The Calculus of Computation

1. Front Matter

   Pages I-XV

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2. Foundations

   1. Front Matter

      Pages 1-1

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   2. Propositional Logic

      Pages 3-34

   3. First-Order Logic

      Pages 35-68

   4. First-Order Theories

      Pages 69-94

   5. Induction

      Pages 95-112

   6. Program Correctness: Mechanics

      Pages 113-152

   7. Program Correctness: Strategies

      Pages 153-179

3. Algorithmic Reasoning

   1. Front Matter

      Pages 181-181

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   2. Quantified Linear Arithmetic

      Pages 183-206

   3. Quantifier-Free Linear Arithmetic

      Pages 207-240

   4. Quantifier-Free Equality and Data Structures

      Pages 241-268

   5. Combining Decision Procedures

      Pages 269-289

   6. Arrays

      Pages 291-310

   7. Invariant Generation

      Pages 311-346

   8. Further Reading

      Pages 347-350

4. Back Matter

   Pages 351-366

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Computational logic is a fast-growing field with applications in artificial intelligence, constraint solving, and the design and verification of software and hardware systems. Written with graduate and advanced undergraduate students in mind, this textbook introduces computational logic from the foundations of first-order logic to state-of-the-art decision procedures for arithmetic, data structures, and combination theories.

This textbook also presents a logical approach to engineering correct software. The increasing ubiquity of computers makes implementing correct systems more important than ever. Verification exercises develop the reader's facility in specifying and verifying software using logic. The treatment of verification concludes with an introduction to the static analysis of software, an important component of modern verification systems.

For readers interested in learning more about computational logic, decision procedures, verification, and other areas of formal methods, the final chapter outlines courses of further study.

• Algorithms
• algorithm
• artificial intelligence
• computer
• data structure
• formal method
• learning
• logic
• verification
• algorithm analysis and problem complexity

"...this book, which addresses the verification of sequential programs, exhibits all the features of a field that has finally fully matured. The material is substantial; it is organized very thoughtfully; the writing is concise but simple, easy to follow, and illustrated with ample examples... Overall, this book is very well written, thoughtfully constructed, and substantive yet accessible. It is bound to become a standard textbook in program verification." (Fatma Mill, ACM Computing Reviews, August 2008)

• Stanford University, Stanford, USA

  Aaron R. Bradley, Zohar Manna