## Structures for Lazy Semantics (1997)

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Venue: | In Programming Concepts and Methods, PROCOMET'98. Chapman |

Citations: | 2 - 0 self |

### BibTeX

@INPROCEEDINGS{Bastonero97structuresfor,

author = {Olivier Bastonero and Alberto Pravato and Simona Ronchi Della Rocca},

title = {Structures for Lazy Semantics},

booktitle = {In Programming Concepts and Methods, PROCOMET'98. Chapman},

year = {1997},

publisher = {Hall}

}

### OpenURL

### Abstract

The paper explores different approaches for modeling the lazy -calculus, which is a paradigmatic language for studying the operational behaviour of programming languages, like Haskell, using a call-by-name and lazy evaluation mechanism. Two models for lazy -calculus in the coherence spaces setting are built. They give a new insight in the behaviour of the language since their local structures are different from the one of all existing models in the literature. In order to compare different models, a class of models for lazy -calculus is defined, namely, the lazy regular models class. All the models adequate for the lazy -calculus studied in the literature belong to this class. Moreover, all the lazy regular model share important properties, like the approximation property, which is a key tool for studying their local structure. 1

### Citations

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(Show Context)
Citation Context ...e coherence spaces and whose morphisms are stable functions, which can be easily proved to be regular. For what concerns the notions relative to coherence spaces and stability, we refer the reader to =-=[7]-=-. 4.1 The models M 1 and M 2 If D is a coherence space, let us denote with jDj its set of atoms (ranged over by ff, fi, fl,...), and by comp D ` jDj \Theta jDj the compatibility relation. Elements of ... |

137 | Full abstraction in the Lazy Lambda Calculus
- Abramsky, Ong
- 1993
(Show Context)
Citation Context ... not in coherence spaces [4] and vice-versa [3]. In this paper we are interested in studying structures for modeling the lazy -calculus. The lazy -calculus, formally introduced by Abramsky and Ong in =-=[1]-=-, can be seen as a paradigm for programming languages, like Haskell [11], using a call-by-name and a lazy evaluation mechanism. An evaluation mechanism is call-by-name when parameters are passed to a ... |

83 |
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(Show Context)
Citation Context ...nterested in studying structures for modeling the lazy -calculus. The lazy -calculus, formally introduced by Abramsky and Ong in [1], can be seen as a paradigm for programming languages, like Haskell =-=[11]-=-, using a call-by-name and a lazy evaluation mechanism. An evaluation mechanism is call-by-name when parameters are passed to a function before to be evaluated, moreover it is lazy when a procedure is... |

52 | A syntactic characterization of the equality in some models of the lambda calculus
- Hyland
- 1976
(Show Context)
Citation Context ... is an immediate consequence of the fact that all the lazy regular models share an approximation property w.r.t. the same notion of approximant, which is an adaptation of the one introduced by Hyland =-=[12]-=- and Wadsworth [17] for analyzing Scott's D1 model. The approximation property says that the interpretation of a term is the supremum of the interpretations of a set of normal forms in an extended lan... |

43 |
Set-theoretical models of lambda calculus: Theories, expansions and isomorphisms
- Longo
- 1983
(Show Context)
Citation Context ...adequate with respect to the operational semantics modeling the call-byname lazy evaluation mechanism. Models for lazy -calculus, adequate w.r.t. its operational semantics, have been studied by Longo =-=[14]-=- and Abramsky and Ong [1]. The model of Longo (ML ) is built in the Engeler's algebras setting, while the model of Abramsky and Ong (MAO ) is built in the Scott's domains setting (they present it also... |

37 |
Lambda calculus models and extensionality
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Citation Context ...e -calculus, a semantic account of the notion of valuable terms must be given. This can be done by enriching the well--known set--theoretical definition of -calculus model in Hindley-Longo style, see =-=[8]-=-, by explicitly introducing a subset V of the interpretation domain, where all valuable terms have to be interpreted. Definition 2.2 A model for the lazy -calculus is a 4-tuple M = (D; ffl; V; [[\Delt... |

31 | Categories Types and Structures - Asperti, Longo - 1991 |

26 |
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Citation Context ... is not adequate to the one induced by the normalizing machine (whose values are all the normal-forms). An example of a model adequate w.r.t. this last operational semantics is the model described in =-=[5]-=-. 2.1 Lazy regular models For our purposes, we need to consider only a particular class of models for the lazy -calculus, the lazy-regularmodels, based on the notion of domains. All the models we are ... |

17 |
Algebras and combinators
- Engeler
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(Show Context)
Citation Context ...local structures with the models M 1 and M 2 defined in the present paper. Longo model The Longo's model ML (defined in [14] as D + A and called D lazy A in [15]) is based on the free PSEalgebras(see =-=[6]-=-) built over a given set A, namely the pair DA = (P(B); ffl) where B = S n Bn with B 0 = A and Bn+1 = Bn [ f(b; fi) j b 2 P fin (Bn ); fi 2 Bn g, and d 1 ffl d 2 = fff j 9a 2 P fin (d 2 ):(a; ff) 2 d ... |

14 | Some results on the full abstraction problem for restricted lambda calculi
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- 1993
(Show Context)
Citation Context ...der to mimic the lifting construction for modeling the lazy call-by-value evaluation in coherence spaces, Honsell and Lenisa defined a different notion of coherence space, the pointed coherence space =-=[9]. Inside c-=-artesian closed categories whose objects are cpo and morphisms are continuous functions, we define a class of models for lazy -calculus, the class of "lazy regular models", to which both the... |

