### BibTeX

@INPROCEEDINGS{Abramsky96semanticsof,

author = {Samson Abramsky},

title = {Semantics of interaction},

booktitle = {},

year = {1996},

pages = {1},

publisher = {Springer-Verlag}

}

### OpenURL

### Abstract

The “classical ” paradigm for denotational semantics models data types as domains, ��� � structured sets of some kind, and programs as (suitable) functions between domains. The semantic universe in which the denotational modelling is carried out is thus a category with domains as objects, functions as morphisms, and composition of morphisms given by function composition. A sharp distinction is then drawn between denotational and operational semantics. Denotational semantics is often referred to as “mathematical semantics ” because it exhibits a high degree of mathematical structure; this is in part achieved by the fact that denotational semantics abstracts away from the dynamics of computation—from time. By contrast, operational semantics is formulated in terms of the syntax of the language being modelled; it is highly intensional in character; and it is capable of expressing the dynamical aspects of computation. The classical denotational paradigm has been very successful, but has some definite limitations. Firstly, fine-structural features of computation, such as sequentiality,

### Citations

615 | Linear logic
- Girard
- 1987
(Show Context)
Citation Context ...n as refinements of what we present. Some background in category theory, type theory and linear logic would be helpful in reading these notes; suitable references are (Crole 1994)(Girardset al. 1989)(=-=Girard 1995-=-) (which contain much more than we will actually need). Acknowledgements I would like to thank the Edinburgh interaction group (Kohei Honda, Paul-Andre Mellies, Julo Chroboczek, Jim Laird and Nobuko Y... |

352 |
Proofs and Types
- Girard, Lafont, et al.
- 1989
(Show Context)
Citation Context ...g 1995) can be seen as refinements of what we present. Some background in category theory, type theory and linear logic would be helpful in reading these notes; suitable references are (Crole 1994), (=-=Girard et al. 1989-=-), (Girard 1995) (which contain much more than we will actually need). Acknowledgements I would like to thank the Edinburgh “interaction group” (Kohei Honda, Paul-André Melliès, Julo Chroboczek, Jim L... |

209 | Games and full completeness for multiplicative linear logic - Abramsky, Jagadeesan - 1992 |

197 |
On full abstraction for PCF
- Hyland, Ong
(Show Context)
Citation Context ...the recent work on Game semantics, which has led to some striking advances in the Full Abstraction problem for PCF and other programming languages (Abramsky et al. 1995) (Abramsky and McCusker 1995) (=-=Hyland and Ong 1995-=-) (McCusker 1996a) (Ong 1996). Our aim is to give a genuinely elementary first introduction; we therefore present a simplified version of game semantics, which nonetheless 1s2 �������� contains most o... |

122 | Interaction categories and the foundations of typed concurrent programming - Abramsky, Gay, et al. - 1996 |

80 |
Categories for Types
- Crole
- 1993
(Show Context)
Citation Context ...(Hyland and Ong 1995) can be seen as refinements of what we present. Some background in category theory, type theory and linear logic would be helpful in reading these notes; suitable references are (=-=Crole 1994-=-), (Girard et al. 1989), (Girard 1995) (which contain much more than we will actually need). Acknowledgements I would like to thank the Edinburgh “interaction group” (Kohei Honda, Paul-André Melliès, ... |

58 | Hereditarily sequential functionals - Nickau - 1994 |

48 |
Games and full abstraction for a functional metalanguage with recursive types
- McCusker
- 1996
(Show Context)
Citation Context ...e semantics, which has led to some striking advances in the Full Abstraction problem for PCF and other programming languages (Abramsky et al. 1995) (Abramsky and McCusker 1995) (Hyland and Ong 1995) (=-=McCusker 1996-=-a) (Ong 1996). Our aim is to give a genuinely elementary first introduction; we therefore present a simplified version of game semantics, which nonetheless 2 Abramsky contains most of the essential co... |

21 | Specification structures and propositions-as-types for concurrency
- Abramsky, Gay, et al.
- 1995
(Show Context)
Citation Context ...is idea. Before introducing this approach, we make a brief digression to allow the ideas to be presented at an appropriate level of generality. For further references on specification structures see (=-=Abramsky et al. 1996-=-a). Specification Structures with a more subtle notion of type. A specificaOur aim is to “refine” a category tion structure on is given by: a set of “properties over ” for each object of . a relation ... |

19 | and full abstraction for FPC
- McCusker, Games
- 2000
(Show Context)
Citation Context ...e semantics, which has led to some striking advances in the Full Abstraction problem for PCF and other programming languages (Abramsky et al. 1995) (Abramsky and McCusker 1995) (Hyland and Ong 1995) (=-=McCusker 1996-=-a) (Ong 1996). Our aim is to give a genuinely elementary first introduction; we therefore present a simplified version of game semantics, which nonetheless 2 Abramsky contains most of the essential co... |

