Disciplined Software Engineering Lecture #12

1. Disciplined Software Engineering Lecture #12 • Software Engineering Institute • Carnegie Mellon University • Pittsburgh, PA 15213 • Sponsored by the U.S. Department of Defense • Additional material by • James P Alstad • March 2002 • Indicated by italics

2. Design Verification • Design verification is covered in 2 lectures. This lecture addresses • the reasons for design verification • state machine correctness • execution tables • proof by induction • The next lecture covers • trace tables • mathematical program verification • program proofs

3. Need for Design Verification - 1 • As you work to improve your personal software process, you will likely find it hard to significantly reduce the numbers of design defects you make. • By using checklists and taking increased care, you can improve the yield of your code reviews. • To improve the yield of design reviews, you need to use disciplined verification methods.

4. Defects Injected in Coding - Range 250 200 Max 150 Avg. 100 Min 50 0 Program Number

5. Defects Injected in Design - Range 100 80 Max 60 Avg 40 Min 20 0 Program Number

6. Need for Design Verification - 2 • An orderly approach to design verification is essential because • many common design defects are caused by overlooked conditions • what seem like unlikely situations become more likely with high-powered computing systems • conditions that were not possible with an initial program version may be induced by later modifications

7. Need for Design Verification - 3 • By following a structured design verification procedure, you are more likely to • see overlooked conditions • identify rarely exposed risks • recognize possible future exposures • By recording data on your design reviews, you can simplify later design inspections.

8. Using Design Verification - 1 • Design verification methods should be used • during design • during design reviews • during design inspections • Your design verification methods should focus on the defect types that have caused you the most trouble in test.

9. Using Design Verification- 2 • The topics covered in this and the next lecture were selected because they address the design defect categories that caused me the most trouble • state machine structures • loop constructs • I would use additional verification methods for the following defect types if they were available • pointers • interfaces

10. Design Verification Topics • The design verification topics covered in this and the next lecture are • verifying state machine correctness • execution tables • proof by induction • trace tables • mathematical program verification

11. State Machine Correctness • Any program that changes the state of the computing system is a state machine. • A program is a state machine if it can behave differently with identical inputs. • Seemingly simple state machines can have sophisticated behavior. It is thus important to verify them carefully. • Important assumption: When you do design, you select where to use state machines, and then treat them as such.

12. State Machine Verification • The steps in state machine verification are to • check to ensure the state machine has no hidden traps or loops • check that the set of all states is complete and orthogonal • check that the set of all transitions from every state are complete and orthogonal • After verifying state machine correctness (i.e., does the state machine go through correct transitions, etc?), ensure that the program performs the intended application functions (i.e., when in a state, does the program do the right thing, etc?).

13. Hidden Traps or Loops - 1 • To check for hidden traps and loops • construct the state template • construct a state machine diagram • determine if any exit states are unreachable from any other states • If any exit states are unreachable from any other state, this is not a proper state machine.

14. Hidden Traps or Loops - 2 • Example: consider an object BSet as follows • 2 states: EmptyState, MemberState • 4 methods: Push, Pop, Add, Subtract • Push adds a member to BSet • Pop removes a member from BSet • Add adds a member to BSet if it does not already contain an identical member • Subtract removes a member from BSet if it contains an identical member Note: this design is perhaps not as cohesive as it might be.

15. Hidden Traps or Loops - 3 • The state template for BSet would be as follows: n = 0 EmptyState Pop or Subtract EmptyState MemberState Push or Add MemberState n >= 1 Pop(n=1) or Subtract(n=1)(D in BSet) EmptyState Add or Push or Pop(n>1) or Subtract(D not in BSet) or Subtract(n>1) MemberState

16. Hidden Traps and Loops - 4 Pop or Subtract EmptyState n = 0 Push or Add MemberState n > 0 Pop(n=1) or Subtract(n=1)(D in BSet) Add or Push or Pop(n>1) or Subtract(D not in BSet) or Subtract(n>1)

17. Hidden Traps or Loops - 5 • It is thus clear that this state machine has no hidden traps or loops. • However, for a more complex state machine nothing may be “clear”. (Example: in a complex state machine, a particular transition out of state S may be necessary in order to reach the final state. But perhaps conditions for that transition cannot arise for any possible input which leads to state S.) In such complex cases, it may be necessary to provide additional argument for the no hidden traps or loops demonstration.

18. All Possible States - 1 • A common problem is to overlook some state machine state. • Examples are initial states, empty states, error states, and so forth. • Examine all possible conditions of the state parameters to ensure they are either included or truly impossible.

