## A game semantics of local names and good variables (2004)

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Venue: | of Lecture Notes in Computer Science |

Citations: | 19 - 4 self |

### BibTeX

@INPROCEEDINGS{Laird04agame,

author = {J. Laird},

title = {A game semantics of local names and good variables},

booktitle = {of Lecture Notes in Computer Science},

year = {2004},

pages = {289--303},

publisher = {Springer}

}

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### Abstract

Abstract. We describe a game semantics for local names in a functional setting. It is based on a category of dialogue games acted upon by the automorphism group of the natural numbers; this allows properties of names such as freshness and locality to be characterized semantically. We describe a model of the nu-calculus in this category, and extend it with named references (without bad variables) using names as pointers to a store. After refining the semantics via a notion of garbage collection, we prove that the compact elements are definable as terms, and hence obtain a full abstraction result. 1 Introduction Local names are a pervasive and subtle feature of programming languages and other calculi. Not only are they used for manipulating important constructs such as locally bound references and exceptions, name-passing is itself a very expressive computational paradigm, as demonstrated by the ss-calculus, for example. Local names can also represent items of secret information which are dynamically generated, passed between agents and used to access further information or activity. They therefore have a key r^ole in specifying properties of secure systems [1, 24].

### Citations

828 | A calculus for cryptographic protocols: The Spi calculus - Abadi, Gordon - 1999 |

218 |
On Full Abstraction for PCF
- Hyland, Ong
- 2000
(Show Context)
Citation Context ...gies to finitary innocent strategies composed with multiple copies of a strategy cell : I → (N ⇀ I + I) ⊙ (I + I ⇀ N). (A strategy is innocent if its behaviour is always determined by the Player view =-=[8, 15]-=-, an innocent strategy is finitary if its set of views is finite.) The cell strategy corresponds to (a lifting of) the cell strategy defined in [2], in the “read component” N ⇀ I + I it returns the la... |

205 | Full abstraction for PCF
- Abramsky, Jagadeesan, et al.
(Show Context)
Citation Context ... naturally to legal sequences. Lemma 1. If A is a ν-arena, then there is a continuous action of G on LA defined π(m1m2 . . . mn) = π(m1)π(m2) . . . π(mn). 2 A similar notion of equivalence is used in =-=[5]-=-, also to preserve parametricity in games with a countable set of labels. The key difference is that in the model of λν! names can be passed between strategies, and so equivalence cannot be described ... |

123 |
A fully abstract games semantics for general references
- Abramsky, Honda, et al.
- 1998
(Show Context)
Citation Context ...it responds to the initial question in A with the initial answer in B. A sequence in which this occurs is said to be total. Our further condition on total strategies is essentially thread independence=-=[4]-=- up to ∼, plus conditions on the introduction and sharing of names across threads. Definition 8. The thread of a total sequence qasb ∈ LA→B is a legal sequence of A → B defined as follows: thread(qasb... |

105 | Linearity, sharing and state: a fully abstract game semantics for Idealized Algol with active expressions
- Abramsky, McCusker
- 1997
(Show Context)
Citation Context ... S (with triple ( ⊙ S, πl, assoc; δ)) is a closed Freyd category and a model of the nu-calculus.sTo interpret assignment and dereferencing we adapt the approach used in previous games models of state =-=[2, 4]-=-; we fix the store object S to be the product of its “write” and “read” methods: S = (N ⊙ N ⇀ I) ⊙ (N ⇀ N) 3 . We define assignment and dereferencing simply in terms of projections from this product: ... |

64 | Call-by-value games - Abramsky, McCusker - 1998 |

63 | Hereditarily sequential functionals
- Nickau
- 1994
(Show Context)
Citation Context ...C[ ] : o of L,sC[M] ⇓ tt if and only if C[N] ⇓ tt. (Where M ⇓ V if M, (0, ⊥) ⇓ V, E for some E.) 3 Games with Names Our notion of game is based on the dialogue games of Hyland and Ong [8] (and Nickau =-=[18]-=-), to which we add structure for manipulating a countable set of names, in the form of an action of the automorphism group of the natural numbers. This generates an equivalence on strategies correspon... |

60 | Game-theoretic analysis of call-by-value computation
- Honda, Yoshida
- 1999
(Show Context)
Citation Context ...name, and how can knowledge of it pass from one to the other? In Section 4 we use our category of games (and constructions for interpreting call-by-value function types developed by Honda and Yoshida =-=[7]-=-) to give a semantics for the nu-calculus. By adding an object corresponding to the store, and using names as pointers to it we are able to give a simple interpretation of the extension with reference... |

56 |
Names and Higher-Order Functions
- Stark
- 1994
(Show Context)
Citation Context ...truct a model of storage in a language without bad variables in which names are pointers to the store. In Section 2 we describe a language with local names based on the nu-calculus of Pitts and Stark =-=[20, 22]-=-. The latter aims to capture the key features of names in a functional setting, in the absence of associated imperative features such as reference cells. Modelling it may thus be considered a first te... |

42 | Categorical models for local names
- Stark
- 1996
(Show Context)
Citation Context ...(σ) : A → B ⇀ C be the least set of legal sequences such that ε, qa ∈ Λ(σ), and if s ∈ Λ(σ), sab is thread-independent with respect to names and φ(thread(sab)) ∈ σ then sab ∈ σ. 4 Semantics of λν! In =-=[23]-=-, Stark describes a notion of categorical model for the nu-calculus. It is based on monadic models of the computational λ-calculus, but transfers readily to the more direct description used here. (Not... |

40 | Logical relations for encryption
- Sumii, Pierce
- 2003
(Show Context)
Citation Context ...secret information which are dynamically generated, passed between agents and used to access further information or activity. They therefore have a key rôle in specifying properties of secure systems =-=[1, 24]-=-. Game semantics has proved successful in characterizing several features with local names, as demonstrated by fully abstract models of functional languages with locally bound references [2–4], except... |