16 | Games for Recursive Types
- Abramsky, McCusker
- 1994
(Show Context)
Citation Context ... Semantics. We will focus on the recent work on Game semantics, which has led to some striking advances in the Full Abstraction problem for PCF and other programming languages (Abramsky et al. 1995) (=-=Abramsky and McCusker 1995-=-) (Hyland and Ong 1995) (McCusker 1996a) (Ong 1996). Our aim is to give a genuinely elementary first introduction; we therefore present a simplified version of game semantics, which nonetheless 2 Abra... |

5 |
A semantic view of classical proofs
- Ong
- 1996
(Show Context)
Citation Context ...h has led to some striking advances in the Full Abstraction problem for PCF and other programming languages (Abramsky et al. 1995) (Abramsky and McCusker 1995) (Hyland and Ong 1995) (McCusker 1996a) (=-=Ong 1996-=-). Our aim is to give a genuinely elementary first introduction; we therefore present a simplified version of game semantics, which nonetheless 2 Abramsky contains most of the essential concepts. The ... |

4 |
Specification Structures and Propositionsas -Types for Concurrency
- Abramsky, Gay, et al.
- 1996
(Show Context)
Citation Context ...is idea. Before introducing this approach, we make a brief digression to allow the ideas to be presented at an appropriate level of generality. For further references on specification structures see (=-=Abramsky et al. 1996a). Specification St-=-ructures Our aim is to "refine" a category C with a more subtle notion of type. A specification structure on C is given by: ffl a set PA of "properties over A" for each object A of... |

4 | Games and abstract machines - Danos, Herbelin, et al. - 1996 |

1 |
Interaction categories', Marktoberdorf proceedings
- Abramsky, Gay, et al.
- 1996
(Show Context)
Citation Context ...is idea. Before introducing this approach, we make a brief digression to allow the ideas to be presented at an appropriate level of generality. For further references on specification structures see (=-=Abramsky et al. 1996a). Specification St-=-ructures Our aim is to "refine" a category C with a more subtle notion of type. A specification structure on C is given by: ffl a set PA of "properties over A" for each object A of... |

1 |
Full abstraction for PCF', Submitted for publication, ftp-able at theory.doc.ic.ac.uk in directory papers/Malacaria
- Abramsky, Jagadeesan, et al.
- 1995
(Show Context)
Citation Context ...his goal of Intensional Semantics. We will focus on the recent work on Game semantics, which has led to some striking advances in the Full Abstraction problem for PCF and other programming languages (=-=Abramsky et al. 1995-=-) (Abramsky and McCusker 1995) (Hyland and Ong 1995) (McCusker 1996a) (Ong 1996). Our aim is to give a genuinely elementary first introduction; we therefore present a simplified version of game semant... |

1 |
Games and full abstraction for the lazy -calculus', in the LICS'95 proceedings
- Abramsky, McCusker
- 1995
(Show Context)
Citation Context ... Semantics. We will focus on the recent work on Game semantics, which has led to some striking advances in the Full Abstraction problem for PCF and other programming languages (Abramsky et al. 1995) (=-=Abramsky and McCusker 1995-=-) (Hyland and Ong 1995) (McCusker 1996a) (Ong 1996). Our aim is to give a genuinely elementary first introduction; we therefore present a simplified version of game semantics, which nonetheless 2 Abra... |

1 |
On full abstraction for PCF: I, II, and III', submitted for publication, ftp-able at theory.doc.ic.ac.uk in directory papers/Ong
- Hyland, Ong
- 1995
(Show Context)
Citation Context ...the recent work on Game semantics, which has led to some striking advances in the Full Abstraction problem for PCF and other programming languages (Abramsky et al. 1995) (Abramsky and McCusker 1995) (=-=Hyland and Ong 1995-=-) (McCusker 1996a) (Ong 1996). Our aim is to give a genuinely elementary first introduction; we therefore present a simplified version of game semantics, which nonetheless 2 Abramsky contains most of ... |

1 |
Games and full abstraction for the lazy in the LICS’95 proceedings
- Abramsky, McCusker
- 1995
(Show Context)
Citation Context ... Semantics. We will focus on the recent work on Game semantics, which has led to some striking advances in the Full Abstraction problem for PCF and other programming languages (Abramsky et al. 1995) (=-=Abramsky and McCusker 1995-=-) (Hyland and Ong 1995) (McCusker 1996a) (Ong 1996). Our aim is to give a genuinely elementary first introduction; we therefore present a simplified version of game semantics, which nonetheless 1s1 Ga... |

1 | Categories for Types - -calculus’ - 1994 |