## Full abstraction for polymorphic pi-calculus. Online edition with proofs (2005)

Venue: | Theoretical Computer Science |

Citations: | 4 - 0 self |

### BibTeX

@ARTICLE{Jeffrey05fullabstraction,

author = {Alan Jeffrey and Julian Rathke},

title = {Full abstraction for polymorphic pi-calculus. Online edition with proofs},

journal = {Theoretical Computer Science},

year = {2005}

}

### OpenURL

### Abstract

Abstract. The problem of finding a fully abstract model for the polymorphic π-calculus was stated in Pierce and Sangiorgi’s work in 1997 and has remained open since then. In this paper, we show that a slight variant of their language has a direct fully abstract model, which does not depend on type unification or logical relations. This is the first fully abstract model for a polymorphic concurrent language. In addition, we discuss the relationship between our work and Pierce and Sangiorgi’s, and show that their conjectured fully abstract model is, in fact, sound but not complete. 1

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Citation Context ...ction for Polymorphic Pi-Calculus 273 3 Equivalences for Asynchronous Polymorphic Pi-Calculus Process equivalence has a long history, including Milner’s [19] bisimulation, Brookes, Hoare and Roscoe’s =-=[4]-=- failures-divergences equivalence, and Hennessy’s [11] testing equivalence. In this paper, we will follow Pierce and Sangiorgi [23] and investigate contextual equivalence on processes [13, 22]. Contex... |

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Citation Context ...cks, but at the cost of complexity.sFull Abstraction for Polymorphic Pi-Calculus 273 3 Equivalences for Asynchronous Polymorphic Pi-Calculus Process equivalence has a long history, including Milner’s =-=[19]-=- bisimulation, Brookes, Hoare and Roscoe’s [4] failures-divergences equivalence, and Hennessy’s [11] testing equivalence. In this paper, we will follow Pierce and Sangiorgi [23] and investigate contex... |

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Citation Context ...n due to reduction closure. The problem of showing processes to be contextually equivalent is not restricted to polymorphic π-calculi, for example this problem comes up in treatments of the λcalculus =-=[2]-=-, monomorphic π-calculus [20] and object languages [1]. The standard solution is to ask for a fully abstract model, which coincides with contextual equivalence, but is hopefully more tractable. The pr... |

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Citation Context ...bject features. In this paper, we will investigate a minimal impure polymorphic language with equality testing, based on Pierce and Sangiorgi’s work [23] on a polymorphic extension of Milner et al.’s =-=[21, 20]-=- π-calculus. Pierce and Sangiorgi have established a sound model for a polymorphic π-calculus, but they only conjectured completeness [23–Sec. 12.2]. In this paper, we develop a sound and complete mod... |

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Citation Context ...cesses to be contextually equivalent is not restricted to polymorphic π-calculi, for example this problem comes up in treatments of the λcalculus [2], monomorphic π-calculus [20] and object languages =-=[1]-=-. The standard solution is to ask for a fully abstract model, which coincides with contextual equivalence, but is hopefully more tractable. The problem of finding fully abstract models of programming ... |

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Citation Context ...bject features. In this paper, we will investigate a minimal impure polymorphic language with equality testing, based on Pierce and Sangiorgi’s work [23] on a polymorphic extension of Milner et al.’s =-=[21, 20]-=- π-calculus. Pierce and Sangiorgi have established a sound model for a polymorphic π-calculus, but they only conjectured completeness [23–Sec. 12.2]. In this paper, we develop a sound and complete mod... |

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Citation Context ...for Asynchronous Polymorphic Pi-Calculus Process equivalence has a long history, including Milner’s [19] bisimulation, Brookes, Hoare and Roscoe’s [4] failures-divergences equivalence, and Hennessy’s =-=[11]-=- testing equivalence. In this paper, we will follow Pierce and Sangiorgi [23] and investigate contextual equivalence on processes [13, 22]. Contextual equivalence has a very natural definition: it is ... |

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Citation Context ...th contextual equivalence, but is hopefully more tractable. The problem of finding fully abstract models of programming languages originates with Milner [18], and was investigated in depth by Plotkin =-=[25]-=- for the functional language PCF. For polymorphic languages, logical relations [27] allow for the construction of fully abstract models [24] but require an induction on type, and so break down in the ... |

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Citation Context ...evidently broken by the addition of impurity and equality testing. Much of the work in finding models of pure polymorphic languages comes in finding appropriate techniques for modelling parametricity =-=[26, 27]-=- to show that programs are completely independent of the instantiations for their type parameters. Such parametricity results are surprisingly strong, and can be used to establish ‘theorems for free’ ... |

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Citation Context ...uivalence The proof of soundness for bisimulation required some non-standard techniques. In comparison, the proof of completeness is quite straightforward, and follows the usual definability argument =-=[11, 9, 15]-=- of showing that for every visible action α, we can find a process R which exactly tests for the ability to perform α. Once we have established definability, completeness follows in a straightforward ... |

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Citation Context ...ave recently shown that a hybrid of context bisimulation and logical relations [30] yields a fully abstract model in the presence of recursive types. The monomorphic first order [20] and higher-order =-=[29]-=- π-calculus have quite simple fully abstract models, but to date the only known models for polymorphic π-calculus have been sound but not complete [23, 3]. We will now show that a very direct treatmen... |

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Citation Context ...and Roscoe’s [4] failures-divergences equivalence, and Hennessy’s [11] testing equivalence. In this paper, we will follow Pierce and Sangiorgi [23] and investigate contextual equivalence on processes =-=[13, 22]-=-. Contextual equivalence has a very natural definition: it is the most generous equivalence satisfying three natural properties: reduction closure (that is, respecting the operational semantics), cont... |

