SE 504
Formal Methods and Models
Spring 2009

Time: Thursdays, 7:20pm -- 10:00pm
Place: St. Thomas 412
Instructor: Dr. R. McCloskey
Office: St. Thomas 480
Telephone: 941-4221 (office), 941-7774 (CS Dept. office), 941-4250 (fax)
E-mail: mccloskeyr1@scranton.edu
Home Page: www.cs.uofs.edu/~mccloske/
Office Hours: To be posted on office door and on home page.

Text: Programming: The Derivation of Algorithms, by A. Kaldewaij, Prentice Hall, 1990. (Photocopies of excerpts from the book, which is no longer in print, will be distributed, with permission of Prentice Hall.)

Homeworks:: Approximately eight.

Exams:: Possibly a mid-term in-class exam in March. Take-home final exam near end of semester, due near end of final exam week.

Grading: Based on homework assignments, exams, and class participation.

Objective: The student will become proficient in the practice of calculational programming, an approach in which a program and its proof of correctness are developed together.

Topics:

• predicate logic (review)
• notion of state and correspondence of a predicate to a set of states
• state space of a program
• specification of programs via pre- and post-conditions
• design/programming by contract
• Hoare triples and notion of weakest precondition
• Dijkstra's Guarded Command Language
  • skip command
  • assignment command
  • selection (if) command
  • repetition (loop) command and loop invariants
  • subprograms
• program derivation techniques
  • calculating expressions in assignments
  • deriving selection (if) commands
  • developing loops and loop invariants
    • by deleting a conjunct
    • by replacing a constant (or one of multiple occurrences of a variable) by a variable
    • by strengthening the invariant
    • using tail recursion
• derivations of interesting programs
  • polynomial evaluation
  • Linear and Binary Search
  • Dutch National Flag Problem (array partition)
  • The Celebrity Problem
  • Majority Vote Problem
  • Maximum Segment Sum
  • array rotation
  • longest increasing subsequence
  • sorting
• Proving the correctness of recursive algorithms