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COSC 4P42 Formal Methods in Software Engineering

COSC 4P42 Formal Methods in Software Engineering. Course: Mon, 3:30pm - 5:00pm, Winter 2013, Room: WH327 Fri, 3:30pm - 5:00pm, Winter 2013, Room: MCD205 Instructor: Michael Winter Office J323 Office Hours: Mon & Fri 1:00pm – 3:00pm email: mwinter@brocku.ca

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COSC 4P42 Formal Methods in Software Engineering

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  1. COSC 4P42Formal Methods in Software Engineering • Course: • Mon, 3:30pm - 5:00pm, Winter 2013, Room: WH327 • Fri, 3:30pm - 5:00pm, Winter 2013, Room: MCD205 • Instructor: Michael Winter • Office J323 • Office Hours: Mon & Fri 1:00pm – 3:00pm • email: mwinter@brocku.ca • Webpage: www.cosc.brocku.ca/~mwinter/Courses/4P42/

  2. Course Description (Brock Calendar): Specification and correctness of software. Topics include algebraic specifications, semantics of programming languages, Hoare/dynamic logic, specification languages, program transformation. • Prerequisites: 3.5 COSC credits and MATH 1P67 or permission of the instructor • course procedures • plagiarism

  3. Textbooks • Main Text • None (course material is on the web page). • Supplemental Texts • The Formal Semantics of Programming Languages: An Introduction, G. Winskel, The MIT Press (1993), ISBN 0-262-23169-7 (hc), 0-262-73103-7 (pb) • The Design of Well-Structured and Correct Programs, S. Alagic & M.A. Arbib, Springer-Verlag (1978), ISBN 0-387-90299-6 • Fundamentals of Algebraic Specifications 1: Equations and Initial Semantics, H. Ehrig & B. Mahr, Springer-Verlag (1985), ISBN 0-387-13718-1

  4. Course Work • Marking Scheme • Lab Tests (3x20%) 60% • Final Exam (Lab D205) 40% • Important Dates Test Length Date (D205)/Time 1 45 mins Feb 01 (3:30pm-4:15pm) 2 45 mins Mar 01 (3:30pm-4:15pm) 3 45 mins Mar 22 (3:30pm-4:15pm) Exam 90 mins Apr 10 (10am-11:30am)

  5. Course Outline * February 18-22 is Reading Week, no classes. March 29 is Good Friday, no classes. Make up on April 08.

  6. A mark of at least 40% on the final exam is required to achieve a passing grade in this course. No electronic devices and especially no calculators will be allowed in the examination room. • Consideration regarding illness for test or exam dates will only be considered if accompanied with the completed Departmental Medical Excuse form.

  7. Motivation Assume you are a project coordinator in a software company. The latest project your team is working on has the following constraints: • avoid integer multiplication (there are issues with the hardware); • the operation square(n)=n2 will frequently be used in the program. You present this problem to a member of your team. He comes up with the following piece of code:

  8. A program r := 0; s := 1; i := 0; while i < n do r := r+s; s := s+2; i := i+1; od The program above computes n2 in the variable r.

  9. Testing

  10. Problems with Testing Testing may unveil errors in the code, but • You may only test finitely many examples. • Testing cannot verify that the code is bug-free. “Correctness cannot be established through testing. Testing can only delete errors, but never exclude errors.” Are you satisfied with the testing procedure? Yes?!?, but what if this program • controls a machine producing toys worth $10,000 an hour? • controls a rocket sending a new television satellite into orbit? An error in the code might cause a big financial loss for our company!!!

  11. n-1  2i+1. i=0 A proof The programmer says: “My program obviously computes Here is the proof that this is equal to n2.” (Compare this approach to Math 1P66/67.)

  12. n-1  2i+1. i=0 Further Problems? Are you satisfied with this proof? Yes?!?, but what if this program • controls the reentry of a space shuttle? • controls the rollercoaster you are sitting in? • controls the cooling system of the nuclear plant next door? The previous argument still contains the informal step: “My program obviously computes “ This could be wrong!!!!!

  13. Hoare logic Hoare logic is a calculus that can be used to prove partial correctness assertion of the form: {} c {} where ,  are formulas and c is a command (or program). The intended meaning of such a statement is as follows: If the precondition  is satisfied and the program c terminates, then the postcondition  will be satisfied (after the execution of c). Example: {n≥0} p {r=n2} where p is our program.

  14. Hoare logic – proof rules (Skip): {} skip {} (Assignment): {[a/x]} x:=a {} (Sequencing): {} c0 {} {} c1 {} {} c0;c1 {} (Conditional): {b} c0 {} {b} c1 {} {} if b then c0else c1fi {} (Loop): {b} c{} {} while b do c od {b} (Consequence): ’ {’} c {’} ’   {} c {}

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