Principles of Abstract Interpretation

by Cousot

ISBN: 9780262361514 | Copyright 2021

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Introduction to abstract interpretation, with examples of applications to the semantics, specification, verification, and static analysis of computer programs.

Formal methods are mathematically rigorous techniques for the specification, development, manipulation, and verification of safe, robust, and secure software and hardware systems. Abstract interpretation is a unifying theory of formal methods that proposes a general methodology for proving the correctness of computing systems, based on their semantics. The concepts of abstract interpretation underlie such software tools as compilers, type systems, and security protocol analyzers. This book provides an introduction to the theory and practice of abstract interpretation, offering examples of applications to semantics, specification, verification, and static analysis of programming languages with emphasis on calculational design.

The book covers all necessary computer science and mathematical concepts—including most of the logic, order, linear, fixpoint, and discrete mathematics frequently used in computer science—in separate chapters before they are used in the text. Each chapter offers exercises and selected solutions. Chapter topics include syntax, parsing, trace semantics, properties and their abstraction, fixpoints and their abstractions, reachability semantics, abstract domain and abstract interpreter, specification and verification, effective fixpoint approximation, relational static analysis, and symbolic static analysis. The main applications covered include program semantics, program specification and verification, program dynamic and static analysis of numerical properties and of such symbolic properties as dataflow analysis, software model checking, pointer analysis, dependency, and typing (both for forward and backward analysis), and their combinations. Principles of Abstract Interpretation is suitable for classroom use at the graduate level and as a reference for researchers and practitioners.

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Cover (pg. Cover)
1. Abstract Interpretation and Its Main Applications (pg. 3)
2. Basic Set Theory (pg. 9)
3. Syntax, Semantics, Properties, and Static Analysis of Expressions (pg. 17)
4. Syntax (pg. 39)
5. Parsing (pg. 49)
6. Structural Deductive Stateless Prefix Trace Semantics (pg. 65)
7. Maximal Trace Semantics (pg. 81)
8. Program Properties (pg. 89)
9. Undecidability and Rice Theorem (pg. 97)
10. Posets, Lattices, and Complete Lattices (pg. 105)
11. Galois Connections and Abstraction (pg. 111)
12. Relational and Transformer Semantics (pg. 135)
13. Topology (pg. 147)
14. Safety and Liveness Trace Properties (pg. 151)
15. Fixpoints (pg. 165)
16. Fixpoint, Deductive, Inductive, Structural, Coinductive, and Bi-inductive Definitions (pg. 175)
17. Structural Fixpoint Prefix and Maximal Trace Semantics (pg. 185)
18. Fixpoint Abstraction (pg. 193)
19. Structural Forward Reachability Semantics (pg. 215)
20. Calculational Design of the Forward Reachability Semantics (pg. 229)
21. Abstract Domain and Abstract Structural Semantics (pg. 245)
22. Chaotic Iterations (pg. 253)
23. Abstract Equational Semantics (pg. 259)
24. Fixpoint Induction (pg. 275)
25. Abstract Reachability Invariance Safety Verification Semantics (pg. 281)
26. Hoare Logic (pg. 292)
27. Abstraction (pg. 307)
28. Abstract Cartesian Semantics (pg. 321)
29. Reduction (pg. 347)
30. Basic Number Theory (pg. 351)
31. Cartesian Congruence Analysis (pg. 357)
32. Dynamic Interval Analysis (pg. 367)
33. Static Interval Analysis (pg. 389)
34. Fixpoint Approximation by Extrapolation and Interpolation (pg. 401)
35. Fixpoint Checking (pg. 413)
36. Reduced Product (pg. 417)
37. Basic Linear Algebra (pg. 437)
38. Linear Equality Analysis (pg. 453)
39. Graphs (pg. 459)
40. Zone and Octagon Analysis (pg. 481)
41. Dataflow Analysis (pg. 497)
42. Stateful Prefix Trace Semantics (pg. 515)
43. Transition Semantics (pg. 521)
44. Software Model Checking (pg. 527)
45. Flow-Insensitive Static Analysis (pg. 553)
46. Points-To Analysis (pg. 559)
47. Dependency Analysis (pg. 591)
48. The Herbrand Abstract Domain of Symbolic Terms (pg. 623)
49. Typing (pg. 649)
50. Backward Accessibility Semantics (pg. 675)
51. Reduced Forward—Backward Analysis (pg. 695)
52. Semantic Soundness, Completeness, and Definedness (pg. 705)
53. Static Analysis Tools (pg. 713)
54. Conclusion (pg. 721)
Index (pg. 789)

Patrick Cousot

Patrick Cousot is Julius Silver, Roslyn S. Silver, and Enid Silver Winslow Professor in the Computer Science Department at New York University.

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