# Generalized Multisets for Chemical Programming

1 PARIS - Programming distributed parallel systems for large scale numerical simulation
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, ENS Cachan - École normale supérieure - Cachan, Inria Rennes – Bretagne Atlantique
Abstract : Gamma is a programming model where computation can be seen as chemical reactions between data represented as molecules floating in a chemical solution. This model can be formalized as associative, commutative, conditional rewritings of multisets where rewrite rules and multisets represent chemical reactions and solutions, respectively. In this article, we generalize the notion of multiset used by Gamma and present applications through various programming examples. First, multisets are generalized to include rewrite rules which become first-class citizen. This extension is formalized by the $\gamma$-calculus, a chemical model that summarizes in a few rules the essence of higher-order chemical programming. By extending the $\gamma$-calculus with constants, operators, types and expressive patterns, we build a higher-order chemical programming language called . Finally, multisets are further generalized by allowing elements to have infinite and negative multiplicities. Semantics, implementation and applications of this extension are considered.
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Cited literature [20 references]

https://hal.inria.fr/inria-00070276
Contributor : Rapport de Recherche Inria <>
Submitted on : Friday, May 19, 2006 - 7:50:40 PM
Last modification on : Monday, February 15, 2021 - 10:42:44 AM
Long-term archiving on: : Sunday, April 4, 2010 - 8:48:44 PM

### Identifiers

• HAL Id : inria-00070276, version 1

### Citation

Jean-Pierre Banâtre, Pascal Fradet, Yann Radenac. Generalized Multisets for Chemical Programming. [Research Report] RR-5743, INRIA. 2005, pp.26. ⟨inria-00070276⟩

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