A Formal System: Rigorous Constructions of Computer Models

TL;DR

This paper introduces a formal system for constructing discrete computer models using simple deterministic rules and finite state arithmetic, emphasizing their operational realism and validation aligned with real-world computers.

Contribution

It presents a novel formal framework for designing and analyzing discrete computer models based on functional programming and finite state arithmetic.

Findings

Models are highly compatible with real-world computer operations

Validation aligns with allowable machine computations

Provides a rigorous formal basis for discrete model construction

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.