## Closure Analysis in Constraint Form (1995)

Venue: | ACM Transactions on Programming Languages and Systems |

Citations: | 57 - 5 self |

### BibTeX

@ARTICLE{Palsberg95closureanalysis,

author = {Jens Palsberg},

title = {Closure Analysis in Constraint Form},

journal = {ACM Transactions on Programming Languages and Systems},

year = {1995},

volume = {17},

pages = {47--62}

}

### Years of Citing Articles

### OpenURL

### Abstract

Interpretation Bondorf's definition can be simplified considerably. To see why, consider the second component of CMap(E) \Theta CEnv(E). This component is updated only in Closure Analysis in Constraint Form \Delta 9 b(E 1 @ i E 2 )¯ae and read only in b(x l )¯ae. The key observation is that both these operations can be done on the first component instead. Thus, we can omit the use of CEnv(E). By rewriting Bondorf's definition according to this observation, we arrive at the following definition. As with Bondorf's definition, we assume that all labels are distinct. Definition 2.3.1. We define m : (E : ) ! CMap(E) ! CMap(E) m(x l )¯ = ¯ m( l x:E)¯ = (m(E)¯) t h[[ l ]] 7! flgi m(E 1 @ i E 2 )¯ = (m(E 1 )¯) t (m(E 2 )¯) t F l2¯(var(E1 )) (h[[ l ]] 7! ¯(var(E 2 ))i t h[[@ i ]] 7! ¯(var(body(l)))i) . We can now do closure analysis of E by computing fix(m(E)). A key question is: is the simpler abstract interpretation equivalent to Bondorf's? We might attempt to prove this u...

### Citations

1115 |
The Lambda Calculus: Its Syntax and Semantics
- Barendregt
- 1981
(Show Context)
Citation Context ...simpler abstract interpretation, and one in constraint form. In Section 3 we prove that they are equivalent, and in Section 4 we prove that they are correct. 2. CLOSURE ANALYSIS Recall the -calculus [=-=Barendregt 1981-=-]. Definition 2.1. The languagesof -terms has an abstract syntax which is defined by the grammar: E ::= x l (variable) jsl x:E (abstraction) j E 1 @ i E 2 (application) 6 \Delta Jens Palsberg The labe... |

554 | Self: The power of simplicity
- Ungar, Smith
- 1987
(Show Context)
Citation Context ... analyses can be found in the Similix system of Bondorf [Bondorf 1993; Bondorf and Danvy 1991], the Schism system of Consel [1990], and the system of Agesen et al. [1993] for analyzing Self programs [=-=Ungar and Smith 1987-=-]. The last of these implementations demonstrates that closure analysis can handle dynamic and multiple inheritance. Closure analysis and its extensions have been formulated using constraints by other... |

298 | Control-flow analysis of higher-order languages of taming lambda - SHIVERS - 1991 |

221 | Object-oriented type inference - PALSBERG, SCHWARTZBACH - 1991 |

159 | Object-Onented Type Systems - Palsberg, M - 1994 |

117 | Automatic autoprojection of recursive equations with global variables and abstract data types
- Bondorf, Danvy
- 1991
(Show Context)
Citation Context ...lation. We will refer to all analyses based on closure analysis as flow analyses. Examples of large-scale implementations of such analyses can be found in the Similix system of Bondorf [Bondorf 1993; =-=Bondorf and Danvy 1991-=-], the Schism system of Consel [1990], and the system of Agesen et al. [1993] for analyzing Self programs [Ungar and Smith 1987]. The last of these implementations demonstrates that closure analysis c... |

113 |
Set-Based Analysis of ML Programs
- Heintze
- 1994
(Show Context)
Citation Context ...ntze [1992; 1994], and Wand and Steckler [1994]. Their constraint systems are in spirit close to ours, although they are technically somewhat different. A key difference between Heintze's definition [=-=Heintze 1994-=-] and ours is that he attempts to avoid analyzing code that will not be executed under call-by-value. This goal is shared by an analysis of Palsberg and Schwartzbach [1992a]. The idea of defining prog... |

95 | Set Based Program Analysis - Heintze - 1993 |

90 | Automatic autoprojection of higher order recursive equations - Bondorf - 1991 |

81 |
Replacing function parameters by global variables
- Sestoft
- 1989
(Show Context)
Citation Context ...ample of such a constraint system is given in Section 1.3. ---We prove that the constraint-based analysis is equivalent to the closure analysis of Bondorf [1991], which in turn is based on Sestoft's [=-=Sestoft 1989-=-]. We also 4 \Delta Jens Palsberg prove that these analyses are equivalent to a novel simplification of Bondorf's definition. The proofs of correctness and subject-reduction then proceed by considerin... |

80 | Type Inference of SELF: Analysis of Objects with Dynamic and Multiple Inheritance - Agesen, Palsberg, et al. - 1995 |

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29 | Safety analysis versus type inference for partial types - Palsberg, Schwartzbach - 1992 |

19 |
Similix 5.0
- Bondorf
- 1993
(Show Context)
Citation Context ...program in isolation. We will refer to all analyses based on closure analysis as flow analyses. Examples of large-scale implementations of such analyses can be found in the Similix system of Bondorf [=-=Bondorf 1993-=-; Bondorf and Danvy 1991], the Schism system of Consel [1990], and the system of Agesen et al. [1993] for analyzing Self programs [Ungar and Smith 1987]. The last of these implementations demonstrates... |

17 | Correctness of binding-time analysis - Palsberg - 1993 |

15 | Characterization of typings in polymorphic type discipline - Giannini, Rocca, et al. - 1988 |

9 | Binding-time analysis: Abstract interpretation versus type inference - Palsberg, Schwartzbach - 1994 |

6 | Efficient closure analysis with reachability, in - Ayers - 1992 |

3 | Safety analysis versus type inference. Information and Computation - Palsberg, Schwartzbach - 1992 |

1 | Closure Analysis in Constraint Form · 15 - Agesen, Palsberg, et al. - 1993 |