## Representing Demand by Partial Projections (1993)

Venue: | J. of Functional Programming |

Citations: | 2 - 0 self |

### BibTeX

@ARTICLE{Launchbury93representingdemand,

author = {John Launchbury and Gebreselassie Baraki},

title = {Representing Demand by Partial Projections},

journal = {J. of Functional Programming},

year = {1993},

volume = {6},

pages = {6--4}

}

### OpenURL

### Abstract

The projection-based strictness analysis of Wadler and Hughes is elegant and theoretically satisfying except in one respect: the need for lifting. The domains and functions over which the analysis is performed need to be transformed, leading to a less direct correspondence between analysis and program than might be hoped for. In this paper we shall see that the projection analysis may be reformulated in terms of partial projections, so removing this infelicity. There are additional benefits of the formulation: the two forms of information captured by the projection are distinguished, and the operational significance of the range of the projection fits exactly with the theory of unboxed types. 1 Introduction The method of projection-based backwards strictness analysis for first-order, lazy functional languages was first presented by Wadler and Hughes (1987) in 1987, and has undergone significant development since then. The method is elegant and theoretically satisfying except in one r...

### Citations

245 | The lazy lambda-calculus
- Abramsky
- 1990
(Show Context)
Citation Context ...A ! A) ! A. If function spaces are not lifted, then there seems no choice but to use Hunt's scheme with strict PERs. On the other hand, if function spaces are lifted as advocated by Abramsky and Ong (=-=Abramsky, 1990-=-; Ong, 1988), the problem seems to vanish. Interestingly, Davis found it essential to use lifted function spaces in his work on higher-order projection analysis (Davis, 1994). Though more work is need... |

108 | Unboxed values as first class citizens in a non-strict functional language
- Jones, Launchbury
- 1991
(Show Context)
Citation Context ...ctness analysis (Burn, Hankin and Abramsky, 1986), and the latter with the equivalence classes of Hunt's PERs (Hunt, 1991). Furthermore, the link between projection analysis and unboxed types (Peyton =-=Jones and Launchbury, 1991-=-) becomes clearer, though the full implications remain to be studied. Projection analysis has progressed significantly since the early days, yet this paper is fairly complete in its coverage of modern... |

70 | Strictness analysis for higher-order functions - Burn, Hankin, et al. - 1986 |

69 | Data flow analysis of applicative programs using mii~imal function graphs : abridged version - Jones, Mycroft - 1986 |

66 |
Backwards analysis of functional programs
- Hughes
- 1988
(Show Context)
Citation Context ...er to practicality. The first introduced abstractions of Hughes' original context domains which were much more tractable, and demonstrated a number of other analyses which fitted the backwards mould (=-=Hughes, 1987-=-). In addition, he showed how the technique could be extended to higher-order functions, as a combination of abstract interpretation and backwards analysis. The second paper, written in conjunction wi... |

47 |
Projection Factorisations in Partial Evaluation
- Launchbury
- 1991
(Show Context)
Citation Context ...lysis (Burn, Hankin and Abramsky, 1986), and the latter with the equivalence classes of Hunt's PERs (Hunt, 1991). Furthermore, the link between projection analysis and unboxed types (Peyton Jones and =-=Launchbury, 1991-=-) becomes clearer, though the full implications remain to be studied. Projection analysis has progressed significantly since the early days, yet this paper is fairly complete in its coverage of modern... |

34 | Binding time analysis: A new PERspective
- Hunt, Sands
- 1991
(Show Context)
Citation Context ... projection analysis? More recently still, Hunt developed analyses based on partial equivalence relations (PERs). The analysis was applied both to strictness and to binding-time analysis (Hunt, 1991; =-=Hunt and Sands, 1991-=-). At the base types, the PERs used by Hunt corresponded exactly to the non-lifted projections, except for an anomolous one introduced especially to capture strictness. We shall discuss this more in S... |

15 |
Projections for specialisation
- Launchbury
- 1987
(Show Context)
Citation Context ...e discuss this device in more detail in Section 3.1. In the same year, Launchbury demonstrated that the same projection framework could be used in partial evaluation to express binding-time analysis (=-=Launchbury, 1987-=-), though here there was no need for lifting. Interestingly, this analysis was a forwards analysis, demonstrating that projections had no inherent direction of 2 analysis. Indeed this was shown in lat... |

13 | Higher-order Binding-time Analysis
- Davis
- 1993
(Show Context)
Citation Context ...aunchbury, 1992), it has been implemented both for binding-time and strictness analysis (Launchbury, 1991a; Kubiak, Hughes and Launchbury, 1992), and further refined to handle higher-order functions (=-=Davis, 1993-=-), though nonpolymorphically as yet. In addition, the relationship between projection-based backwards analysis and BHA abstract interpretation (Burn, Hankin and Abramsky, 1986) has received some atten... |

8 | Towards relating forwards and backwards analyses - Hughes, Launchbury - 1990 |

6 | Projections for polymorphic first-order strictness analysis
- Hughes, Launchbury
- 1992
(Show Context)
Citation Context ...ng between these worlds was nontrivial. Since then, projection-based analysis has been generalised to handle polymorphism and arbitrary user-defined data types, though only for first order functions (=-=Hughes and Launchbury, 1992-=-), it has been implemented both for binding-time and strictness analysis (Launchbury, 1991a; Kubiak, Hughes and Launchbury, 1992), and further refined to handle higher-order functions (Davis, 1993), t... |

5 | Implementing projection-based strictness analysis. Departmental Research - Kubiak, Hughes, et al. - 1992 |

4 |
The Lazy Lambda Calculus: An Investigation
- Ong
- 1988
(Show Context)
Citation Context ...unction spaces are not lifted, then there seems no choice but to use Hunt's scheme with strict PERs. On the other hand, if function spaces are lifted as advocated by Abramsky and Ong (Abramsky, 1990; =-=Ong, 1988-=-), the problem seems to vanish. Interestingly, Davis found it essential to use lifted function spaces in his work on higher-order projection analysis (Davis, 1994). Though more work is needed, it appe... |

3 | Projection-based Program Analysis
- Davis
- 1994
(Show Context)
Citation Context ...ed by Abramsky and Ong (Abramsky, 1990; Ong, 1988), the problem seems to vanish. Interestingly, Davis found it essential to use lifted function spaces in his work on higher-order projection analysis (=-=Davis, 1994-=-). Though more work is needed, it appears that this device will also make the PER theory more elegant. 7 Acknowledgements Some parts of this paper are based closely on a previous joint paper with Kubi... |