## SProc Categorically (1994)

Venue: | in: Proceedings CONCUR'94 (Springer-Verlag |

Citations: | 7 - 2 self |

### BibTeX

@INPROCEEDINGS{Cockett94sproccategorically,

author = {J.R.B. Cockett and D. A. Spooner},

title = {SProc Categorically},

booktitle = {in: Proceedings CONCUR'94 (Springer-Verlag},

year = {1994},

publisher = {Springer-Verlag}

}

### Years of Citing Articles

### OpenURL

### Abstract

. We provide a systematic reconstruction of Abramsky's category SProc of synchronous processes [Abr93]: SProc is isomorphic to a span category on a category of traces. The significance of the work is twofold: It shows that the original presentation of SProc in mixed formulations is unnecessary --- a simple categorical description exists. Furthermore, the techniques employed in the reconstruction suggest a general method of obtaining process categories with structure similar to SProc. In particular, the method of obtaining bisimulation equivalence in our setting, which represents an extension of the work of Joyal, Nielsen and Winskel [JNW93], has natural application in many settings. 1 Introduction In [Abr93], Abramsky proposed a new paradigm for the semantics of computation, interaction categories, where the following substitutions are made: Denotational semantics Categories Interaction categories Domains objects Interface specifications Continuous functions maps Commun...

### Citations

313 |
Calculi for synchrony and asynchrony
- Milner
- 1983
(Show Context)
Citation Context ...ization trees p 2 ST \Sigma A \Theta\Sigma B such that: fst (traces(p)) ` SAssnd (traces(p)) ` SB : \Delta Composition is given by a combination of synchronous product and restriction, following SCCS =-=[Mil83]-=-: p; q = f((a; c); p 0 ; q 0 ) j 9b: p (a;b) \Gamma!p 0sq (b;c) \Gamma!q 0 g: \Delta Identities are synchronous buffers, or wires, through which information flows unchanged instantaneously: 1A = f((a;... |

209 | Games and full completeness for multiplicative linear logic
- Abramsky, Jagadeesan
- 1992
(Show Context)
Citation Context ...d composition is given by interaction. The category is presented in the style of a linear type theory emphasizing the similarity to other examples of interaction categories (e.g. Games and Strategies =-=[AJ92]-=-). Linear negation ? and multiplicative conjunction\Omega are defined on the objects (types) of SProc, inducing multiplicative disjunction A \Phi B def = (A ?\Omega B ? ) ? and linear implication A \G... |

201 | Non-Well-Founded Sets - Aczel - 1988 |

112 | Introduction to distributive categories
- Cockett
- 1993
(Show Context)
Citation Context ..., and the property that in the following diagram (2) (1) B A+B A Y Z X b 1 b 0 y x (1) and (2) are pullbacks exactly when the top row is a coproduct (see Carboni, Lack and Walters [CLW92], or Cockett =-=[Coc93]-=-). It is important to realize that, foundationally, this is all the structure that is required: although we shall need some extra ingredients to carry through the subsequent construction of processes,... |

92 |
Introduction to extensive and distributive categories
- Carboni, Lack, et al.
- 1993
(Show Context)
Citation Context ...s, finite coproducts, and the property that in the following diagram (2) (1) B A+B A Y Z X b 1 b 0 y x (1) and (2) are pullbacks exactly when the top row is a coproduct (see Carboni, Lack and Walters =-=[CLW92]-=-, or Cockett [Coc93]). It is important to realize that, foundationally, this is all the structure that is required: although we shall need some extra ingredients to carry through the subsequent constr... |

75 |
Cartesian Bicategories I
- Carboni, Walters
- 1987
(Show Context)
Citation Context ...SProc is the resulting process category. The relationship of interaction categories to span categories is already implicit in Abramsky's work when he refers to the bicategories of Carboni and Walters =-=[CW87]-=-. We maintain that the explicit reconstruction of this aspect of SProc is of considerable interest as it indicates much more clearly the categorical foundation required. 2 SProc Recounted Abramsky pre... |

