## Uniform Ideals and Strictness Analysis (1991)

Venue: | In Proc. 18th Int'l Coll. on Automata, Languages and Programming (ICALP |

Citations: | 6 - 2 self |

### BibTeX

@INPROCEEDINGS{Ernoult91uniformideals,

author = {Christine Ernoult and Alcatel Alsthom Recherche and Alan Mycroft},

title = {Uniform Ideals and Strictness Analysis},

booktitle = {In Proc. 18th Int'l Coll. on Automata, Languages and Programming (ICALP},

year = {1991},

pages = {47--59},

publisher = {Springer-Verlag}

}

### Years of Citing Articles

### OpenURL

### Abstract

We propose a notion of uniform ideal (certain Scott-closed sets) to characterise strictness properties. This enables us to explain why Hughes' and Wadler's H projection for lazy list strictness analysis is not in general expressible as an abstract interpretation property of the standard semantics. We give circumstances when it is so expressible. Doing so casts light on Burn's HB projection and his question of its relationship to H. Uniform ideals are a generalisation of the sets of values corresponding to types in (simple) polymorphic type systems. Wadler's doubly-lifted abstract domain constructor for lazy lists can be seen as a special case which only uses certain uniform ideals. The conuence of strictness and type theory furthers Kuo and Mishra's notion of \strictness types". Summary of results We characterise strictness properties as uniform ideals. This enables us to give abstract interpretation properties to show that a function on list(t 1 +t 2 ) is H-strict (Wadler an...

### Citations

128 |
An Ideal Model for Recursive Polymorphic Types
- MacQueen, Plotkin, et al.
- 1986
(Show Context)
Citation Context ...o mean that I is a uniform ideal of t. Let I t be the set of all ideals of D t . The archetype notion of uniform ideal is that of classical type (modelled as an ideal | see MacQueen Plotkin and Sethi =-=[10]-=-) in which we consider ideals which model types to include, using ML-style notation, the values [1; 2] and (1; true), but not [1; true]. 6 Our intent is to use uniform ideals to model strictness prope... |

101 | Projections for strictness analysis
- Wadler, Hughes
- 1987
(Show Context)
Citation Context ...tically based than Burn, Hankin and Abramsky's and in retrospect their use of power-sets of variable names in their `strictness pair' domain was both unnecessary and over-syntactic. Wadler and Hughes =-=[1-=-5] suggested using projections to characterise strictness properties ofsrstorder functions operating on lazy lists as solutions of equations likesfs =sf where andsare projections. This is projection-... |

93 |
Abstract Interpretation and Optimising Transformations for Applicative Programs
- Mycroft
- 1981
(Show Context)
Citation Context ...Burn's HB -strictness is seen as the best possible analogue to H-strictness subject to these conditions, but it is a non-uniform property. 1 Introduction Strictness analysis was originated by Mycroft =-=[11]-=- for thesrst-order case oversat domains, using a formalism based on abstraction and concretisation functions. Temporarily, suppose that D is asat cpo. Let 2 stand for the the set f0; 1g ordered by 0s1... |

58 |
Strictness analysis: A new perspective based on type inference
- Kuo, Mishra
- 1989
(Show Context)
Citation Context ...ype instance) type property of nth is represented by nth(ZZ ? )(2ZZ ? ) ZZ ? . 11 So there is a fundamental sense in which strictness properties behave like types, which was noted by Kuo and Mishra [=-=9-=-] and could be used to underpin Wright [16]. Moreover, treating types and strictness properties both as ideals has the benet of giving a uniform treatment of strictness properties as types and to a un... |

28 |
Topology via Logic. Cambridge Tracts in Theor
- Vickers
- 1985
(Show Context)
Citation Context ...) a !. This is analogous to the distinction between the ML type system 1 , in which -bound variables are not polymorphic, and the 2nd-order polymorphic -calculus, 2 , in which they are. Vickers [13]=-=-=- observes that the rules for lists may be extended to include intersections and unions of our listed properties, viz Is0 0 I \ I 0 Is0 0 I [ I 0 : Such rules add all joins and meets to our lattice of ... |

