Interaction based simulation of dynamical system with a dynamical structure (DS) 2 in MGS

We present the domain specific programming language MGS and its approach to the specification of dynamical systems with a dynamical structure or (DS)2. MGS stands for "encore un Modele General de Simulation", that is, "yet another general model of simulation". Its declarative approach is based on the notions of chains and cochains well studied in algebraic topology. A careful discussion of the design goals lead us to relax some of the constraints on these mathematical structures to represent in a uniform way various data structures and transformations. In particular, our computational notion of transformation relies on a rewriting mechanism encompassing the usual notions of set, string and term rewriting. These notions are illustrated on two examples involving the implicit computation of a time varying neighborhood: the simulation of the trajectories of flocking birds and the growth of an epithelial tissue. The second example illustrates also the compositionality achieved by the declarative framework. The MGS concepts have been further validated on several large scale simulations of complex biological systems.