## Interaction Combinators (1995)

Venue: | Information and Computation |

Citations: | 31 - 2 self |

### BibTeX

@ARTICLE{Lafont95interactioncombinators,

author = {Yves Lafont},

title = {Interaction Combinators},

journal = {Information and Computation},

year = {1995},

volume = {137},

pages = {69--101}

}

### OpenURL

### Abstract

This paper is the continuation of the author 's work on interaction nets, inspired by Girard's proof nets for linear logic, but no preliminary knowledge of these topics is required for its reading. Introduction

### Citations

163 |
Interaction nets
- Lafont
- 1990
(Show Context)
Citation Context ...Kxy ! x; Sxyz ! xz(yz): But again, is it reasonable to consider erasing and duplication as atomic operations? Following this tradition of rewrite systems, the interaction nets have been introduced in =-=[Laf90]-=- as a model of distributed computation with local synchronization (section 1). These nets, which are related to the connection graphs of [Baw86], appeared as a generalization of Girard's proof nets fo... |

159 | logic: its syntax and semantics - Linear - 1995 |

119 | An algorithm for optimal lambda calculus reduction
- Lamping
- 1990
(Show Context)
Citation Context ...impler because it uses the same symbols for different purposes. Among the other related systems, let us mention the infinite one introduced by John Lamping for the optimal reduction of -calculus (see =-=[Lam90]-=-) and the variants proposed by Georges Gonthier, Martin Abadi, and Jean-Jacques Levy, in connection with linear logic (see [GAL92a, GAL92b]). Apart from its simplicity, the system of interaction combi... |

100 | Geometry of Interaction I: interpretation of system F - Girard - 1989 |

97 | The geometry of optimal lambda reduction, in - Gonthier, Abadi, et al. - 1992 |

55 | From Proof Nets to Interaction Nets
- Lafont
- 1995
(Show Context)
Citation Context ... sequential computation (section 3). This section benefited from discussions with Vincent Danos and Laurent Regnier. 1 Interaction nets The origin of our favorite model of computation is explained in =-=[Laf95]-=-. Here, it is introduced from scratch, without explicit reference to proof theory. 1.1 Nets From now on, a symbol ff will always be given with its arity ns0. An occurrence of such a symbol is called a... |

53 | Linear logic without boxes - Gonthier, Abadi, et al. - 1992 |

50 | Proof-nets and the Hilbert space
- Danos, Regnier
- 1995
(Show Context)
Citation Context .... 4 Discussion If a netsreduces to a wiring !, one may wonder whether the execution is an efficient algorithm for computing !. This question was already raised by Vincent Danos and Laurent Regnier in =-=[DR95]-=-. They considered a linear - term which corresponds to the following net: fl . . . fl fl fl fl fl Clearly, such a net reduces to a single wire in a linear number of steps, whereas one can show that th... |

13 |
Connection graphs
- Bawden
- 1986
(Show Context)
Citation Context ...e systems, the interaction nets have been introduced in [Laf90] as a model of distributed computation with local synchronization (section 1). These nets, which are related to the connection graphs of =-=[Baw86], appeared-=- as a generalization of Girard's proof nets for linear logic (see [Gir95, Laf95]). By "local synchronization", we mean that there is no need to consider a global time for computation. In oth... |

9 | Combinators for interaction nets
- Gay
- 1995
(Show Context)
Citation Context ...ted system suggested by Samson Abramsky for implementing the proof boxes of linear logic (see [Mac94]). Independently, Simon Gay has also obtained a universal system, with 8 symbols instead of 3 (see =-=[Gay95]-=-). Our system is simpler because it uses the same symbols for different purposes. Among the other related systems, let us mention the infinite one introduced by John Lamping for the optimal reduction ... |

3 |
The Geometry of Implementation (an investigation into using the Geometry of Interaction for language implementation
- Mackie
- 1994
(Show Context)
Citation Context ...m of interaction combinators has been obtained by a kind of distillation, starting from some more complicated system suggested by Samson Abramsky for implementing the proof boxes of linear logic (see =-=[Mac94]-=-). Independently, Simon Gay has also obtained a universal system, with 8 symbols instead of 3 (see [Gay95]). Our system is simpler because it uses the same symbols for different purposes. Among the ot... |