26 |
Strictness analysis and polymorphic invariance
- Abramsky
- 1985
(Show Context)
Citation Context ...amsky [4] showed that the Hoare (or relational) power-domain 3 (also used in Nielson's thesis [12]) could be used to generate a theory of strictness analysis for the simply typed -calculus. Abramsky [=-=1-=-] showed that this framework could also encompass Hindley-Milner style polymorphism. Around the same time Hudak and Young [6] gave a denition of strictness pairs which enabled them to analyse the unty... |

18 |
The theory and practice of strictness analysis for higher order functions
- Burn, Hankin, et al.
- 1986
(Show Context)
Citation Context ... functions which map a family of ideals into another family of ideals is itself an ideal of the function space, i.e. ff 2 D ! D j (8k)(f(I k ) J k )g is an ideal of D ! D. Burn, Hankin and Abramsky [=-=4-=-] showed that the Hoare (or relational) power-domain 3 (also used in Nielson's thesis [12]) could be used to generate a theory of strictness analysis for the simply typed -calculus. Abramsky [1] showe... |

16 |
A relationship between abstract interpretation and projection analysis (extended abstract
- Burn
- 1990
(Show Context)
Citation Context .... The main worry is that PERs are very general and it is not clear what are appropriate restrictions on them for strictness analysis. Certainly a notion like uniformity is liable to be relevant. Burn =-=[2]-=- investigated the relationship between ideal- and projection-based strictness notions using smash projections which seem to represent the intersection of the ideal- and projection-based regimes. Our u... |

16 | PERs generalise projections for strictness analysis
- Hunt
- 1990
(Show Context)
Citation Context ...y a less dened function. On the other hand, such equations cannot express even Mycroft's simple notion of strictness onsat domains without introducing articial elements by `lifting'. Recently, Hunt [7=-=]-=- has developed a new theory of abstract interpretation using PERs (partial (here: relaxing re exivity) equivalence relations) which seems to be able both to characterise the Hstrictness property and t... |

14 |
Abstract Interpretation Using Domain Theory
- Nielson
- 1984
(Show Context)
Citation Context ... of the function space, i.e. ff 2 D ! D j (8k)(f(I k ) J k )g is an ideal of D ! D. Burn, Hankin and Abramsky [4] showed that the Hoare (or relational) power-domain 3 (also used in Nielson's thesis [=-=12-=-]) could be used to generate a theory of strictness analysis for the simply typed -calculus. Abramsky [1] showed that this framework could also encompass Hindley-Milner style polymorphism. Around the ... |

7 |
Higher order strictness analysis in untyped lambda calculus
- Hudak, Young
- 1986
(Show Context)
Citation Context ...e a theory of strictness analysis for the simply typed -calculus. Abramsky [1] showed that this framework could also encompass Hindley-Milner style polymorphism. Around the same time Hudak and Young [=-=-=-6] gave a denition of strictness pairs which enabled them to analyse the untyped -calculus. This work was less semantically based than Burn, Hankin and Abramsky's and in retrospect their use of power-... |

6 |
Strictness analysis on non- domains (by Abstract interpretation over domains
- Wadler
- 1987
(Show Context)
Citation Context ... projection-based strictness notions using smash projections which seem to represent the intersection of the ideal- and projection-based regimes. Our uniform ideals further this investigation. Wadler =-=[14]-=- suggested use of a precursor domain to ours for abstracting lists via a four element domain ? v 1 v ?2 v >2 This work was attractive because it gave domain-theoretic characterisations of the sets of ... |

4 | editors. Programs as Data Objects - Ganzinger, Jones - 1985 |

2 | Lazy functional languages: interpretation and compilation. Unpublished manuscript, forthcoming book - Burn - 1990 |

1 |
Higher-order strictness analysis over non- domains. INRIA (Rocquencourt) rapport 1190
- Ernoult
- 1990
(Show Context)
Citation Context ...bramsky's [1] polymorphic invariance seems a little removed from polymorphism in types. Further work It would be nice to extend this work to cover lists dened by their -calculus coding to formalise [5=-=]-=-. The notion of uniform properties developed here has parallels with Nielson's expected forms analysis. More work should be done on deciding exactly what uniform properties on lists are `useful' for s... |