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| - | ====== Abstract Interpretation and Examples ====== | + | ====== Abstract Interpretation ====== |
| [[Sign Analysis of Expressions and Programs]] | [[Sign Analysis of Expressions and Programs]] | ||
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| [[Galois Connection on Lattices]] | [[Galois Connection on Lattices]] | ||
| - | |||
| - | Examples: | ||
| - | * [[Conjunctions of Predicates]] - example of finite lattice. two different orders | ||
| - | * [[Constant Propagation]] - infinite lattice with finite ascending chain property | ||
| - | * Bitwidth analysis | ||
| - | * Interval analysis | ||
| - | * Polyhedra - linear inequalities | ||
| - | * [[Converging in Infinite-Height Lattice]] - dropping conjuncts | ||
| - | |||
| - | [[Designing Abstract Domains]] | ||
| - | |||
| - | [[:sav07_lecture_7|Approximation Expressed Using Formulas]] | ||
| ===== References ===== | ===== References ===== | ||
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| * [[Calculus of Computation Textbook]] Chapter 12, including Section 12.4 | * [[Calculus of Computation Textbook]] Chapter 12, including Section 12.4 | ||
| * [[http://www.di.ens.fr/~cousot/COUSOTpapers/POPL77.shtml|Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints]] (original abstract interpretation paper) | * [[http://www.di.ens.fr/~cousot/COUSOTpapers/POPL77.shtml|Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints]] (original abstract interpretation paper) | ||
| - | * [[http://www.brics.dk/~mis/static.pdf|Lecture notes on static analysis by Michael Schwartzbach]] (sections 4,5,6,7 in particular) | + | * [[http://www.brics.dk/~mis/static.pdf|Lecture notes on static analysis by Michael Schwartzbach]] (sections 4,5,6,7 in particular) ({{schwartzbach.pdf|local pdf}} |
| * [[http://www.math.tau.ac.il/~sagiv/courses/pa/notes.ps|Notes on program analysis]], by Alex Aiken | * [[http://www.math.tau.ac.il/~sagiv/courses/pa/notes.ps|Notes on program analysis]], by Alex Aiken | ||
| * [[http://web.mit.edu/16.399/|Patrick Cousot's MIT Class]] | * [[http://web.mit.edu/16.399/|Patrick Cousot's MIT Class]] | ||