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# BFR06-MSCS

Jean-Pierre Banātre, Pascal Fradet, Yann Radenac. Generalised multisets for chemical programming. Mathematical Structures in Computer Science, 16(4):557-580, August 2006.

## 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 HOCL. Finally, multisets are further generalized by allowing elements to have infinite and negative multiplicities. Semantics, implementation and applications of this extension are considered

## Keywords

[ Chemical programming ] [ Higher-order conditional multiset rewriting ] [ Infinite multisets ] [ Negative multiplicities ]

## Contact

Pascal Fradet http://pop-art.inrialpes.fr/people/fradet/

## BibTex Reference

@article{BFR06-MSCS,

Author = {Banātre, Jean-Pierre and Fradet, Pascal and Radenac, Yann},

Title = {Generalised multisets for chemical programming},

Journal = {Mathematical Structures in Computer Science},

Volume = { 16},

Number = {4},

Pages = {557--580},

Month = {August},

Year = {2006}

}

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