## Strictness Analysis in Logical Form (1991)

Citations: | 45 - 2 self |

### BibTeX

@INPROCEEDINGS{Jensen91strictnessanalysis,

author = {Thomas P. Jensen},

title = {Strictness Analysis in Logical Form},

booktitle = {},

year = {1991},

pages = {352--366},

publisher = {Springer Verlag}

}

### Years of Citing Articles

### OpenURL

### Abstract

This paper presents a framework for comparing two strictness analysis techniques: Abstract interpretation and non--standard type inference. The comparison is based on the representation of a lattice by its ideals. A formal system for deducing inclusions between ideals of a lattice is presented and proved sound and complete. Viewing the ideals as strictness properties we use the formal system to define a program logic for deducing strictness properties of expressions in a typed lambda calculus. This strictness logic is shown to be sound and complete with respect to the abstract interpretation, which establishes the main result that strictness analysis by type--inference and by abstract interpretation are equally powerful techniques. 1 Introduction Abstract interpretation is a well--established technique for static analysis of programs. Its virtue is its strong connection with denotational semantics which provides a means of proving the analysis correct. Its vice is that the process of...

### Citations

1190 |
Introduction to lattices and order
- Davey, Priestley
- 1990
(Show Context)
Citation Context ...sformation forming an adjunction between the two functors Fil and Idl. It is well outside the scope of this paper to go into more details about this subject and we shall only refer the reader to [1], =-=[5]-=- and [9]. The work reported here is of course inspired by previous work on strictness analysis via type inference reported by Kuo and Mishra in [11]. The difference between our work and theirs is that... |

236 | Domain theory in logical form
- Abramsky
- 1991
(Show Context)
Citation Context ...een as a special case of the relationship between denotational and axiomatic semantics. This topic has been investigated by a number of researchers and we shall be following a line similar to that of =-=[1]-=-. This work was partially supported by ESPRIT grant BRA 3124 SEMANTIQUE y Author's address: Department of Computing, Imperial College, 180 Queen's Gate, London SW7 2BZ, U.K. Email: tpj@doc.ic.ac.uk We... |

119 |
editors. Abstract Interpretation of Declarative Languages
- Abramsky, Hankin
- 1987
(Show Context)
Citation Context ... to define a program logic for strictness analysis which is then proved sound and complete with respect to the abstract interpretation. For a general introduction to abstract interpretation see e.g., =-=[2]-=-. We shall be using the simply typed lambda calculus with constants including a conditional and a fixpoint operator. The set of terms,sT , of the language is given by the grammar: e = x j c j x:e j e ... |

94 |
Abstract interpretation and optimising transformations for applicative programs
- Mycroft
- 1981
(Show Context)
Citation Context ...s of program analyses aimed at detecting when a given function is strict. We shall not go into the details of how strictness information can be used to optimise functional programs, but only refer to =-=[12]-=- and [3]. 4.1 Strictness analysis by abstract interpretation Strictness analysis by abstract interpretation works by interpreting the terms ofsT over non--standard domains built up from the two--point... |

92 | Is there a use for linear logic
- Wadler
- 1991
(Show Context)
Citation Context ... fixpoints have improved the situation substantially [7]. Recently, a number of researchers have suggested that analyses be based on non--standard type systems. Examples include Wadler's linear types =-=[14]-=- and Kuo and Mishra's strictness types [11]. The advantage of this approach is that there exist efficient algorithms for checking and inferring types of programs. However, the correctness of these ana... |

58 |
Strictness analysis: A new perspective based on type inference
- Kuo, Mishra
- 1989
(Show Context)
Citation Context ...tantially [7]. Recently, a number of researchers have suggested that analyses be based on non--standard type systems. Examples include Wadler's linear types [14] and Kuo and Mishra's strictness types =-=[11]-=-. The advantage of this approach is that there exist efficient algorithms for checking and inferring types of programs. However, the correctness of these analyses has received rather less attention th... |

50 |
Partial type inference for untyped functional programs (extended abstract
- Gomard
- 1990
(Show Context)
Citation Context ...the developments reported here are of limited use if they are not accompanied by advances in the technology of implementing these program logics. Fortunately, work is going on in this area, see e.g., =-=[6]-=-. We have not made any attempt to prove the strictness logic correct with respect to a standard semantics for the language. This is because once we have established the equivalence to the abstract int... |

38 |
Spaces, volume 3 of Cambridge
- Stone
- 1982
(Show Context)
Citation Context ...on forming an adjunction between the two functors Fil and Idl. It is well outside the scope of this paper to go into more details about this subject and we shall only refer the reader to [1], [5] and =-=[9]-=-. The work reported here is of course inspired by previous work on strictness analysis via type inference reported by Kuo and Mishra in [11]. The difference between our work and theirs is that whereas... |

34 | Binding time analysis: A new PERspective
- Hunt, Sands
- 1991
(Show Context)
Citation Context ...ther program analyses. We are currently investigating the relationship between the binding--time analysis via type--inference described in [10] and the PER--based abstract interpretation presented in =-=[8]-=-. Another analysis worth considering is the system of use-- types suggested in [14] which is aimed at estimating how many times a given value is used during execution of a program. There is currently ... |

34 |
Denotational Semantics
- Schmidt
- 1986
(Show Context)
Citation Context ...inable over the domain together with the logical entailment relation associated with these properties. In this paper we shall take an abstract interpretation to be a denotational semantics (see e.g., =-=[13]-=-) for which the denotation of any program is effectively computable. One way of achieving effectiveness is by requiring the domains used in the interpretation to be finite. This on the other hand intr... |

22 |
Abstract Interpretation and the Parallel Evaluation of Functional Languages
- Burn
- 1987
(Show Context)
Citation Context ...ram analyses aimed at detecting when a given function is strict. We shall not go into the details of how strictness information can be used to optimise functional programs, but only refer to [12] and =-=[3]-=-. 4.1 Strictness analysis by abstract interpretation Strictness analysis by abstract interpretation works by interpreting the terms ofsT over non--standard domains built up from the two--point domain ... |

19 |
The theory and practice of strictness analysis for higher order functions
- Burn, Hankin, et al.
- 1985
(Show Context)
Citation Context ...e]]ae[x 7! v] [[e 1 e 2 ]]ae = [[e 1 ]]ae([[e 2 ]]ae) [[fix(e)]]ae = t n2! ([[e]]ae) n (?) [[cond(e 1 ; e 2 ; e 3 )]]ae = 8 ! : ? if [[e 1 ]]ae = ? [[e 2 ]]ae t[[e 3 ]]ae otherwise The main result in =-=[4]-=- is that if the abstract interpretation of a term denotes a strict function then the standard interpretation of the function is strict as well, i.e., by studying the abstract version of the function w... |

14 |
Fixed points and frontiers: A new perspective
- Hunt, Hankin
- 1991
(Show Context)
Citation Context ... process of doing abstract interpretation is quite costly in terms of computation time, although developments in the area of algorithms for finding fixpoints have improved the situation substantially =-=[7]-=-. Recently, a number of researchers have suggested that analyses be based on non--standard type systems. Examples include Wadler's linear types [14] and Kuo and Mishra's strictness types [11]. The adv... |

12 | A selfapplicable partial evaluator for the lambda calculus
- Jones, Gomard, et al.
- 1990
(Show Context)
Citation Context ...nuation of the work reported here to apply similar ideas to other program analyses. We are currently investigating the relationship between the binding--time analysis via type--inference described in =-=[10]-=- and the PER--based abstract interpretation presented in [8]. Another analysis worth considering is the system of use-- types suggested in [14] which is aimed at estimating how many times a given valu... |