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EbookBell Team
5.0
80 reviews
ISBN 13: 9780470848821
Author: Roland Backhouse
Most texts on logic or discrete math fail to show why math and logic are fundamental tools for programmers. Program Construction illustrates the importance of math and logic to programming, providing a complete, self-contained account of the principles of logical reasoning. Designed specifically so users can construct programs that meet their specifications, the book details program construction principles in a straightforward fashion, avoiding overly complicated theory, and then illustrating each with convincing examples.
1 A Science of Computing
1.1 Debugging
1.2 Testing a Correct Program
1.3 Testing an Incorrect Program
1.4 Correct by Construction
2 A Searching Problem and Its Solution
2.1 Problem Statement
2.2 Problem Solution
2.3 Proof of Correctness
2.4 What, Why and How
2.5 Exercises
2.6 Summary
3 Calculational Proof
3.1 The Nature of Proof
3.2 Construction versus Verification
3.3 Formatting Calculations
3.3.1 Basic Structure
3.3.2 Hints
3.3.3 Relations between Steps
3.3.4 'If' and 'Only If'
3.4 A Classic Example
3.5 Summary
4 Implementation Issues
4.1 Binary Search
4.1.1 Implementation
4.2 Verifying Correctness—A Taster
4.3 Summary
5 Calculational Logic: Part 1
5.1 Logical Connectives
5.2 Boolean Equality
5.3 Examples of the Associativity of Equivalence
5.4 Continued Equivalences
5.5 The Island of Knights and Knaves
5.6 Negation
5.7 Summary
6 Number Conversion
6.1 The Floor Function
6.2 Properties of Floor
6.3 Indirect Equality
6.4 Rounding Off
6.5 Summary
7 Calculational Logic: Part 2
7.1 Disjunction
7.2 Conjunction
7.3 Implication
7.3.1 Definitions and Basic Properties
7.3.2 Replacement Rules
7.4 Exercises: Logic Puzzles
7.5 Summary
8 Maximum and Minimum
8.1 Definition of Maximum
8.2 Using Indirect Equality
8.3 Exercises
8.4 Summary
9 The Assignment Statement
9.1 Hoare Triples
9.2 Ghost Variables
9.3 Hoare Triples as Program Specifications
9.4 Assignment Statements
9.5 The Assignment Axiom
9.6 Calculating Assignments
9.7 Complications
9.8 Summary
10 Sequential Composition and Conditional Statements
10.1 Sequential Composition
10.2 The skip Statement
10.3 Conditional Statements
10.4 Reasoning about Conditional Statements
10.5 Constructing Conditional Statements
10.6 Combining the Rules
10.7 Summary
11 Quantifiers
11.1 DotDotDot and Sigmas
11.2 Introducing Quantifier Notation
11.2.1 Summation
11.2.2 Free and Bound Variables
11.2.3 Properties of Summation
11.2.4 The Gauss Legend
11.2.5 Warning
11.3 Universal and Existential Quantification
11.3.1 Universal Quantification
11.3.2 Existential Quantification
11.3.3 De Morgan's Rules
11.4 Quantifier Rules
11.4.1 The Notation
11.4.2 Free and Bound Variables
11.4.3 Dummies
11.4.4 Range Part
11.4.5 Trading
11.4.6 Term Part
11.4.7 Distributivity Properties
11.5 Summary
12 Inductive Proofs and Constructions
12.1 Patterns and Invariants
12.2 Mathematical Induction
12.3 Strong Induction
12.4 From Verification to Construction
12.5 Summary
13 Iteration
13.1 The do-od Statement
13.2 Constructing Loops
13.3 Basic Arithmetic Operations
13.3.1 Summing the Elements of an Array
13.3.2 Evaluating a Polynomial
13.3.3 Evaluation of Powers
13.4 Summary
14 Sorting and Searching Algorithms
14.1 The Dutch National Flag
14.1.1 Problem Statement
14.1.2 The Solution
14.1.3 Verifying the Solution
14.2 Finding the K Smallest Values
14.2.1 The Specification
14.2.2 The Algorithm
14.3 Summary
15 Remainder Computation
15.1 Formal Specification
15.2 Elementary Algorithm
15.3 The mod and div Functions
15.3.1 Basic Properties
15.3.2 Separating mod from ÷
15.3.3 Separating ÷ from mod
15.3.4 Modular Arithmetic
15.4 Long Division
15.4.1 Implementing Long Division
15.4.2 Discarding Auxiliary Variables
15.5 On-line Remainder Computation
15.6 Casting Out Nines
15.7 Summary
16 Cyclic Codes
16.1 Codes and Codewords
16.2 Boolean Polynomials
16.3 Data and Generator Polynomials
16.4 Long Division
16.5 Hardware Implementations
16.6 Summary
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Tags: Roland Backhouse, Program, Construction