36 | Bisimulation and open maps
- Joyal, Nielsen, et al.
- 1993
(Show Context)
Citation Context ...ess categories with structure similar to SProc. In particular, the method of obtaining bisimulation equivalence in our setting, which represents an extension of the work of Joyal, Nielsen and Winskel =-=[JNW93]-=-, has natural application in many settings. 1 Introduction In [Abr93], Abramsky proposed a new paradigm for the semantics of computation,sinteraction categories, where the following substitutions are ... |

20 |
Interaction categories (extended abstract
- Abramsky
- 1993
(Show Context)
Citation Context ... of Calgary, Department of Computer Science, 2500 University Drive N.W., Calgary, Canada T2N 1N4 Abstract. We provide a systematic reconstruction of Abramsky's categorysSProc of synchronous processes =-=[Abr93]-=-: SProc is isomorphic to a span category on a category of traces. The significance of the work is twofold: It shows that the original presentation of SProc in mixed formulations is unnecessary --- a s... |

11 |
A compositional proof system on a category of labelled transition systems
- Winskel
- 1990
(Show Context)
Citation Context ...sive category C, we define the category T ran(C) as the category of models in C of the following sketch: S SSS 1 R s 0 r T ran(Set) is the category of labelled transition systems presented by Winskel =-=[Win87]-=-: the objects are structures (\Sigma; S; s 0 2 S; R ` S \Theta \Sigma \Theta S) and morphisms A \Gamma! B are pairs of functions (oe : SA \Gamma! SB ;s: \Sigma A \Gamma! \Sigma B ) which preserve tran... |

7 |
A formalism for the specification of essentially algebraic structures
- Power, Wells
- 1992
(Show Context)
Citation Context ...hose maps f : A \Gamma! B are pairs (f \Sigma ; f S ) for which S B * S A * S B S A f S * f S commutes. T race(C) may be viewed as the category of models of a higher-order sketch (see Power and Wells =-=[PW92]-=-) involving the list functor in C. It is perhaps unexpected to find that: Proposition 3.2 T race(C) is a lextensive category. Proof. Initial and final objects are given by ffl 0 : 1 \Gamma! 0 and id 1... |

5 | Games and full abstraction for PCF: Preliminary announcement
- Abramsky, Jagadeesan, et al.
- 1993
(Show Context)
Citation Context ...ry, had an immediate effect. The problem of finding fully abstract models for programming languages --- a problem that had dogged the semantics community for two decades --- suddenly became tractable =-=[AJM93]-=-: game theoretic interaction categories could be constructed in a relatively straightforward manner to capture the key operational aspects of computation. It was a construction that had eluded the cla... |

2 |
List-arithmetic open categories: Locoi
- Cockett
- 1990
(Show Context)
Citation Context ...roc is to construct a category whose objects are trace specifications and whose maps are simply homomorphisms. We show how this can be done for lextensive categories with list arithmetic (see Cockett =-=[Coc90]-=-). A lextensive category has finite limits, finite coproducts, and the property that in the following diagram (2) (1) B A+B A Y Z X b 1 b 0 y x (1) and (2) are pullbacks exactly when the top row is a ... |

1 |
Constructing and verifying typed processes. Available by FTP
- Abramsky, Gay, et al.
- 1993
(Show Context)
Citation Context ...dard models for interleaved concurrency. It does, however, illustrate a considerable latitude in the choice of starting point when constructing a specific process category. Abramsky's category ASProc =-=[AGN93]-=- is similarly obtained. In this setting, the monads of delay occur at the level of the base category T race(C), DT ran(C), or T ran(C). These monads are special in that the associated Kleisli categori... |

1 |
The category of Protocols. Presented at Dagstuhl
- Cockett, Spooner
- 1993
(Show Context)
Citation Context ...odified transition system. 2 The functors and natural transformations involved belong to Cov. The methods described in this paper may also be applied to obtain rather different interaction categories =-=[CS93]-=-. For example, categories of games and strategies [AJ92] can be obtained as a restricted process category of a basic category of games and homomorpisms --- the restriction concerns the legs of the spa... |