PPT-Quantified Invariants in Rich Domains

using Model Checking and Abstract Interpretation Anvesh Komuravelli CMU Joint work with Ken McMillan The Problem ArrayManipulating Program P Assertions Automatic analysis for assertion failures. With Liquid . Types. Ranjit. . Jhala. , UC San Diego. (with Pat . Rondon. , Ming Kawaguchi). Part I. First-Order Verification. Part II. Higher-Order Verification. char* . rev_copy. (. char* . a, . int. . Işil. . Dillig. , Thomas . Dillig. , and Alex Aiken. Stanford University. Simplifying Loop Invariant Generation Using Splitter Predicates. Loops and Loop Invariants. Invariant. evaluates . to . true. Dr. Cynthia Bailey Lee. Dr. . Shachar. Lovett. .  .                          . Peer Instruction in Discrete Mathematics by . Cynthia . Lee. is. licensed under a . Creative Commons Attribution-. in. Constraint Programming. Shant Karakashian. , . Robert . J. Woodward. , Berthe . Y. Choueiry,. Steven D. Prestwich . and Eugene C. Freuder. 1. Outline. Interchangeability: Basics . Microsoft Research. Redmond, WA, USA. Angela Wallenburg. Chalmers University of Technology. G. öteborg, Sweden. Class-local object invariants. 20 Feb 2008. ISEC 2008. Hyderabad, India. Program verification. Why. are Quantified Statements Important?. The logical structure of quantified statements provides a basis for the construction and validation of . proofs.. Consider the quantified statements…. “For every positive number . 4th . year. PT student. Former. student . assistant. of QSI. The . Quantified. . Self. What. is . Quantified. . Self. ?. Over . to. . you. :. Whom. of . you. does . it. ?. Why. / . why. . not. (POPL’08). Presented by. M.Raveendra. Kumar. Some of the slides . adopted . from author’s . presentations. Motivating Example. 2. a[0] = 0;. for (. i. =1; . i. <n; . i. ++) a[. i. ] = 0;. Post condition. 22 – 26 August 2016. 3. The Logic of Quantified Statements. Summary. . 1. . 2. . 3. The Logic of Quantified Statements. Summary. 3. . . 3.1 Predicates and Quantified Statements I. Definition 3.1.1 (Predicate). Swarup. Kumar . Sahoo. John Criswell. Chase . Geigle. Vikram. . Adve. 1. Department of Computer Science. University of Illinois at Urbana-Champaign. Motivation - 1. 2. Software bugs cost ~$59.5 billion annually (about 0.6% of the GDP). -X. : A Comprehensive Invariant based . Approach for . Performance Diagnosis in Big Data Platform. Pengfei. Chen. Xi’an . Jiaotong. university. 2014-9-2. Background. National Defense. Health. SDN Data & Control Planes:. Header Space Analysis. SDN Stack. State layers . hold a . representation . of the . network’s configuration. . Code layers implement. logic . to maintain the . mapping between . Ranjit. . Jhala. , UC San . Diego. (with Pat . Rondon. , Ming Kawaguchi). char* . rev_copy. (. char* . a, . int. n){. . i. = 0;. j = n – 1;. b = . malloc. (n);. . while. (0<=j){. b[. Ranjit Jhala, UC San Diego. Checking. Properties. Of Software. Static Safety Verification. Dynamic Liveness Testing. char* . rev_copy. (. char* . a, . int. n){. . i. = 0;. j = n – 1;. b = .