Data Structure as Topological Spaces

  • Authors:
  • Jean-Louis Giavitto;Olivier Michel

  • Affiliations:
  • -;-

  • Venue:
  • UMC '02 Proceedings of the Third International Conference on Unconventional Models of Computation
  • Year:
  • 2002

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Abstract

In this paper, we propose a topological metaphor for computations: computing consists in moving through a path in a data space and making some elementary computations along this path. This idea underlies an experimental declarative programming language called MGS. MGS introduces the notion of topological collection: a set of values organized by a neighborhood relationship. The basic computation step in MGS relies on the notion of path : a path C is substituted for a path B in a topological collection A. This step is called a transformation and several features are proposed to control the transformation applications. By changing the topological structure of the collection, the underlying computational model is changed. Thus, MGS enables a unified view on several computational mechanisms. Some of them are initially inspired by biological or chemical processes (Gamma and the CHAM, Lindenmayer systems, Paun systems and cellular automata).