## Symmetry and Interactivity in Programming (2001)

Venue: | Bulletin of Symbolic Logic |

Citations: | 6 - 1 self |

### BibTeX

@INPROCEEDINGS{Curien01symmetryand,

author = {P.-L. Curien},

title = {Symmetry and Interactivity in Programming},

booktitle = {Bulletin of Symbolic Logic},

year = {2001},

pages = {479--513}

}

### OpenURL

### Abstract

We recall some of the early occurrences of the notions of interactivity and symmetry in the operational and denotational semantics of programming languages. We suggest some connections with ludics.

### Citations

688 | On the unity of logic
- Girard
- 1993
(Show Context)
Citation Context ...ching Gentzen's sequent calculus closely and directly, which was a door open to exhibiting more symmetries in syntax [10]. A fundamental new theoretical input of this period was Girard's linear logic =-=[13], whi-=-ch entailed a thorough revisiting of proof theory, but also of the semantics of programming languages. A keyword behind linear logic is \resource consciousness", which in turn may have a declinat... |

609 |
Communicating and Mobile Systems: The π-Calculus
- Milner
- 1999
(Show Context)
Citation Context ...adds its argument to the contents of a fixed register and returns the new value of the register. Interaction is also central in models of concurrent computation such as Milner’s CCS or the π-calculus =-=[26]-=-. There, programs and agents may be active simultaneously but have to synchronize at appropriate points of their execution. The synchronization may involve the transmission of a value, one process bei... |

474 |
The formulae-as-types notion of construction
- Howard
- 1980
(Show Context)
Citation Context ...ion steps of the programs. It turns out that cut-elimination in logic, and normalization in formal semantics of programming languages match closely. It has been remarked by Howard, who pointed out in =-=[18-=-] that there exists a one-to-one correspondence between proofs in natural deduction style and (typed) -terms: this is the celebrated Curry-Howard isomorphism. More recently, Herbelin [17] noticed that... |

261 | A formulae-as-types notion of control
- Griffin
- 1990
(Show Context)
Citation Context ...turn has been influential on the design principles of ludics, or the extension of the Curry/Howard correspondence from pure effect-free programs to ones with effects such as the raising of exceptions =-=[16]-=-. The so-called continuationpassing-style translations developed by computer scientists to capture the meaning of such effects happen to match precisely so-called double-negation translations (from cl... |

226 |
C.H.L.: On full abstraction for PCF
- Hyland, Ong
- 2000
(Show Context)
Citation Context ...hat the observational equivalence for PCF is not eective. As a matter of fact, the game-theoretic models of PCF given in 1994 by Abramsky, Jagadeesan, and Malacaria (AJM), and by Hyland and Ong (H0) [=-=19, 2] oer-=- syntax-free presentations of term-models, and the fully abstract model of PCF is obtained from them by a rather brutal quotient, called \extensional collapse", which gives little more informatio... |

212 | Full abstraction for PCF
- Abramsky, Jagadeesan, et al.
(Show Context)
Citation Context ...hat the observational equivalence for PCF is not eective. As a matter of fact, the game-theoretic models of PCF given in 1994 by Abramsky, Jagadeesan, and Malacaria (AJM), and by Hyland and Ong (H0) [=-=19, 2] oer-=- syntax-free presentations of term-models, and the fully abstract model of PCF is obtained from them by a rather brutal quotient, called \extensional collapse", which gives little more informatio... |

210 | Linear objects: Logical processes with built-in inheritance
- Andreoli, Pareschi
- 1991
(Show Context)
Citation Context ... you discover that there is no room left for it on the shelves... Important transfers inspired by the above lexicon include a revisiting of proof search in logic programming in uenced by linear logic =-=[-=-5], which in turn has been in uential on the design principles of ludics, or the extension of the Curry/Howard correspondence from pure eect-free programs to ones with eects such as the raising of exc... |

186 | The duality of computation
- Curien, Herbelin
- 2000
(Show Context)
Citation Context ...morphism. More recently, Herbelin [17] noticed that -caclulus could be seen as matching Gentzen's sequent calculus closely and directly, which was a door open to exhibiting more symmetries in syntax [=-=10]-=-. A fundamental new theoretical input of this period was Girard's linear logic [13], which entailed a thorough revisiting of proof theory, but also of the semantics of programming languages. A keyword... |

180 | D.B.: Coroutines and networks of parallel processes - Kahn, MacQueen - 1977 |