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Citation Context ...iables or type unification would be subtyping with intersection types [6, 28], which ensure that meets exist in the subtype relation. Subtyping with meets are used, for example, by Hennessy and Riely =-=[12]-=- to ensure subject reduction. Intersection types would provide this language with pleasant properties such as principal typing, which it currently lacks, but at the cost of complexity.sFull Abstractio... |

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Citation Context ...and Roscoe’s [4] failures-divergences equivalence, and Hennessy’s [11] testing equivalence. In this paper, we will follow Pierce and Sangiorgi [23] and investigate contextual equivalence on processes =-=[13, 22]-=-. Contextual equivalence has a very natural definition: it is the most generous equivalence satisfying three natural properties: reduction closure (that is, respecting the operational semantics), cont... |

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Citation Context ...g can be surprisingly straightforward. We believe that the techniques discussed here will extend to the polymorphic features of languages such as Java 5.0 [17], and C# 2.0 [7]: F-bounded polymorphism =-=[5]-=-, subtyping, recursive types and object features. In this paper, we will investigate a minimal impure polymorphic language with equality testing, based on Pierce and Sangiorgi’s work [23] on a polymor... |

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Citation Context ... for a fully abstract model, which coincides with contextual equivalence, but is hopefully more tractable. The problem of finding fully abstract models of programming languages originates with Milner =-=[18]-=-, and was investigated in depth by Plotkin [25] for the functional language PCF. For polymorphic languages, logical relations [27] allow for the construction of fully abstract models [24] but require ... |

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Citation Context ...s a model which is sound, but not complete, as we discuss in Section 4. An alternative strategy to either multiple typings for variables or type unification would be subtyping with intersection types =-=[6, 28]-=-, which ensure that meets exist in the subtype relation. Subtyping with meets are used, for example, by Hennessy and Riely [12] to ensure subject reduction. Intersection types would provide this langu... |

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Citation Context ... synchronous input is distinct from the label used for receptivity. 4. We have used a variable-name distinction, and so have used Honda and Yoshida’s definition of observational equivalence [13]. See =-=[8]-=- for a discussion of this issue. 5. Our type system keeps track explicitly of free type variables, rather than treating them implicitly: this makes some of the book-keeping easier, at the cost of some... |

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Citation Context ... polymorphism [5], subtyping, recursive types and object features. In this paper, we will investigate a minimal impure polymorphic language with equality testing, based on Pierce and Sangiorgi’s work =-=[23]-=- on a polymorphic extension of Milner et al.’s [21, 20] π-calculus. Pierce and Sangiorgi have established a sound model for a polymorphic π-calculus, but they only conjectured completeness [23–Sec. 12... |

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Citation Context ...ct models [24] but require an induction on type, and so break down in the presence of recursive types. Sumii and Pierce have recently shown that a hybrid of context bisimulation and logical relations =-=[30]-=- yields a fully abstract model in the presence of recursive types. The monomorphic first order [20] and higher-order [29] π-calculus have quite simple fully abstract models, but to date the only known... |

42 | A fully abstract may testing semantics for concurrent objects - Jeffrey, Rathke - 2002 |

26 | N.: Sequentiality and the pi-calculus
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Citation Context ... outstanding conjecture, by demonstrating their model to be sound but not complete. This is the first sound and complete model for a polymorphic π-calculus: Pierce and Sangiorgi [23] and Honda et al. =-=[3]-=- have established soundness results, but not completeness.s268 A. Jeffrey and J. Rathke a,b,c,d (Names) x,y,z (Variables) n,m ::= a | x (Values) P,Q,R ::= n(�X;�x : �T ) . P | n〈�T ;�n〉|0 | P|Q (Proce... |

23 |
Contextual equivalence for higher-order pi-calculus revisited
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Citation Context ...uivalence The proof of soundness for bisimulation required some non-standard techniques. In comparison, the proof of completeness is quite straightforward, and follows the usual definability argument =-=[11, 9, 15]-=- of showing that for every visible action α, we can find a process R which exactly tests for the ability to perform α. Once we have established definability, completeness follows in a straightforward ... |

12 |
A new type assignment for λ-terms
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Citation Context ...s a model which is sound, but not complete, as we discuss in Section 4. An alternative strategy to either multiple typings for variables or type unification would be subtyping with intersection types =-=[6, 28]-=-, which ensure that meets exist in the subtype relation. Subtyping with meets are used, for example, by Hennessy and Riely [12] to ensure subject reduction. Intersection types would provide this langu... |

3 |
An introduction to logical relations and parametric polymorphism (abstract
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(Show Context)
Citation Context ... and equality testing (such as a == x in this case) can significantly impact the distinguishing power of tests. In the case of pure languages such as System F [10], the technique of logical relations =-=[27, 24]-=- can be used to establish equivalence of all of the above calls to or, which is evidently broken by the addition of impurity and equality testing. Much of the work in finding models of pure polymorphi... |

1 |
ECMA and ISO/IEC c# and common language infrastructure standards
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Citation Context ...nguages with equality testing can be surprisingly straightforward. We believe that the techniques discussed here will extend to the polymorphic features of languages such as Java 5.0 [17], and C# 2.0 =-=[7]-=-: F-bounded polymorphism [5], subtyping, recursive types and object features. In this paper, we will investigate a minimal impure polymorphic language with equality testing, based on Pierce and Sangio... |

1 |
Release notes Java 2 platform standard edition development kit 5.0
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Citation Context ...plete. 1 Introduction Finding sound and complete models for languages with polymorphic types is notoriously difficult. Consider the following implementation of a polymorphic ‘or’ function in Java 5.0 =-=[17]-=-: static<X> X or (X t, X a, X b) { if (a == t) { return a; } else { return b; } } This implementation of or takes a type parameter X, which will be instantiated with the representation chosen for the ... |