## Games and definability for system F (1997)

Venue: | In 12th LICS |

Citations: | 15 - 1 self |

### BibTeX

@INPROCEEDINGS{Hughes97gamesand,

author = {Dominic J. D. Hughes},

title = {Games and definability for system F},

booktitle = {In 12th LICS},

year = {1997},

pages = {76--86},

publisher = {IEEE}

}

### Years of Citing Articles

### OpenURL

### Abstract

We present a game-theoretic model of the polymorphic λ-calculus, system F, as a fibred category. Every morphism σ of the model defines an η-expanded, β-normal form ˆσ of system F whose interpretation is σ. Thus the model gives a precise, non-syntactic account of the calculus. 1

### Citations

1115 |
The Lambda Calculus: Its Syntax and Semantics
- Barendregt
- 1981
(Show Context)
Citation Context ...n of 2-reference which relates 2-arenas back to previous 1-arenas? A long-term objective is to try and adapt the modelling techniques used in this paper in order to conquer every vertex of the λ-cube =-=[Bar84]-=-. Acknowledgements Many thanks to Luke Ong, who originally suggested polymorphism as a thesis topic in March 1996. Also to Martin Hyland, Ralph Loader and Guy McCusker for helpful discussions and comm... |

104 |
Proofs and types. Cambridge Tracts
- Girard, Lafont, et al.
- 1989
(Show Context)
Citation Context ...listY )). The notation is designed according to the intuition that this type is a “product” indexed by X and Y ranging over all possible types. A key tool for the analysis of polymorphism is system F =-=[Gir89]-=-, which is the simply-typed λ-calculus extended by quantification over type variables, as above. Models of system F do not come about easily. The impredicative nature of the definition of T, that T it... |

80 |
Categories for Types
- Crole
- 1993
(Show Context)
Citation Context ...me about easily. The impredicative nature of the definition of T, that T itself is in the range of X and Y , raises problems for the semanticist. The two standard classes of models are the PER models =-=[Cro93]-=-, and the domain models [CGW89]. Recent advances in our understanding of the nature of sequential computation were made through the paradigm of modelling term(term) application intensionally, by inter... |

58 | Hereditarily sequential functionals - Nickau - 1994 |

36 | Semantics of Interaction
- Abramsky
- 1997
(Show Context)
Citation Context ...tion of the long-standing full abstraction problem for PCF [AJM94, HO94, Nic94]. In this paper we present a games model for 1���� �� ���� �� system F. A games model for polymorphism was presented in =-=[Abr95]-=-. The new concept in our approach is that we model not only term(term) application intensionally, but also term(type) application; interaction occurs not only through the communication of basic data t... |

34 | Domain theoretic models of polymorphism
- Coquand, Gunter, et al.
- 1989
(Show Context)
Citation Context ...ive nature of the definition of T, that T itself is in the range of X and Y , raises problems for the semanticist. The two standard classes of models are the PER models [Cro93], and the domain models =-=[CGW89]-=-. Recent advances in our understanding of the nature of sequential computation were made through the paradigm of modelling term(term) application intensionally, by interaction between function and arg... |

23 |
An introduction to fibrations, topos theory, the effective topos and modest sets. Lecture
- Phoa
(Show Context)
Citation Context ...ion of the adjunction is trivial because the first 2n+3 moves of any sequence on ∀n(A) are a simple permutation of start(A,n + 1). This structure provides an interpretation of system F as detailed in =-=[Pho]-=-. We now present a lemma which will help us to construct our model F. The proof is by structural induction on normal forms. Lemma 4 Every normal form is interpreted in G as a winning strategy. The pro... |

1 | Full abstraction for PCF (extended abstract). Number 789 - Abramsky, Jagadeesan, et al. - 1994 |

1 |
On Full Abstraction for PCF: I, II and III. ftp-able at ftp.comlab.ox.ac.uk
- Hyland, Ong
- 1994
(Show Context)
Citation Context ...data tokens, but also by the direct exchange of types themselves. A type is modelled as a first-order polymorphic arena, the analogue for system F of the computational arena of Hyland and Ong for PCF =-=[HO94]-=- 1 . A second-order polymorphic arena is an arena which has first-order polymorphic arenas as moves. The HO notion of a justified sequence of moves is enriched to a structure which we call a located s... |

1 |
polymorphism and parametricity
- Games
(Show Context)
Citation Context ... The generic object is a(⋆1) ∈ G1. 3 As stated here in the informal outline of the fibration, composition is only associative up to ∼. Further technical details are to be found in the author’s thesis =-=[Hug]-=-. 10Cartesian maps are based on a form of copy-cat strategy. Indexed products are provided by universal quantification of 1-arenas, and the verification of the adjunction is trivial because the first... |

1 | Games and Full Abstraction for FPC. LiCS - McCusker - 1996 |