COSC 4P42 Formal Methods in Software Engineering

1
COSC 4P42Formal Methods in Software Engineering

• Instructor Michael Winter
• Office J323
• Office Hours Tue Thu 1000am noon
• email mwinter_at_brocku.ca
• Webpage www.cosc.brocku.ca/Offerings/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 COSC 3F00(minimum 60 percent) and
  3P03 (minimum 60 percent).
• 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
• Assignments (3x10) 30
• Project 30
• Final Exam (oral, 30min each) 40
• Important Dates
• Assignment Due Late Class presentation
• 1 Jan 26 _at_ 100 pm Jan 28 _at_ 100 pm Jan
  29 _at_ 200 pm
• 2 Feb 09 _at_ 100 pm Feb 11 _at_ 100 pm Feb
  12 _at_ 200 pm
• 3 Mar 02 _at_ 100 pm Mar 04 _at_ 100 pm Mar
  05 _at_ 200 pm
• Project Mar 30 _at_ 100 pm no late date Mar
  31/Apr 02 _at_ 200 pm

5
Course Outline
6

• Assignments will be available on-line.
  Assignments will be returned via room J333 at the
  times posted.
• Assignments are due at the times specified above
  and will be accepted late until the indicated
  time, subject to a penalty of 25. After the late
  period, assignments will not be accepted.
• 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.
• Assignments will be carefully examined regarding
  plagiarism. Cases of suspected plagiarism will be
  dealt with according to the University
  regulations and Departmental procedures.
• Consideration regarding illness for assignment
  submission or test 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 lt n do
• r rs
• s s2
• i i1
• 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
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
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 n0 p rn2
• where p is our program.

14
Hoare logic proof rules

• (Skip) ? skip ?
• (Assignment) ?a/x xa ?
• (Sequencing) ? c0 ? ? c1 ?
• ? c0c1 ?
• (Conditional) ??b c0 ? ???b c1 ?
• ? if b then c0 else c1 fi ?
• (Loop) ??b c ?
• ? while b do c od ???b
• (Consequence) ??? ? c ? ? ? ?
• ? c ?