116 |
Fully abstract models of typed lambda-calculi
- Milner
- 1977
(Show Context)
Citation Context ...full abstraction problem was a very interesting, but poorly specied, problem. One looked for a \domain theory"-like presentation of the fully abstract model which was known to exist and to be uni=-=que [2-=-5]. But what domain-like meant exactly was not really spelled out. In particular, the eectivity criterion came only to light when it was made possible to contrast dierent sorts of game models. Indeed,... |

113 |
Communicating and Mobile Systems: The ⇡-calculus
- Milner
- 1999
(Show Context)
Citation Context ...t adds its argument to the contents of asxed register and returns the new value of the register. Interaction is also central in models of concurrent computation such as Milner's CCS or the -calculus [=-=26]-=-. There, programs and agents may be active simultaneously but have to synchronize at appropriate points of their execution. The synchronization may involve the transmission of a value, one process bei... |

104 |
Geometry of Interaction I: interpretation of Systef F
- Girard
- 1988
(Show Context)
Citation Context ... or references (see [3] for a survey). The whole approach received many insights from the developments of linear logic, and in particular of the geometry-of-interaction interpretation of linear logic =-=[14, 1]-=-. For instance, Lamarche's decomposition of the function space in the model of sequential algorithms allowed me to give a more symmetric presentation of ane sequential algorithms, as pairs of two func... |

85 |
Sequential algorithms on concrete data structures
- Berry, Curien
- 1982
(Show Context)
Citation Context ...ut behaviour of programs. For example, the two above schedules for the logical and function are given dierent interpretations in the model. The insight resulted in the model of sequential algorithms [=-=-=-6], which I presented in 1978 in a Spring School on - calculus in La Ch^atre. In this model, morphisms are not functions but pairs of a function and a computation strategy for it, that species a sched... |

74 | New foundations for the geometry of interaction
- Abramsky, Jagadeesan
- 1994
(Show Context)
Citation Context ... or references (see [3] for a survey). The whole approach received many insights from the developments of linear logic, and in particular of the geometry-of-interaction interpretation of linear logic =-=[14, 1]-=-. For instance, Lamarche's decomposition of the function space in the model of sequential algorithms allowed me to give a more symmetric presentation of ane sequential algorithms, as pairs of two func... |

60 |
Recursive functionals and quantifiers of finite types
- Kleene
- 1959
(Show Context)
Citation Context ...erience of a need to record internal information in addition to the plain underlying functions, and as a matter of fact he essentially built the BerryCurien sequential algorithms at lower order types =-=[21]-=-. In his flourished vocabulary, he modelled higher-order recursive computations as “machines” communicating via “oracles”, or “envelopes” that are handed by the sender and opened by the receiver. In t... |

55 | Game Semantics
- Abramsky, McCusker
- 1999
(Show Context)
Citation Context ...reated a new era in denotational semantics, and the HO presentation of games led to an important classication of some features of sequential programming languages such as control, or references (see [=-=3]-=- for a survey). The whole approach received many insights from the developments of linear logic, and in particular of the geometry-of-interaction interpretation of linear logic [14, 1]. For instance, ... |

52 | Fully abstract semantics for observably sequential languages
- Cartwright, Curien, et al.
- 1994
(Show Context)
Citation Context ...y 8 Sequential algorithms did provide a fully abstract model, not for PCF, but for extensions of PCF with control primitives, as oered in the language CDS, or in PCF extended with an operation catch [=-=-=-9]. The model is eective in the sense that observational equivalence classes can be eectively enumerated, and are evensnite when the base types are themselvessnite (such as the Booleans). Again, this ... |

47 |
A semantics of evidence for classical arithmetic
- Coquand
- 1995
(Show Context)
Citation Context ...ce of programs and processes in computer science. Unfortunately, the dialogue games' school remained at a static, descriptive level. The fullsavour comes when cut-elimination is interpreted as a play =-=[11]-=- (see also below). Computation as interaction From the computer science perspective, the history of the computation-asinteraction paradigm is inseparable from the study of sequentiality. Vuillemin, an... |

34 |
On the symmetry of sequentiality, in
- Curien
- 1993
(Show Context)
Citation Context ...In terms of the discussion above, the two functions take care of 9 the pairs (xc 0 ; output v 0 ) (input x, piece of output (c 0 ; v 0 )) and (xc 0 ; valof c) (\input" c 0 , \output" c), res=-=pectively [8]-=-. Last but not least, we discovered later that Kleene had the same experience of a need to record internal information in addition to the plain underlying functions, and as a matter of fact he essenti... |

32 |
Theory and practice of sequential algorithms: the kernel of the applicative language CDS
- Berry, Curien
- 1985
(Show Context)
Citation Context ...d a computation strategy for it, that species a schedule of interaction of the function with its argument. The model was then turned into syntax, and a programming language called CDS was developped [=-=7]-=-. The operational semantics of the language, which I presented in 1982 in a joint French-US workshop held in Fontainebleau, was { as far as I know { thesrst appearance of the notion of function compos... |

