@INPROCEEDINGS{Sands:FMP93,
  semno = {D-171},
  author = {David Sands},
  title = {A Compositional Semantics of Combining Forms 
                 for {G}amma Programs},
  booktitle = {Formal Methods in 
                 Programming and Their Applications, International
		  Conference, Academgorodok, Novosibirsk, Russia, June/July 1993.},
  editor = {D. Bj{\"o}rner and M. Broy and I. Pottosin},
  year = {1993},
  pages = {43--56},
  series = {Lecture Notes in Computer Science},
  publisher = {Springer-Verlag},
  optaddress = {},
  optmonth = {},
  optnote = {},
  summary = {The Gamma model is a minimal programming language based on local
multiset rewriting (with an elegant chemical reaction metaphor); 
Hankin {\em et al\/} derived a calculus of Gamma programs built 
from basic reactions and two composition operators, and 
applied it  to the study of relationships between parallel and
sequential program composition, and related program transformations.
The main shortcoming of the ``calculus of Gamma programs'' 
is that the refinement and
equivalence laws described are not compositional, so that a refinement
of a sub-program does not necessarily imply a refinement of the
program.  

In this paper we  address this problem by 
defining  a compositional (denotational) semantics for
Gamma, based on the {\em transition trace\/} method of Brookes,
and by showing how this can be used to verify substitutive
refinement laws, potentially widening the applicability and scalability 
of program transformations previously described. 

The compositional  semantics is also useful in the study of
 relationships between alternative combining forms at a deeper semantic
level. We consider the semantics and properties of
a number of new combining forms for the Gamma
model.
},
}

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