## Full abstraction for HOPLA (2003)

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Venue: | In Proc. CONCUR’03, LNCS |

Citations: | 8 - 4 self |

### BibTeX

@INPROCEEDINGS{Nygaard03fullabstraction,

author = {Mikkel Nygaard and Glynn Winskel},

title = {Full abstraction for HOPLA},

booktitle = {In Proc. CONCUR’03, LNCS},

year = {2003},

pages = {2761},

publisher = {Springer Verlag}

}

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### Abstract

### Citations

3400 | Communicating Sequential Processes
- Hoare
- 1985
(Show Context)
Citation Context ...hing power of the notion of computation path underlying the presheaf semantics (in contrast to the distinguishing power of the presheaf structure itself). Path semantics is similar to trace semantics =-=[10]-=- in that processes denote downwards-closed sets of computation paths and the corresponding notion of process equivalence, called path equivalence, isgivenby equality of such sets; computation paths, h... |

493 | Algebraic laws for nondeterminism and concurrency
- Hennessy, Milner
- 1985
(Show Context)
Citation Context ...path equivalence and show that this coincides with logical equivalence for a fragment of Hennessy-Milner logic which is characteristic for simulation equivalence in the case of image-finite processes =-=[8]-=-. To increase the expressiveness of HOPLA (for example, to include the type used in [24] for CCS with late value-passing), while still ensuring that every operation in the language has a canonical sem... |

259 |
Domains for denotational semantics
- Scott
- 1982
(Show Context)
Citation Context ...ple with j-component µj � T. � T, and confuse a closed expression for a path order with the path order itself. Simultaneous recursive equations for path orders can be solved using information systems =-=[21, 12]-=-. Here, it will be convenient to give a concrete, inductive characterisation based on a language of paths: p, q ::= P ↦→ q | βp | P | abs p. (16) Above, P ranges over finite sets of paths. We use P ↦→... |

239 |
The Formal Semantics of Programming Languages
- Winskel
- 1993
(Show Context)
Citation Context ...e “operationally realised” by t. Because of recursive types, these relations cannot be defined by structural induction on the type P and we therefore employ a trick essentially due to Martin-Löf (see =-=[23]-=-, Ch. 13). We define auxiliary relations pɛP tbetween paths p : P and closed terms t of type P, by induction on the structure of p: X �P t ⇐⇒def ∀p ∈ X. p ɛP t P ↦→ qɛP→Qt⇐⇒def ∀u. (P �P u =⇒ qɛQtu) β... |

189 | A calculus of mobile processes, parts
- Milner, Parrow, et al.
- 1992
(Show Context)
Citation Context ... of mobility, in particular that present in the ambient calculus with public names [3, 19]. Another kind of mobility, mobility of communication links, arises from name-generation as in the π-calculus =-=[14]-=-. Inspired by HOPLA, Francesco Zappa Nardelli and GW have defined a higher-order process language with name-generation, allowing encodings of full ambient calculus and π-calculus. Bisimulation propert... |

170 |
Winskel G, Petri nets, event structures and domains
- Nielsen, Plotkin
- 1980
(Show Context)
Citation Context ...the empty path set, the inactive process, written ∅. A second important property of � P is that any X ∈ � P is the join of certain “prime” elements below it; � P is a prime algebraic complete lattice =-=[16]-=-. Primes are down-closures yPp = {p ′ : p ′ ≤P p} of individual elements p ∈ P, representing a process that may perform the computation path p. ThemapyP reflects as well as preserves order, so that p ... |

162 | Anytime, anywhere. Modal logics for mobile ambients
- Cardelli, Gordon
- 2000
(Show Context)
Citation Context ...e obtained here. Being a higher-order process language, HOPLA allows process passing and so can express certain forms of mobility, in particular that present in the ambient calculus with public names =-=[3, 19]-=-. Another kind of mobility, mobility of communication links, arises from name-generation as in the π-calculus [14]. Inspired by HOPLA, Francesco Zappa Nardelli and GW have defined a higher-order proce... |