32 | A semantic analysis of control
- Laird
- 1999
(Show Context)
Citation Context ...e. The logicians have shown that Booleans can be dened in second-order logic as 8 X X ! (X ! X). It was observed by Laird that there exists a suitable game o for which o ! (o ! o) is isomorphic to B [=-=22]-=-. To begin, note that this is not true with usual domains: either X consists of just ?, and then X ! (X ! X) is also a singleton (the map that sends ? and ? to ?), or X has at least one non-bottom ele... |

29 |
Dialogues as a foundation for intuitionistic logic
- Felscher
- 1986
(Show Context)
Citation Context ...(con uence and normalization). Proofs can be given a \dialogue-game" interpretation, and are then called strategies. This wassrst observed by Lorenzen and his coworkers in the earlysfties (see e=-=.g. [12-=-]). Under this interpretation, a formula is checked for correctness through a dialogue between an opponent who doubts some formulas, and the player who justies his proof step-bystep by exhibiting the ... |

26 |
Domains and Lambda-Calculi
- Amadio, Curien
- 1998
(Show Context)
Citation Context ...ity. Vuillemin, and Milner have given thesrst denotational denitions of a sequential function, which were later generalized by Kahn and Plotkin to the framework of concrete data structures (see e.g. [=-=4]-=-). Intuitively, a sequential function is one for which a sequential schedule can be given. The best way to grasp it more exactly is to think of a sequential function as one of the programs in a system... |

16 |
A formulae-as-types notion of control
- Grin
- 1990
(Show Context)
Citation Context ...in turn has been in uential on the design principles of ludics, or the extension of the Curry/Howard correspondence from pure eect-free programs to ones with eects such as the raising of exceptions [1=-=6-=-]. The so-called continuation2 passing-style translations developed by computer scientists to capture the meaning of such eects happen to match precisely so-called double-negation translations (from c... |

12 |
Séquents qu’on calcule, Thèse de Doctorat, Université Paris 7, available from http://pauillac.inria.fr/˜herbelin
- Herbelin
- 1995
(Show Context)
Citation Context ...inted out in [18] that there exists a one-to-one correspondence between proofs in natural deduction style and (typed) -terms: this is the celebrated Curry-Howard isomorphism. More recently, Herbelin [=-=17-=-] noticed that -caclulus could be seen as matching Gentzen's sequent calculus closely and directly, which was a door open to exhibiting more symmetries in syntax [10]. A fundamental new theoretical in... |

6 |
games and linear logic, manuscript
- Lamarche, Sequentiality
- 1992
(Show Context)
Citation Context ...tivity criterion came only to light when it was made possible to contrast dierent sorts of game models. Indeed, the model of sequential algorithms was given a game-theoretic presentation by Lamarche [=-=2-=-3]: the main dierence with the AJM and HO models lies in the denition of the ! connective, which is set-based for sequential algorithms (whence itssnitary character) and multiset-based for the AJM and... |

5 |
The formulae-as-types notion of construction. In To h. b. curry: Essays on combinatory logic, lambda calculus and formalism (pp. 480–490
- Howard
- 1980
(Show Context)
Citation Context ...ion steps of the programs. It turns out that cut-elimination in logic, and normalization in formal semantics of programming languages match closely. It has been remarked by Howard, who pointed out in =-=[18]-=- that there exists a one-to-one correspondence between proofs in natural deduction style and (typed) λ-terms: this is the celebrated Curry-Howard isomorphism. More recently, Herbelin [17] noticed that... |

2 |
Recursive Functionals and Quanti of Finite Types Revisited
- Kleene
- 1985
(Show Context)
Citation Context ...erience of a need to record internal information in addition to the plain underlying functions, and as a matter of fact he essentially built the BerryCurien sequential algorithms at lower order types =-=[21]. In hissourish-=-ed vocabulary, he modelled higher-order recursive computations as \machines" communicating via \oracles", or \envelopes" that are handed by the sender and opened by the receiver. In the... |

1 |
Finitary PCF is undecidable, manuscript
- Loader
- 1996
(Show Context)
Citation Context ... the base types are themselvessnite (such as the Booleans). Again, this full abstraction result was not the intended goal: we wanted a fully abstract model of PCF for short. But Loader's later result =-=[24-=-] settled the question negatively: he showed that the observational equivalence for PCF is not eective. As a matter of fact, the game-theoretic models of PCF given in 1994 by Abramsky, Jagadeesan, and... |