PPT-Counterexample Generation for Separation-Logic-Based Proofs

Arlen Cox Samin Ishtiaq Josh Berdine Christoph Wintersteiger SLA YER Abstractionbased Static Analyzer Uses Separation Logic Proves Memory Safety of Heap Manipulating Programs Shape Analysis. Logic and Proof. Fall . 2011. Sukumar Ghosh. Predicate Logic. Propositional logic has limitations. Consider this:. Is . x. . > 3. a proposition? No, it is a . predicate. . Call it . P(x. ). . Chapter 1, Part III: Proofs. With Question/Answer Animations. Summary. Valid Arguments and Rules of Inference. Proof Methods. Proof Strategies. Rules of Inference. Section 1.6. Section Summary. Valid Arguments. Chapter 1, Part II: Predicate Logic. With Question/Answer Animations. Summary. Predicate Logic (First-Order Logic (FOL), Predicate Calculus). The Language of Quantifiers. Logical Equivalences. Nested Quantifiers. Chapter 1, Part III: Proofs. Summary. Proof Methods. Proof Strategies. Introduction to Proofs. Section 1.7. Section Summary. Mathematical Proofs. Forms of Theorems. Direct Proofs. Indirect Proofs. Proof of the . Chapter 1, Part II: Predicate Logic. With Question/Answer Animations. Summary. Predicate Logic (First-Order Logic (FOL), Predicate Calculus). The Language of Quantifiers. Logical Equivalences. Nested Quantifiers. Chapter 1, Part III: Proofs. With Question/Answer Animations. Summary. Valid Arguments and Rules of Inference. Proof Methods. Proof Strategies. Rules of Inference. Section 1.6. Section Summary. Valid Arguments. Logic and Proof. Fall 2014. Sukumar Ghosh. Predicate Logic. Propositional logic has limitations. Consider this:. Is . x. . > 3. a proposition? No, it is a . predicate. . Call it . P(x. ). . P(4) . t. o Programming Language Semantics,. to Program Verification. Grigore . Rosu. University of Illinois at Urbana-Champaign, USA. 1. How it all started. 1996: Started PhD with Joseph . Goguen. Discovered Maude as “fast OBJ”, then rewriting logic. Structures. Logic and Proof. Spring 2014. Sukumar Ghosh. Predicate Logic. Propositional logic has limitations. Consider this:. Is . x. . > 3. a proposition? No, it is a . predicate. . Call it . 1.1 Propositional Logic. 1.2 Propositional Equivalences. 1.3 Predicates and Quantifiers. 1.4 Nested Quantifiers. 1.5 Rules of Inference. 1.6 Introduction to Proofs. 1.7 Proof Methods and Strategy. We wish to establish the truth of. 1.1 Propositional Logic. 1.2 Propositional Equivalences. 1.3 Predicates and Quantifiers. 1.4 Nested Quantifiers. 1.5 Rules of Inference. 1.6 Introduction to Proofs. 1.7 Proof Methods and Strategy. To prove an argument is valid or the conclusion follows . Chapter 1, Part III: Proofs. Summary. Proof Methods. Proof Strategies. Introduction to Proofs. Section 1.7. Section Summary. Mathematical Proofs. Forms of Theorems. Direct Proofs. Indirect Proofs. Proof of the . Fall . 2011. Sukumar Ghosh. Predicate Logic. Propositional logic has limitations. Consider this:. Is . x. . > 3. a proposition? No, it is a . predicate. . Call it . P(x. ). . P(4) . is true, but . DeLiang. Wang. Perception & Neurodynamics Lab. Ohio State University. . & Northwestern . Polytechnical. University. http://www.cse.ohio-state.edu/pnl/. Outline of presentation. Introduction.