## An internal language for interaction categories (1995)

Venue: | In Theory and Formal Methods 1994: Proceedings of the Second Imperial College Department of Computing Workshop on Theory and Formal Methods. Imperial |

Citations: | 3 - 0 self |

### BibTeX

@INPROCEEDINGS{Gay95aninternal,

author = {Simon Gay and Rajagopal Nagarajan},

title = {An internal language for interaction categories},

booktitle = {In Theory and Formal Methods 1994: Proceedings of the Second Imperial College Department of Computing Workshop on Theory and Formal Methods. Imperial},

year = {1995},

publisher = {College Press}

}

### OpenURL

### Abstract

1 Introduction It has been known for some years that formal systems of various kinds correspond to certain flavours of categorical structure. The first person to observe this phenomenon seems to have been Lawvere, who formulated a connection between certain kinds of algebraic theories and categories with finite products. Since Lawvere's original insight, there has been much progress in understanding

### Citations

448 |
Introduction to higher order categorical logic, volume 7 of Camb
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(Show Context)
Citation Context ...egories with finite products. Since Lawvere's original insight, there has been much progress in understanding 1sthe connections between category theory and formal systems. Expositions can be found in =-=[6, 11, 12, 13, 14]-=-; there are many other references--these few will be of particular interest to Computer Scientists. The precise way in which such correspondences can be realised has been perfected during the last dec... |

125 | Interaction categories and the foundations of types concurrent programming
- Abramsky, Gay, et al.
- 1996
(Show Context)
Citation Context ... formal systems which will be given by mutually inverse theory translations. In this paper we describe a particular instance of a correspondence between a variety of category (an interaction category =-=[1, 3]-=-) and a formal system for equational reasoning in which the individuals of the intensional object level equality judgements are processes. The formal system contains a number of constructs for buildin... |

64 |
Elementary categories, elementary toposes
- McLarty
- 1992
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Citation Context ...egories with finite products. Since Lawvere's original insight, there has been much progress in understanding 1sthe connections between category theory and formal systems. Expositions can be found in =-=[6, 11, 12, 13, 14]-=-; there are many other references--these few will be of particular interest to Computer Scientists. The precise way in which such correspondences can be realised has been perfected during the last dec... |

56 | A typed calculus of synchronous processes
- Gay, Nagarajan
- 1995
(Show Context)
Citation Context ...rocesses In this section we introduce some syntax which will be used to write down an equational theory of typed processes. The syntax is a restricted version of the typed process calculus studied in =-=[7, 8]-=-. A general exposition of the techniques of categorical type theory can be found in [6]. We begin by defining a notion of signature for such a theory. A signature Sg (for a process theory) is specifie... |

49 |
Polymorphism is set-theoretic constructively
- Pitts
- 1988
(Show Context)
Citation Context ...egories with finite products. Since Lawvere's original insight, there has been much progress in understanding 1sthe connections between category theory and formal systems. Expositions can be found in =-=[6, 11, 12, 13, 14]-=-; there are many other references--these few will be of particular interest to Computer Scientists. The precise way in which such correspondences can be realised has been perfected during the last dec... |

45 |
Autonomous Categories, volume 752
- Barr
- 1979
(Show Context)
Citation Context ...itable category is SProc [1, 3], Abramsky's category of synchronous processes; another is ASProc [2, 4], his category of asynchronous processes. Abstractly, C should be a \Lambda -autonomous category =-=[5]-=- with a monoidal endofunctor fl which is self-dual and has the Unique Fixed Point Property (UFPP). The UFPP says that for any objects A and B of C , and morphisms f : A ! flA, g : flB ! B, there is a ... |

35 |
Interaction categories and communicating sequentim processes
- Abramsky
- 1995
(Show Context)
Citation Context ... now define the semantics of a process theory in a suitably structured category C . One example of a suitable category is SProc [1, 3], Abramsky's category of synchronous processes; another is ASProc =-=[2, 4]-=-, his category of asynchronous processes. Abstractly, C should be a \Lambda -autonomous category [5] with a monoidal endofunctor fl which is self-dual and has the Unique Fixed Point Property (UFPP). T... |

21 | Specification structures and propositions-as-types for concurrency. In Logics ]or Concurrency: Structure vs
- Abramsky, Gay, et al.
- 1996
(Show Context)
Citation Context ... now define the semantics of a process theory in a suitably structured category C . One example of a suitable category is SProc [1, 3], Abramsky's category of synchronous processes; another is ASProc =-=[2, 4]-=-, his category of asynchronous processes. Abstractly, C should be a \Lambda -autonomous category [5] with a monoidal endofunctor fl which is self-dual and has the Unique Fixed Point Property (UFPP). T... |

20 |
Interaction categories (extended abstract
- Abramsky
- 1993
(Show Context)
Citation Context ... formal systems which will be given by mutually inverse theory translations. In this paper we describe a particular instance of a correspondence between a variety of category (an interaction category =-=[1, 3]-=-) and a formal system for equational reasoning in which the individuals of the intensional object level equality judgements are processes. The formal system contains a number of constructs for buildin... |

13 |
From lambda-calculus to cartesian closed categories
- Lambek
- 1980
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Citation Context |

4 |
Categories for Types, Cambridge
- Crole
- 1993
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Citation Context |

4 |
Theoretical Computer Science
- logic
- 1987
(Show Context)
Citation Context ...e processes. The formal system contains a number of constructs for building larger processes from elementary processes, using operations (such as cut, tensor and par) mainly derived from linear logic =-=[9]-=-. There are two fundamental object level judgements. First, processes-in-context specify a process together with a list of its communicating ports. Second, there are judgements of equality between pro... |