| Preface |
| The Abstract Rational Outlook / Chapter 1： |
| Abstract Computation |
| Rational Thought |
| Human Psychology |
| Mythological Language |
| Literate Programming |
| Hand-Crafted Software |
| Technical Programming |
| A Grab Bag of Computational Models / Chapter 2： |
| Abstract and Virtual Machines |
| State Machines |
| State Machines in Action |
| Turing Machine |
| Non-Deterministic Machines |
| Von Neumann Machine |
| Stack Machine |
| Register Machine |
| Analogue Machine |
| Cellular Automata |
| Unorthodox Models |
| The Game of Life |
| The Modern Desktop Computer |
| Aspects of Virtual Machines |
| Aspects of Programming |
| Register Indirection |
| Pure Expression Substitution |
| Lists Pure and Linked |
| Pure String Substitution |
| The Face Value of Numerals |
| Solving Equations |
| Pure Unification |
| Equality of Expressions |
| Equational Reasoning |
| Unification Reduction |
| Code Reduction |
| Programming With Logic |
| Negation in Logic Programming |
| Impure Lambda Calculus |
| Pure Lambda Calculus |
| Pure Lambda Arithmetic |
| Pure Lambda Flow Control |
| S-K Combinators |
| Some Formal Technology / Chapter 3： |
| The Ellipsis Is Not a Definition |
| The Summation Operator |
| Propositional Calculus |
| Boolean Algebra |
| Predicate Calculus |
| Formal Mathematical Models |
| The Formal State Machine |
| Several Types of Networks |
| Informal Petri Nets |
| Formal Turing Machine |
| The Table-Driven State Machine |
| Factors of Graphs |
| Products of Graphs |
| Constructive Numerics |
| Prime Programs |
| Showing that Factorial Works |
| Reasoning About Code |
| Logical Conditions |
| Limitations on Exact Knowledge / Chapter 4： |
| Finite-State Limitations |
| N log N sorting |
| Russell's Paradox |
| Pure Lambda Paradoxes |
| Godel's Theorem |
| Non-Computability |
| Solving Polynomials |
| Churche's Thesis |
| Algorithmic Complexity |
| P and NP |
| NP completeness |
| Turing Test |
| Natural Language Processing |
| The Computable Reals |
| The Diagonal Argument |
| Some Orthodox Languages / Chapter 5： |
| C Pointers to Functions |
| Taking C on Face Value |
| Functions and Other Data in C |
| The C Preprocessor |
| C Functions are Data Again |
| Java Code |
| Pointer Casting |
| The Object Data Type |
| Manual Objects |
| Inheritance and Dynamic Type |
| CODASYL and Objects |
| Typecasting |
| The Concept of Type |
| Type-Checking |
| Subtypes and Programming |
| New Datatypes |
| Scheme Code |
| Declarative and Imperative |
| Sorting with Pure Substitution |
| Fast Sorting in Haskell |
| Logic in Prolog |
| Functions in Prolog |
| Arithmetic in Prolog |
| Meta-Logic in Prolog |
| What Is HTML Code? |
| Illogical markup language |
| HTML Forgive and Forget |
| Expanding Beyond Recognition |
| Arithmetic Computation / Chapter 6： |
| Natural Arithmetic |
| Modulo Arithmetic |
| Integer Arithmetic |
| Rational Arithmetic |
| Complex Arithmetic |
| Exact Arithmetic |
| Showing That a Power Loop Works |
| When Is a Proof Not a Proof? |
| Real-Valued Memory |
| Cellular Matrix Multiplication |
| Repetitive Computation / Chapter 7： |
| The Use of Recursion |
| Doing Without the While Loop |
| Defining the Generic While-Loop |
| Design of the Power Function |
| Powers by Multiplication |
| Computing Powers by Squaring |
| Language or Algorithm? |
| Repetitive Program Design |
| Recursive Code Compilation |
| Functions as Data |
| Lambda Expressions in Java |
| The Y-combinator definition |
| Y-combinator factorial |
| Y-combinator Fibonacci |
| Temporal Interaction / Chapter 8： |
| Virtual Interaction |
| Incorruptible Operations |
| Temporal Computing |
| Multi-Threaded Code |
| Graphs of State Machines |
| Direct Thread Composition |
| Concurrent Thread Interference |
| Control Structures |
| Thread Point of Execution |
| The Transition Network |
| High-Level Interference |
| Incorruptible Commands Again |
| Thread Interaction |
| Pure String Interaction |
| Showing That a Parser Works |
| Mutual Exclusion |
| Good Mutual Exclusion |
| A Partial Mutex Protocol |
| Guarded Commands |
| Blocking Commands |
| Hardware Assistance |
| Proving That a Protocol Works |
| Two Partial Exclusion Protocols |
| The Peterson Protocol |
| The Decker Protocol |
| Container Datatypes / Chapter 9： |
| Abstract Arrays |
| Pure Containers |
| Generic Maps |
| Showing That Infinite Lists Work |
| Generic Lists |
| Computing with Infinite Lists |
| Sequence Builder |
| Infinite Lists in Haskell |
| Infinite Lists in Scheme |
| Primitive List Recursion |
| Appendices |
| End notes |
| Bibliography |
| Glossary |
| Index |
| Preface |
| The Abstract Rational Outlook / Chapter 1： |
| Abstract Computation |
| Rational Thought |
| Human Psychology |
| Mythological Language |
