## An investigation into Functions as Processes (1993)

Venue: | In Proc. Ninth International Conference on the Mathematical Foundations of Programming Semantics (MFPS'93 |

Citations: | 11 - 1 self |

### BibTeX

@INPROCEEDINGS{Sangiorgi93aninvestigation,

author = {Davide Sangiorgi},

title = {An investigation into Functions as Processes},

booktitle = {In Proc. Ninth International Conference on the Mathematical Foundations of Programming Semantics (MFPS'93},

year = {1993},

pages = {143--159},

publisher = {Springer Verlag}

}

### Years of Citing Articles

### OpenURL

### Abstract

. In [Mil90] Milner examines the encoding of the -calculus into the ß-calculus [MPW92]. The former is the universally accepted basis for computations with functions, the latter aims at being its counterpart for computations with processes. The primary goal of this paper is to continue the study of Milner's encodings. We focus mainly on the lazy -calculus [Abr87]. We show that its encoding gives rise to a -model, in which a weak form of extensionality holds. However the model is not fully abstract: To obtain full abstraction, we examine both the restrictive approach, in which the semantic domain of processes is cut down, and the expansive approach, in which -calculus is enriched with constants to obtain a direct characterisation of the equivalence on -terms induced, via the encoding, by the behavioural equivalence adopted on the processes. Our results are derived exploiting an intermediate representation of Milner's encodings into the Higher-Order ß-calculus, an !-order extension of ...

### Citations

3202 | Communication and Concurrency - Milner |

995 | A calculus of mobile processes
- Milner, Parrow, et al.
- 1992
(Show Context)
Citation Context ...made of the fully abstract compilation from the Higher-Order -calculus to the -calculus studied in [San92a]. 1 Introduction In [Mil90] Milner examines the encoding of the -calculus into the -calculus =-=[MPW92]-=-; the former is the universally accepted basis for computations with functions, the latter aims at being its counterpart for computations with processes. More precisely, Milner shows how the evaluatio... |

654 | Concurrency and automata on infinite sequences - Park - 1981 |

286 |
The Lambda-Calculus, its Syntax and Semantics, volume 103
- Barendregt
- 1984
(Show Context)
Citation Context ...zig) Theorem3 (full abstraction for C). For each HO agent A 1 and A 2 , it holds that A 1sA 2 iff C[[A 1 ]]sC[[A 2 ]]s3 The lazy -calculus We take for granted the basic concepts of the -calculus (see =-=[Bar84]-=-). We usesfor the class of closed pure -terms and M;N;L to range over . We denote by\Omega the divergent term (x:xx)(x:xx). In Abramsky's lazy -calculus [Abr87], a redex is always at the extreme left ... |

272 | The Polyadic -Calculus: A Tutorial - Milner - 1993 |

258 |
Expressing Mobility in Process Algebras: First-Order and Higher-Order Paradigms
- Sangiorgi
- 1992
(Show Context)
Citation Context ..., an !-order extension of -calculus where also agents may be transmitted. For this, essential use is made of the fully abstract compilation from the Higher-Order -calculus to the -calculus studied in =-=[San92a]-=-. 1 Introduction In [Mil90] Milner examines the encoding of the -calculus into the -calculus [MPW92]; the former is the universally accepted basis for computations with functions, the latter aims at b... |

241 | Typing and subtyping for mobile processes
- Pierce, Sangiorgi
- 1996
(Show Context)
Citation Context ...heless, P 2 yields a precise operational correspondence between -terms and their process encodings and, intuitively, one "expects" P 2 to be correct. Recently, in a collaboration with Benjam=-=in Pierce [PS93]-=- we have studied a stronger sorting discipline than Milner's, in which one distinguishes the ability of using channels of a given sort for performing inputs, outputs or both of them. In this system, w... |

219 | Barbed bisimulation, in
- Milner, Sangiorgi
- 1992
(Show Context)
Citation Context ...el, where conditional extensionality holds. It is not fully abstract, though. To obtain full abstraction we follow two directions: In the restrictive approach, based on the use of barbed bisimulation =-=[MS92]-=-, the semantic domain of processes is cut down; in the expansive approach -calculus is enriched with constants to obtain a direct characterisation of the equivalence on -terms induced, via the encodin... |

170 |
Introduction to Combinators and -Calculus
- Hindley, Seldin
- 1986
(Show Context)
Citation Context ...tion is a function from the set of -variables to the domain D of the - model; [d=x]ae is the valuation which maps x to d and which behaves like ae on the remaining elements. Definition6 (-model, from =-=[HS86]-=-). A -model is a triple ! D; \Delta; M ?, where D is a set with at least two elements, `\Delta' is a mapping from D \Theta D to D and M is a mapping which assigns, to each -term M and valuation ae, a ... |

