A Formal System: Rigorous Constructions of Computer Models (1510.04469v3)

Abstract: This book explores an alternative to the current dominant paradigm where a discrete computer model is constructed as an attempt to approximate some continuum theory. We focus on a class of discrete computer models that are based on simple deterministic rules and finite state arithmetic. Such models are highly compatible with the operational parameters of the real world computer on which they are executed and hence their validation can be associated with the allowable computations on the machine. A simple formal system based on a language of functional programs is employed as a tool of analysis.