128 |
Lambda Calculus Models of Programming Languages
- Morris
- 1968
(Show Context)
Citation Context ...Γ, P)-program context C is a term with holes into which a term t with Γ ⊢ t : P may be put to form a program ⊢ C(t) :!O. The denotational semantics gives rise to a type-respecting contextual preorder =-=[15]-=-: Definition 6. Suppose Γ ⊢ t1 : P and Γ ⊢ t2 : P. We say that t1 and t2 are related by contextual preorder, written t1 ❁ ∼ t2, iff for all (Γ, P)-program contexts C, we have �C(t1)� �= ∅ =⇒ �C(t2)� �... |

120 |
Bisimilarity as a theory of functional programming
- Gordon
- 1995
(Show Context)
Citation Context ...constructor contexts: application, projection, and unfolding. This explains the somewhat mysterious function space actions u ↦→ a. A similar use of labels to carry context information appears e.g. in =-=[6]-=-. Soundness says that the operational notion of “successor” is included in the semantic notion. The proof is by rule induction on the transition rules, see [20]. Proposition 10 (Soundness). If P : t a... |

116 | Bisimulation from open maps
- Joyal, Nielsen, et al.
- 1996
(Show Context)
Citation Context ...t1) ! −→ =⇒ C(t2) ! −→. 4.3 Simulation The path semantics does not capture enough of the branching behaviour of processes to characterise bisimilarity (for that, the presheaf semantics is needed, see =-=[11, 19]-=-). As an example, the processes !∅ +!!∅and !!∅ have the same denotation, but are clearly not bisimilar. However, using Hennessy-Milner logic we can link path equivalence to simulation. In detail, we c... |

102 | Linear logic, *-autonomous categories and cofree coalgebras
- Seely
- 1989
(Show Context)
Citation Context ... the category with path orders P, Q,... as objects and join-preserving maps � P → � Q as arrows. It turns out Lin has enough structure to be understood as a categorical model of Girard’s linear logic =-=[5, 22]-=-. Accordingly, we’ll call arrows of Lin linear maps. Linear maps are represented by elements of P�op × Q and so by downwardsclosed subsets of the order Pop × Q. This relational presentation exposes an... |

94 | A Mixed Linear and Non-Linear Logic: Proofs, Terms and Models
- Benton
- 1995
(Show Context)
Citation Context ...an closed, as is well known. The adjunction between Lin and Cts now satisfies the conditions put forward by Benton for a categorical model of intuitionistic linear logic, strengthening those of Seely =-=[1, 22]-=-; see also [13] for a recent survey of such models. 3 Denotational Semantics HOPLA is directly suggested by the structure of Cts. The language is typed with types given by the grammar T ::= T1 → T2 | ... |

90 | Full abstraction for a simple parallel programming language
- HENNESSY, PLOTKIN
- 1979
(Show Context)
Citation Context ...f as a domain of meanings of processes of type P. The poset � P has many interesting properties. First of all, it is a complete lattice with joins given by union. In the sense of Hennessy and Plotkin =-=[7]-=-, � P is a “nondeterministic domain”, with joins used to interpret nondeterministic sums of processes. Accordingly, given a family (Xi)i∈I of elements of � P, we sometimes write Σi∈IXi for their join.... |

53 |
Using Information Systems to Solve Recursive Domain Equations
- Larsen, Winskel
- 1991
(Show Context)
Citation Context ...ple with j-component µj � T. � T, and confuse a closed expression for a path order with the path order itself. Simultaneous recursive equations for path orders can be solved using information systems =-=[21, 12]-=-. Here, it will be convenient to give a concrete, inductive characterisation based on a language of paths: p, q ::= P ↦→ q | βp | P | abs p. (16) Above, P ranges over finite sets of paths. We use P ↦→... |

45 |
A fully abstract denotational model for higher-order processes
- Hennessy
- 1993
(Show Context)
Citation Context ...subsumed by the contexts above. Thus, if t1 ❁ ∼ L t2, then �t1�⊆�t2�and so t1 ❁ ∼ t2 by full abstraction. ⊓⊔ 5 Related and Future Work Matthew Hennessy’s fully abstract semantics for higher-order CCS =-=[9]-=- is a path semantics, and what we have presented here can be seen as a generalisation of his work via the translation of higher-order CCS into HOPLA, see [19]. The presheaf semantics originally given ... |

