## Full Abstraction for Functional Languages with Control (1997)

### Cached

### Download Links

- [www.cogs.susx.ac.uk]
- [www.cs.bath.ac.uk]
- DBLP

### Other Repositories/Bibliography

Venue: | In Proceedings, Twelfth Annual IEEE Symposium on Logic in Computer Science |

Citations: | 69 - 6 self |

### BibTeX

@INPROCEEDINGS{Laird97fullabstraction,

author = {James Laird},

title = {Full Abstraction for Functional Languages with Control},

booktitle = {In Proceedings, Twelfth Annual IEEE Symposium on Logic in Computer Science},

year = {1997},

pages = {58--67},

publisher = {IEEE Computer Society Press}

}

### Years of Citing Articles

### OpenURL

### Abstract

This paper considers the consequences of relaxing the bracketing condition on `dialogue games', showing that this leads to a category of games which can be `factorized' into a well-bracketed substructure, and a set of classically typed morphisms. These are shown to be sound denotations for control operators, allowing the factorization to be used to extend the definability result for PCF to one for PCF with control operators at atomic types. Thus we define a fully abstract and effectively presentable model of a functional language with non-local control as part of a modular approach to modelling non-functional features using games. 1.

### Citations

406 |
LCF considered as a programming language
- Plotkin
- 1977
(Show Context)
Citation Context ... PCF [10],[2] (just using the well-bracketed substructure). To extend this adequacy result to PCF + call=cc, it is sufficient to extend the reducibility style proof of the adequacy of standard models =-=[15]-=-,[3] to the interpretation of call=cc as P eirce in C ' : i.e. to show, in the absence of the Y combinator, that call=cc f:M + m, [[f:M ]]; P eirce = m: Lemma 6.3 (Evaluation contexts) : Let E[] be an... |

205 | Full abstraction for PCF
- Abramsky, Jagadeesan, et al.
(Show Context)
Citation Context ...ed, and no questions asked before it have been answered since it was asked: smtn 2 PAsQA A (m) =sQA A (n) = A ) OE smtn (n)sOE smtn (m): This contrasts with the `well-bracketing condition' applied in =-=[2]-=-, [10], which requires that only the most recently asked open question can be answered. In weakly bracketed games, answering a question closes all of the more recently asked questions as well. This is... |

120 |
A syntactic theory of sequential control
- Felleisen, Friedman, et al.
- 1987
(Show Context)
Citation Context ...spect to a call-by-name operational semantics for PCF in terms of a Martin-Lof style evaluation relation [10]: this can be naturally extended to include call=cc using the notion of evaluation context =-=[8]-=-. Definition 6.1 (Evaluation contexts.) E[] ::= [] j E[]M j IFOE[]MN j call=cc f:E[] j constE[] where const is any constant of PCF. Evaluation contexts serve to pick out subterms which must be evaluat... |

105 | Linearity, sharing and state: a fully abstract game semantics for Idealized Algol with active expressions
- Abramsky, McCusker
- 1997
(Show Context)
Citation Context ...e purely functional behaviour: innocence, well-bracketing and determinacy. A vertex of this cube, at which innocence is lost, allowing Idealized Algol (`PCF with State') to be modelled, is studied in =-=[1]-=-, and the fact that a similar methodology is used there to prove full abstraction (factorization through a morphism which records a history of the play), suggests that this is a fruitful paradigm for ... |

80 | A Curry-Howard foundation for functional computation with control
- Ong, Stewart
- 1997
(Show Context)
Citation Context ...erlined by their types, which are derivable in classical but not intuitionistic logic. This extension to the Curry-Howard correspondence between proofs and programs has been formalised elsewhere [5], =-=[14]-=-; here it suggests that the same basic games model will give a semantics to PCF with a simple escape mechanism, (which can be extended to the higher order control operators) and to proofs of classical... |

64 | Extracting Constructive Content from Classical Proofs - Murthy - 1990 |

54 |
Full abstraction for sequential languages: the state of the art
- Berry, Curien, et al.
- 1985
(Show Context)
Citation Context ...[10],[2] (just using the well-bracketed substructure). To extend this adequacy result to PCF + call=cc, it is sufficient to extend the reducibility style proof of the adequacy of standard models [15],=-=[3]-=- to the interpretation of call=cc as P eirce in C ' : i.e. to show, in the absence of the Y combinator, that call=cc f:M + m, [[f:M ]]; P eirce = m: Lemma 6.3 (Evaluation contexts) : Let E[] be any ev... |

51 | Fully abstract semantics for observably sequential languages
- Cartwright, Curien, et al.
- 1994
(Show Context)
Citation Context ...ding operators which give access to the flow of control to call-byname functional languages using games semantics. Control operators allow programs to use intensional information about their arguments=-=[4]-=-, and PCF augmented with such operators is (arguably) a basis for a notion of sequential computation, as well as a toy `functional language with control'. The extent to which control operators alter t... |

