic time (in contrast to Palsberg's cubic ... |