Continuing Lecture 06

We have seen in exercises Products of Lattices

Abstract Interpretation of Transition System

Collecting Semantics

Galois Connection

Using Galois Connection in Abstraction Interpretation

Abstract Interpretation Recipe

Variable Range Analysis for Example Program

• Principles of Program Analysis Book
• Lecture notes on static analysis by Michael Schwartzbach (sections 4,5,6,7 in particular), and pdf file
• Tiger book, chapters 10, 17
• Abstract Interpretation in a Nutshell by Patrick Cousot (also a course at MIT)

Scala sources illustrating basic concepts of Abstract Interpretation:

• DiGraphs.scala - graphs
• SimpleCFG.scala - simple control-flow graphs
• SimpleAST.scala - simple abstract syntax tre
• SimpleTranslate.scala - translation from AST to CFG

• Lattices.scala - lattices with some examples, and definition of product
• DataFlowAnalysis.scala - simplest fixpoint iteration algorithm parameterized by transfer functions i.e. by sp#
• ConcreteAnalysis.scala - transfer functions for Collecting Semantics
• SignAnalysis.scala - transfer functions for sign analysis