51 |
Games and full abstraction for a functional metalanguage with recursive types
- McCusker
- 1996
(Show Context)
Citation Context ...imply-typed -calculus and PCF; namely, `weakly-well-bracketed' games and innocent strategies. Hence it is easily accommodated within a setting which has been well described elsewhere, particularly in =-=[12]-=-, in which most of these definitions are more comprehensively studied. A game A is a specification of a set of possible plays, i.e. sequences of moves MA , which are alternately made by Opponent and P... |

46 |
A Semantics of Evidence for Classical Arithmetic
- Coquand
- 1995
(Show Context)
Citation Context ...ified in games, and are the same elements which model jumps in the flow of control also gives a way of understanding the computational content of classical reasoning: a similar distinction is used in =-=[6]-=- to extend a games semantics for intuitionistic arithmetic to the classical case by allowing backtracking. The prototypical language PCF has provided a framework in which to study the essential featur... |

33 |
On the symmetry of sequentiality
- CURIEN
- 1993
(Show Context)
Citation Context ...uish between, for instance,s+ l and + r , to achieve this result using Sequential Algorithms. These represent morphisms intensionally as trees, with obvious parallels with various categories of games =-=[7]-=-. However, it was not apparent how the Sequential Algorithms model could be restricted to reflect pure functional behaviour, and hence yield a fully abstract model of PCF itself. Dialogue (and AJM) ga... |

31 | A semantic view of classical proofs: Type-theoretic, categorical, and denotational characterizations
- Ong
- 1996
(Show Context)
Citation Context ... the claim that dropping the bracketing condition gives more than `just another fully abstract model for sPCF'. Extensions of dialogue games to model the -calculus have been considered elsewhere: Ong =-=[13]-=- adds a notion of state, whilst Herbelin [9] suggests the adaptation to the Hyland-Ong framework which is used here: i.e. the relaxation of the bracketing condition, although in the context of a more ... |

29 | On full abstraction for
- Hyland, Ong
- 2000
(Show Context)
Citation Context ...ns may be answered: a question is open if it is unanswered, and no questions asked before it have been answered since it was asked: This contrasts with the ‘well-bracketing condition’ applied in [2], =-=[10]-=-, which requires that only the most recently asked open question can be answered. In weakly bracketed games, answering a question closes all of the more recently asked questions as well. This is in ac... |

28 | Full abstraction for
- Abramsky, Jagadeesan, et al.
- 2000
(Show Context)
Citation Context ...nd no questions asked before it have been answered since it was asked: smtn 2 PAsQA A (m) =sQA A (n) = A ) OE smtn (n)sOE smtn (m): This contrasts with the `well-bracketing condition' applied in [2], =-=[10]-=-, which requires that only the most recently asked open question can be answered. In weakly bracketed games, answering a question closes all of the more recently asked questions as well. This is in ac... |

13 |
Finitary PCF is undecidable
- Loader
- 1996
(Show Context)
Citation Context ...abstract model of sPCF' is effectively presentable. This contrasts with the extensionally fully abstract model of PCF, which is known not to be effectively presentable, as finitary PCF is undecidable =-=[11]-=-. Adding control operators allows intensionally distinct versions of extensionally equal functions to be distinguished - one of the reasons for introducing them in sPCF [4]. Not all of the strategies ... |

3 |
Natural Deduction. Number 3
- Prawitz
- 1965
(Show Context)
Citation Context ...r with which to increment PCF: it denotes the morphism used in the factorization theorem, it can be typed with PCF types, and it has no additional variable bindings to deal with. However, as noted in =-=[16]-=-, adding double negation elimination, (or, equivalently Peirce's law) at atomic types to intuitionistic natural deduction is sufficient to derive classical laws for all arrow types. (The factorization... |

1 |
Games and weak-head reduction for classical logic
- Herbelin
- 1996
(Show Context)
Citation Context ...tion gives more than `just another fully abstract model for sPCF'. Extensions of dialogue games to model the -calculus have been considered elsewhere: Ong [13] adds a notion of state, whilst Herbelin =-=[9]-=- suggests the adaptation to the Hyland-Ong framework which is used here: i.e. the relaxation of the bracketing condition, although in the context of a more syntax-oriented study, in contrast to the pr... |

1 |
Curien andM. Felleisen. Fully abstract semantics for observably sequential languages
- Cartwright, P-L
- 1994
(Show Context)
Citation Context ...ding operators which give access to the flow of control to call-byname functional languages using games semantics. Control operators allow programs to use intensional information about their arguments=-=[4]-=-, and PCF augmented with such operators is (arguably) a basis for a notion of sequential computation, as well as a toy ‘functional language with control’. The extent to which control operators alter t... |