Effective Theories in Programming Practice 9781450399722, 9781450399739, 9781450399715, 9781450399746

Table of contents :
Cover
Halftitle
Title Page
Copyright Page
Dedication
Contents
Preface
Acknowledgment
Chapter 1 Introduction
1.1 Motivation for This Book
1.2 Lessons from Programming Theory
1.3 Formalism: The Good, the Bad and the Ugly
Chapter 2 Set Theory, Logic and Proofs
2.1 Set
2.2 Function
2.3 Relation
2.4 Order Relations: Total and Partial
2.5 Propositional Logic
2.6 Predicate Calculus
2.7 Formal Proofs
2.8 Examples of Proof Construction
2.9 Exercises
Chapter 3 Induction and Recursion
3.1 Introduction
3.2 Examples of Proof by Induction
3.3 Methodologies for Applying Induction
3.4 Advanced Examples
3.5 Noetherian or Well-founded Induction
3.6 Structural Induction
3.7 Exercises
Chapter 4 Reasoning About Programs
4.1 Overview
4.2 Fundamental Ideas
4.3 Formal Treatment of Partial Correctness
4.4 A Modest Programming Language
4.5 Proof Rules
4.6 More on Invariant
4.7 Formal Treatment of Termination
4.8 Reasoning about Performance of Algorithms
4.9 Order of Functions
4.10 Recurrence Relations
4.11 Proving Programs in Practice
4.12 Exercises
4.A Appendix: Proof of Theorem 4.1
4.B Appendix: Termination in Chameleons Problem
Chapter 5 Program Development
5.1 Binary Search
5.2 Saddleback Search
5.3 Dijkstra’s Proof of the am–gm Inequality
5.4 Quicksort
5.5 Heapsort
5.6 Knuth–Morris–Pratt String-matching Algorithm
5.7 A Sieve Algorithm for Prime Numbers
5.8 Stable Matching
5.9 Heavy-hitters: A Streaming Algorithm
5.10 Exercises
Chapter 6 Graph Algorithms
6.1 Introduction
6.2 Background
6.3 Specific Graph Structures
6.4 Combinatorial Applications of Graph Theory
6.5 Reachability in Graphs
6.6 Graph Traversal Algorithms
6.7 Connected Components of Graphs
6.8 Transitive Closure
6.9 Single Source Shortest Path
6.10 Minimum Spanning Tree
6.11 Maximum Flow
6.12 Goldberg–Tarjan Algorithm for Maximum Flow
6.13 Exercises
6.A Appendix: Proof of the Reachability Program
6.B Appendix: Depth-first Traversal
Chapter 7 Recursive and Dynamic Programming
7.1 What is Recursive Programming
7.2 Programming Notation
7.3 Reasoning About Recursive Programs
7.4 Recursive Programming Methodology
7.5 Recursive Data Types
7.6 Dynamic Programming
7.7 Exercises
7.A Appendices
Chapter 8 Parallel Recursion
8.1 Parallelism and Recursion
8.2 Powerlist
8.3 Pointwise Function Application
8.4 Proofs
8.5 Advanced Examples Using Powerlists
8.6 Multi-dimensional Powerlist
8.7 Other Work on Powerlist
8.8 Exercises
8.A Appendices
Bibliography
Author’s Biography
Index

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