SE 504 (Formal Methods and Models)
Spring 2009

Syllabus

Homework Assignments

• Homework #1: Developing Predicates
• Homework #2: Predicate Strength/Weakness
• Homework #3: skip and assignment commands
• Homework #4: Catenation and Selection
• Homework #5: More Selection, Plus an Invariant
• Homework #6: Repetition
• Homework #7: More Repetition, Including Strengthening the Invariant
• Homework #8: More Repetition, Again
• Homework #9: Tail Recursion
• Final Exam Postmortem

Electronic Handouts

• Developing predicates from informal statements: A checklist
• On the strength/weakness relationship between predicates
• On Proofs Involving the Replacement of A by B, where A implies B
• Properties/Laws of Hoare triples and the wp predicate transformer
• Axioms for the (family of) if functions
• Program Verification Summary
• Correctness proofs of some simple programs:
  • A skip command
  • An assignment command
  • A catenation (or sequential composition)
  • A selection (i.e., if) command
  • A derivation of a selection (i.e., if) command
• Repetition (Looping)
  • Notes on Loop Invariants
  • Correctness proof of a program computing 0+1+...+N
  • Correctness proof of a program involving a repetition (loop) command
  • When a selection command is nested inside a loop
  • Development of a linear search program
  • Development of a program to compute N³ without multiplication or exponentation
  • Development of a program to calculate Fibonacci numbers
  • Development of a program that does negative-positive pair counting in an array
  • Development of a program for the Maximum Segment Sum Problem
• Developing programs to compute tail recursive functions
• Arrays
  • Axioms for the (family of) if functions
  • Reasoning about arrays
  • Irrelevant Array Element Axiom
  • Development of a program for the Prefix Sums Problem
  • A solution to the Array Decomposition Problem
  • A solution to the 2-color version of Dutch National Flag Problem
• Development of a program for determining the majority of a bag
• Subprograms
  • Notes on Proofs of Programs Involving Subprograms
  • Example of a correctness proof involving a subprogram invocation (maximum())
  • Richard Denman: Procedure Declarations and Calls

External Links

• Wikipedia entry on Design by Contract

Work by Bertrand Meyer on Program Correctness

• Links to Publications
• A Framework for Proving Contract-equipped Classes
• Towards Practical Proofs of Class Correctness
• Proving Pointer Program Properties Part 1: Context and Overview
• Proving Pointer Program Properties Part 2: The Overall Object Structure