Computer Laboratory

Technical reports

Category theory and models for parallel computation

Glynn Winskel

April 1986, 16 pages

Abstract

This report will illustrate two uses of category theory: Firstly the use of category theory to define semantics in a particular model. How semantic constructions can often be seen as categorical ones, and, in particular, how parallel compositions are derived from a categorical product and a nun-deterministic sum. These categorical notions can provide a basis for reasoning about computations and will be illustrated for the model of Petri nets.

Secondly, the use of category theory to relate different semantics will be examined; specifically, how the relations between various concrete models like Petri nets, event structures, trees and state machines are expressed as adjunctions. This will be illustrated by showing the coreflection between safe Petri nets and trees.

Full text

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BibTeX record

@TechReport{UCAM-CL-TR-85,
  author =	 {Winskel, Glynn},
  title = 	 {{Category theory and models for parallel computation}},
  year = 	 1986,
  month = 	 apr,
  url = 	 {http://www.cl.cam.ac.uk/techreports/UCAM-CL-TR-85.pdf},
  institution =  {University of Cambridge, Computer Laboratory},
  number = 	 {UCAM-CL-TR-85}
}