32 | A semantic analysis of control - Laird - 1999 |

28 | Full abstraction for - Abramsky, Jagadeesan, et al. - 2000 |

27 |
A fully abstract game semantics of local exceptions
- Laird
- 2001
(Show Context)
Citation Context ...e semantics has proved successful in characterizing several features with local names, as demonstrated by fully abstract models of functional languages with locally bound references [2–4], exceptions =-=[11]-=- and channels [12]. However, in one respect, these models do not accurately reflect the way these features are implemented; in the game semantics of references (for example), names are taken to repres... |

26 |
and full abstraction for a functional metalanguage with recursive types
- Games
- 1996
(Show Context)
Citation Context ...ce on strategies corresponding to invariance under substitution of names2 . We give brief (and slightly non-standard) definitions of arenas and legal sequences and refer the reader to the literature (=-=[8, 15, 10, 7]-=- etcetera) for more detailed explanation. An (underlying) arena A is a tuple (MA, M I A , λA, ⊢A) consisting of a set of moves MA, a subset M I A ⊆ MA of initial moves, a question/answer labelling λA ... |

23 | Towards a theory of bisimulation for local names
- Jeffrey, Rathke
- 1999
(Show Context)
Citation Context ...able as terms, and that contextual equivalence can therefore be characterized semantically, and for finitary terms, decidably. This development is reminiscent of the observation of Jeffrey and Rathke =-=[9]-=-, that allowing names to in the same language without bad variables. This result highlights how different Idealized Algol is in this respect from call-by-value languages such as ML (for instance we ca... |

22 | Non-deterministic games and program analysis: An application to security - Malacaria, Hankin - 1999 |

21 | The Regular-Language Semantics of Second-order Idealized Algol
- Ghica, McCusker
(Show Context)
Citation Context ... in λν!, based on our games model. It should, for example, be possible to describe the intrinsic equivalence directly, by characterizing equivalent patterns of behaviour in the store. Recent research =-=[6, 19]-=- has succeeded in associating games models of fragments of Idealized Algol with various classes of formal languages, leading to decidability results for observational equivalence. Analogous results ma... |

17 |
On program equivalence in languages with ground-type references
- Murawski
- 2003
(Show Context)
Citation Context ...l equivalence in λν! is not decidable, because for types generated from {o, →} it coincides with that of finitary RML, for which undecidability of observational equivalence has been shown by Murawski =-=[17]-=-. As we have noted in the introduction, there are many areas in which local names play a key rôle, and which might therefore be studied semantically using the approach developed here. Most obviously, ... |

16 |
Polarized games
- Laurent
- 2004
(Show Context)
Citation Context ...nstruct a premonoidal category of games in which to model the call-by-value λ-calculus aspect of λν!. We follow essentially the constructions of Honda and Yoshida [7] or variants described by Laurent =-=[13]-=-. In each case the group action on compound arenas is defined pointwise. The key novelty thus lies in the definition of composition of strategies, since we must maintain distinctness of fresh names. D... |

11 | L.: Observational equivalence of 3rd-order Idealized Algol is decidable
- Ong
(Show Context)
Citation Context ... in λν!, based on our games model. It should, for example, be possible to describe the intrinsic equivalence directly, by characterizing equivalent patterns of behaviour in the store. Recent research =-=[6, 19]-=- has succeeded in associating games models of fragments of Idealized Algol with various classes of formal languages, leading to decidability results for observational equivalence. Analogous results ma... |

8 | sharing and state: a fully abstract game semantics for IDEALIZED ALGOL with active expressions - Linearity - 1997 |

6 |
A game semantics of ICSP
- Laird
- 2001
(Show Context)
Citation Context ...oved successful in characterizing several features with local names, as demonstrated by fully abstract models of functional languages with locally bound references [2–4], exceptions [11] and channels =-=[12]-=-. However, in one respect, these models do not accurately reflect the way these features are implemented; in the game semantics of references (for example), names are taken to represent storage cells,... |

5 |
On the semantics of the bad-variable constructor in Algol-like languages
- McCusker
- 2003
(Show Context)
Citation Context ...ling names themselves is a significant limitation when interpreting languages without ⋆ Supported by EU FET-GC ‘MyThS: Models and Types for Security in Mobile Distributed Systems’ IST-2001-32617 1 In =-=[16]-=-, McCusker has shown that observational equivalence in Idealized Algol with (active expressions and) bad variables is conservative over observational equivalencesbad variables such as ML. It would app... |

4 |
Environments in Freyd categories and κ-categories
- Power, Thielecke
- 1999
(Show Context)
Citation Context ...ral maps πi : A1 ⊙ A2 → Ai and δ : A → A ⊙ A such that δ; πi = idA, δA1⊙A2 ; π1 ⊙ π2 = idA1⊙A2 thread-independent then δA; (f ⊙ f) = f; δB. and if f : A → B is total andsThus we have a Freyd category =-=[21]-=-; a cartesian category νGt, a symmetric premonoidal category νG, and an identity-on-objects strict symmetric premonoidal functor (inclusion) from νGt to νG. Moreover, this is a closed Freyd category. ... |

2 |
Observable features of higher-order functions that dynamically create local names
- Pitts, Stark
- 1993
(Show Context)
Citation Context ...truct a model of storage in a language without bad variables in which names are pointers to the store. In Section 2 we describe a language with local names based on the nu-calculus of Pitts and Stark =-=[20, 22]-=-. The latter aims to capture the key features of names in a functional setting, in the absence of associated imperative features such as reference cells. Modelling it may thus be considered a first te... |