Generalized Multisets for Chemical Programming Jean-pierre Banâtre, Pascal Fradet,

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 γ-calculus, a chemical model that summarizes in a few rules the essence of higherorder chemical programming. By extending the γ-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. Key-words: multisets, chemical programming model, rewriting, higher-order, infinite and negative multiplicities