Declarative simulation of dynamicals systems: the 812 programming language and its application to the simulation of...

A major part of biological processes can be modeled as dynamical systems (DS), that is, as a time-varying state. In this article, we advocate a declarative approach for prototyping the simulation of DS. We introduce the concepts of collection, stream and fabric. A fabric is a multi-dimensional object that represents the successive values of a structured set of variables. A declarative programming language, called 8 1/2 has been developed to support the concept of fabrics. Several examples of working 8 1/2 programs are given to illustrate the relevance of the fabric data structure for simulation applications and to show how recursive fabric definitions can be easily used to model various biological phenomena in a natural way (a resolution of PDE, a simulation in artificial life, the Turing diffusion-reaction process and various examples of genetic networks). In the conclusion, we recapitulate several lessons we have learned from the 8 1/2 project.