133 | Full abstraction in the lazy lambda calculus
- Abramsky, Ong
- 1993
(Show Context)
Citation Context ...then applicative bisimulation is the -calculus version of weak barbed congruence. This follows from the characterisation of applicative bisimulation in terms of "convergence in all contexts"=-= given in [AO89]-=-. The classical setting in which the full abstraction problem has been developed is the simply typed -calculus. With the introduction of the operational equivalence resulting from applicative bisimula... |

115 | A calculus of higher order communicating systems - Thomsen - 1989 |

109 |
Fully abstract models of the typed lambda calculus
- Milner
- 1977
(Show Context)
Citation Context ...al extensionality. H[[M ]]hpi + p implies H[[x:Mx]]sH[[M ]], for x 62 fv(M ). Proof: Use Proposition 4 and the definition of the encoding.s6 Full abstraction Full abstraction, first studied by Milner =-=[Mil77]-=- and Plotkin [Plo77], is the problem of finding a denotational interpretation for a programming language such that the resulting semantic equality coincides with a notion of operational indistinguisha... |

60 |
Towards a lambda-calculus for concurrent and communicating systems
- Boudol
- 1989
(Show Context)
Citation Context ...impler encoding than Milner's into -calculus [Mil90]. Indeed, there is a one-to-one correspondence between reductions in -terms and in their HO counterparts. Therefore, following Boudol's terminology =-=[Bou89]-=-, we can claim that lazy -calculus is a subcalculus of HO. Proposition4 (operational correspondence for H). Let M and M 0 be closed -terms. 1: If M \Gamma! M 0 then H[[M ]]hpi \Gamma! H[[M 0 ]]hpi, 2:... |

53 | The lazy lambda calculus in a concurrency scenario
- Sangiorgi
- 1994
(Show Context)
Citation Context ...ry 14 (full abstraction for D). DC is a fully abstract model for the lazy -calculus enriched with constants.sStarting from these results, the study of -observational equivalence has been continued in =-=[San92b]-=-. The outcomes suggest that it is a robust equivalence. First, it enjoys simple operational and denotational characterisations. Secondly it coincides with the equivalence obtained when the -calculus i... |

39 | Domain Theory and the Logic of Observable Properties
- Abramsky
- 1987
(Show Context)
Citation Context ...nctions, the latter aims at being its counterpart for computations with processes. The primary goal of this paper is to continue the study of Milner's encodings. We focus mainly on the lazy -calculus =-=[Abr87]-=-. We show that its encoding gives rise to a -model, in which a weak form of extensionality holds. However the model is not fully abstract: To obtain full abstraction, we examine both the restrictive a... |

36 |
Lambda Calculus Models and Extensionality
- Hindley, Longo
- 1980
(Show Context)
Citation Context ...odings are not equivalent, i.e. H[[L 1 ]] 6 H[[L 2 ]]; however, for all closed N it holds that H[[L 1 fN=xg]]sH[[L 2 fN=xg]]. Therefore D is an example of a -model whose interior is not a -model; see =-=[HL80]-=- for two more examples. Now that we know that D is a -model, we can infer all properties of -models for it; in particular we get that ffl Every provable equation of fi is valid for the encoding, up to... |

24 | A Lambda Calculus for (Strict) Parallel Functions - Boudol - 1994 |

23 |
LCF as a programming language
- Plotkin
- 1977
(Show Context)
Citation Context ...[[M ]]hpi + p implies H[[x:Mx]]sH[[M ]], for x 62 fv(M ). Proof: Use Proposition 4 and the definition of the encoding.s6 Full abstraction Full abstraction, first studied by Milner [Mil77] and Plotkin =-=[Plo77]-=-, is the problem of finding a denotational interpretation for a programming language such that the resulting semantic equality coincides with a notion of operational indistinguishability. Inspired by ... |

13 |
Functions as processes. Research Report 1154, INRIA, Sofia Antipolis
- Milner
- 1990
(Show Context)
Citation Context ...alculus where also agents may be transmitted. For this, essential use is made of the fully abstract compilation from the Higher-Order -calculus to the -calculus studied in [San92a]. 1 Introduction In =-=[Mil90]-=- Milner examines the encoding of the -calculus into the -calculus [MPW92]; the former is the universally accepted basis for computations with functions, the latter aims at being its counterpart for co... |

7 | Call by name, call by value and the -calculus - Plotkin - 1975 |