Topological rewriting and the geometrization of programming

Spatial computing is an emerging field that recognizes the importance of explicitly handling spatial relationships at three levels: computer architectures, programming languages and applications. In this context, we present MGS, an experimental programming language where data structures are fields o...

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Veröffentlicht in:Physica. D Jg. 237; H. 9; S. 1302 - 1314
Hauptverfasser: Giavitto, Jean-Louis, Spicher, Antoine
Format: Journal Article Tagungsbericht
Sprache:Englisch
Veröffentlicht: Amsterdam Elsevier B.V 01.07.2008
Elsevier
Schlagworte:
Cognitive science
Computation and Language
Computer science
Data fields
Declarative language
Discrete differential operators
Exact sciences and technology
Logic in Computer Science
Physics
Spatial computing
Topological collection
Topological rewriting
Ubiquitous Computing
Topological rewriting
Declarative language
Spatial computing
Data fields
Topological collection
Discrete differential operators
Models
Differential operator
Cellular automata
Non linear phenomenon
Algebraic topology
ISSN:0167-2789, 1872-8022
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Zusammenfassung:Spatial computing is an emerging field that recognizes the importance of explicitly handling spatial relationships at three levels: computer architectures, programming languages and applications. In this context, we present MGS, an experimental programming language where data structures are fields on abstract spaces. In MGS, fields are transformed using rules. We show that this approach is able to unify, at least for programming purposes, several computational models like Lindenmayer systems and cellular automata. The MGS notions of topological collection and transformation are formalized using concepts developed in algebraic topology. We propose to use transformations in order to implement a discrete version of some differential operators. These transformations satisfy a Stokes-like theorem. This result constitutes a geometric view of programming where data are handled like fields in physics. The relevance of this approach for the design of autonomic software systems is discussed in the conclusion.
ISSN:0167-2789
1872-8022
DOI:10.1016/j.physd.2008.03.039