A Geometrical Refinement of Shape Calculus Enabling Direct Simulation

The Shape Calculus is a bio-inspired timed and spatial calculus for describing 3D geometrical shapes moving in a space. Its purpose is twofold: i) modelling and formally verifying (not only) biological systems, and ii) simulating the models for validation and hypothesis testing. The original geometric primitives of the calculus are highly abstract: the associated simulator needs to attach a lot of code to the model specification in order to perform an effective simulation. In this work we propose a calculus refinement in which a detailed 3D characterization of the geometric primitives is injected into the syntax of the calculus. In this way, models written with the new syntax can be directly simulated