33 | A Presheaf Semantics of Value-Passing Processes
- Winskel
- 1996
(Show Context)
Citation Context ...f Hennessy-Milner logic which is characteristic for simulation equivalence in the case of image-finite processes [8]. To increase the expressiveness of HOPLA (for example, to include the type used in =-=[24]-=- for CCS with late value-passing), while still ensuring that every operation in the language has a canonical semantics, we decompose the “prefixsum” type Σα∈Aα.Pα in [19] into a sum type Σα∈APα and an... |

26 | An Axiomatic Approach to Adequacy
- Bräuner
- 1996
(Show Context)
Citation Context ...th order O. The term-formation rules are displayed below alongside their interpretations as constructors on maps of Cts, taking the maps denoted by the premises to that denoted by the conclusion (cf. =-=[2]-=-). We assume that the variables in any environment list which appears are distinct. Structural rules. The rules handling environment lists are given as follows: x : P ⊢ x : P P 1P −→ P Γ ⊢ t : Q Γ, x ... |

23 | Categorical models of linear logic revisited, to appear
- Melliès
- 2009
(Show Context)
Citation Context ...l. Moreover, k and m commute with the associativity, symmetry and unit maps of Lin and Cts, such as s Lin P,Q : P × Q ∼ = Q × P and r Cts Q : Q & O ∼ = Q, making ! symmetric monoidal. It then follows =-=[13]-=- that the inclusion Lin ↩→ Cts is symmetric monoidal as well, and that the unit and counit are monoidal transformations. Thus, there are maps l : O → and nP,Q : P & Q → P × Q (11) in Cts, withnnatural... |

23 | Domain theory for concurrency
- Nygaard, Winskel
- 2004
(Show Context)
Citation Context ...p −−→ Tj[µ � T. � T/ � T] (30) (31) 3.1 Useful Equivalences We provide some technical results about the path semantics which are used in the proof of soundness, Proposition 10. Proofs can be found in =-=[20]-=-. Lemma 1 (Substitution). Suppose Γ, x : P ⊢ t : Q and Λ ⊢ u : P with Γ and Λ disjoint. Then Γ, Λ ⊢ t[u/x] :Qwith denotation given by the composition �t� ◦ (1Γ & �u�). Corollary 2. If Γ, x : P ⊢ t : P... |

16 | logic. Theoretical Computer Science - Linear - 1987 |

14 |
open maps and bisimulation
- Cattani, Winskel, et al.
- 2005
(Show Context)
Citation Context ..., higher-order CCS and mobile ambients with public names. The language came out of work on a linear domain theory for concurrency, based on a categorical model of linear logic and associated comonads =-=[4, 18]-=-, the comonad used for HOPLA being an exponential ! of linear logic. The denotational semantics given in [19] interpreted processes as presheaves. Here we consider a “path semantics” for HOPLA which a... |

13 | Linearity in process languages
- Nygaard, Winskel
- 2002
(Show Context)
Citation Context ..., higher-order CCS and mobile ambients with public names. The language came out of work on a linear domain theory for concurrency, based on a categorical model of linear logic and associated comonads =-=[4, 18]-=-, the comonad used for HOPLA being an exponential ! of linear logic. The denotational semantics given in [19] interpreted processes as presheaves. Here we consider a “path semantics” for HOPLA which a... |

12 | A higher-order process language
- Nygaard, Winskel
(Show Context)
Citation Context ... respect to computation paths; and simple proofs of soundness and adequacy shows correspondence between the denotational and operational semantics. 1 Introduction HOPLA (Higher-Order Process LAnguage =-=[19]-=-) is an expressive language for higher-order nondeterministic processes. It has a straightforward operational semantics supporting a standard bisimulation congruence, and can directly encode calculi l... |

12 | Profunctors, open maps, and bisimulation - Cattani, Winskel |

5 | Towards an Operational Understanding of Presheaf Models
- Nygaard
- 2001
(Show Context)
Citation Context ...affine linear logic and an affine version of HOPLA, again with a fully abstract path semantics [20]. The tensor operation of Aff can be understood as a simple parallel composition of event structures =-=[17]-=-. Thus, the affine language holds promise of extending our approach to “independence” models like Petri nets or event structures in which computation paths are partial orders of events. Work is in pro... |

1 | A Model for Communicating Sequential Processes - Information, Computation - 1994 |