9 |
An algebraic interpretation of the fiK-calculus and a labelled -calculus
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- 1975
(Show Context)
Citation Context ...ular of the proof of Corollary 3.4. 2 3 Approximation in lazy regular models In this section we will prove that the notion of Levy--Longo tree, introduced by Longo in [14] by adapting an idea of Levy =-=[13]-=-, is a key one for speaking about the theories of lazy regular models. Namely, all the terms having the same Levy--Longo tree are equated in every lazy regular model, and the Levy--Longo preorder is i... |

4 |
Categories,Types and Structures. Foundations of Computing
- Asperti, Longo
- 1991
(Show Context)
Citation Context ...; B) of morphisms from the object A to the object B, through the operationsA;B;C : HomC (A \Theta B; C) ! HomC (A; (B ) C)) and the evaluation morphism: ev B;C : (B ) C) \Theta B ! C, for each C (see =-=[2]-=- for details). Definition 2.6 A regular category C is a c.c.c. such that: i) every object A of C is a pointed complete partial order w.r.t. the order relation A , where ?A denotes the minimum point; i... |

4 |
Ronchi Della Rocca, Reasoning about interpretations in qualitative lambda models
- Honsell, S
- 1990
(Show Context)
Citation Context ...e constant , in the following way: ffls2 T , ffl [oe 1 ; : : : ; oe n ] ! oe 2 T if oe; oe 1 ; : : : ; oe n 2 T and (comp(oe i ; oe j )) (1i;jn) , where ns0 and comp is formalized as in Figure 1 (see =-=[10]-=-). Types are considered modulo the equivalence: [oe 1 ; : : : ; oe n ] ! oes[oe s(1) ; : : : ; oe s(n) ] ! oe, for every permutationss of f1; : : : ; ng. Definition 4.8 Let t : T =! jDj be defined as:... |

4 | Lazy lambda calculus: Theories, models and local structure characterization
- Ong
- 1992
(Show Context)
Citation Context ...ediate consequence of Theorem 4.20 we have that the theory of M 1 is the theory of ML . Moreover, the local structure of M 1 is strictly included in the one of ML , whose local structure is proved in =-=[15]-=- to be characterized by vPSE . Abramsky-Ong model The Abramsky--Ong model, defined in [1], has been built starting from a regular model in the category CPO, whose objects are Scott's domains and whose... |

3 |
Modèles fortement stables du Lambda-calcul et résultats d’incomplétude
- Bastonero
- 1996
(Show Context)
Citation Context ...for grasping unexpected operational properties of -calculus. Indeed, it has been proved that there are -theories which can be modeled in Scott's domains but not in coherence spaces [4] and vice-versa =-=[3]-=-. In this paper we are interested in studying structures for modeling the lazy -calculus. The lazy -calculus, formally introduced by Abramsky and Ong in [1], can be seen as a paradigm for programming ... |

3 |
Strong stability and incompleteness of the class of stable models
- Bastonero, Gouy
(Show Context)
Citation Context ...s been very useful for grasping unexpected operational properties of -calculus. Indeed, it has been proved that there are -theories which can be modeled in Scott's domains but not in coherence spaces =-=[4]-=- and vice-versa [3]. In this paper we are interested in studying structures for modeling the lazy -calculus. The lazy -calculus, formally introduced by Abramsky and Ong in [1], can be seen as a paradi... |

3 |
Categorical semantics of the call-by-value lambda-calculus
- Pravato, Rocca, et al.
- 1995
(Show Context)
Citation Context ...s not fully-abstract. An example of model for lazy (but this time call-by-value) computation built using a modal construction in the category of coherence spaces and linear functions, can be found in =-=[16]-=-. The paper is structured as follows: Section 2 introduces the syntax and the operational semantics of the lazy -calculus and the concept of lazy regular models. Section 3 speaks about the approximati... |

2 |
Approximate Reductions and -calculus Models
- Wadsworth
- 1978
(Show Context)
Citation Context ...nsequence of the fact that all the lazy regular models share an approximation property w.r.t. the same notion of approximant, which is an adaptation of the one introduced by Hyland [12] and Wadsworth =-=[17]-=- for analyzing Scott's D1 model. The approximation property says that the interpretation of a term is the supremum of the interpretations of a set of normal forms in an extended languages (its approxi... |

1 | Some results on the full-abstraction problem for Biography 19 restricted -calculi - Honsell - 1993 |

1 | Reasoning about interpretations in qualitative lambda models - Rocca, S - 1990 |

1 |
Approximate reductions and -calculus models.' SIAM Journal of Computing 7(3), 337 -- 356. BIOGRAPHY Olivier Bastonero was born
- Wadsworth
- 1978
(Show Context)
Citation Context ...of the fact that all the lazy regular models share an approximation property w.r.t. the same notion of approximant, which is an adaptation of the one introduced by Hyland (Hyland 1976) and Wadsworth (=-=Wadsworth 1978-=-) for analyzing Scott's D1 model. The approximation property says that the interpretation of a term is the supremum of the interpretations of a set of normal forms in an extended language (its approxi... |

1 | Pravato was Born in Venizia (Italia - Alberto - 1997 |