  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.