19. All Possible States - 2 • Checking the BSet example: • EmptyState has n = 0 • MemberState has n > 0 • since n cannot be < 0, this covers all cases • To ensure that none of the n > 0 states should be distinct, check to see if any of them exhibit different behavior from the others. This requires considering specifications which are prior to the state machine. • A check of the state template or state diagram shows that all n>0 states behave identically. Added states are thus unnecessary.

20. State Orthogonality • For the states to be orthogonal, the state machine must not be able to be in 2 states at once. • In the example state machine, either • n = 0 or n > 0. • The states are orthogonal because the machine must be in either the EmptyState (n = 0) or the MemberState (n > 0); it cannot be in both at once.

21. State Transitions - 1 • In a proper state machine, the state transitions must all be complete and orthogonal. • For this to be true • every state must have a defined next state for every possible input • every state must have a unique next state for every possible input

22. State Transitions - 2 • First, check EmptyState in the BSet example for completeness: • the conditions are Push, Pop, Add, and Subtract • states are defined for each condition, so the EmptyState transitions are complete. • The following table shows this: Push MemberState EmptyState Pop Add MemberState EmptyState Subtract

23. State Transitions - 3 • Next, check EmptyState transitions for orthogonality. • The transition conditions to EmptyState are Pop and Subtract. • The transition conditions to MemberState are Push and Add. • Since these next state transition conditions do not overlap, the transition conditions are orthogonal.

24. D in BSet D not in BSet n = 1 n > 1 n = 1 n > 1 Push MemberState MemberState MemberState MemberState Pop EmptyState MemberState EmptyState MemberState Add MemberState MemberState MemberState MemberState Subtract EmptyState MemberState MemberState MemberState State Transitions - 4 • For MemberState completeness, the possible cases are Since these are all the possible cases, the MemberState transitions are complete.

25. State Transitions - 5 • For MemberState orthogonality, there must be no overlap between the transitions. • the transitions from MemberState to EmptyState occur when: Pop(n=1) or Subtract[(n=1) and (D in BSet)] • the transitions from MemberState to MemberState occur when: Add + Push + Pop(n>1) + Subtract(D not in BSet) + Subtract(n>1) • As is clear from the previous chart, these two cases have no condition in common and are thus orthogonal.

26. Class Exercise - 1 • The SignOn object is to have the following methods • Open - initiates a sign-on procedure • LogOn - requests a name • if the name is correct, PassWord requests the password • if the PassWord is correct, SignOn terminates with the value true • if there is any error, the program starts again at LogOn • for any two errors, SignOn terminates with the value false

27. Class Exercise - 2 • Construct the SignOn state template and state diagram. • Check for hidden traps and loops. • Check the states for completeness and orthogonality. • Check the transitions for completeness and orthogonality.

28. Class Exercise - State Diagram StandBy LogOn(No) (false) Open LogOn(No) Start Error LogOn(Yes) LogOn(Yes) Trial PassWord(No) NameOk PassWord(Yes) (true) PassWord(No) (false) PassWord(Yes) (true)

29. Exercise - State Template StandBy n = 0 Start Open n = 1 Start NameOk LogOn(Yes) Error LogOn(No) n = 2 NameOk Error PassWord(No) StandBy (true) Password(Yes) Error n = 3 Trial LogOn(Yes) StandBy (false) LogOn(No) n = 4 Trial StandBy (true) PassWord(Yes) StandBy(false) PassWord(No)

30. On the Difficulty of Verification • The difficulty of verifying completeness and orthogonality of state machines depends mainly on whether conditions are used on transitions. • If transitions are caused just by events, then verification will be straightforward. • If transitions include conditions (“Pop occurred and n > 1”) then verification can be difficult.

31. Execution Tables - 1 • An execution table is an orderly way to trace program execution. • it is a manual check of the program flow • it starts with initial conditions • a set of variable values is selected • each execution step is examined • every change in variable values is entered • program behavior is checked against the specification

32. Execution Tables - 2 • The advantages of execution tables are • they are simple • they give reliable proofs • The disadvantages of execution tables are • they only check one case at a time • they are time consuming • they are subject to human error

33. Execution Table Procedure • To use an execution table • identify the key program variables and enter them at the top of the trace table • enter the principal program steps • determine and enter the initial conditions • trace the variable values through each program step • for repeating loops, add additional execution table steps for each additional loop cycle • for long loops, group intermediate steps if their results are obvious

34. Execution Table Example - 1 Cycle 1 ClearSpaces(var Input: string; State: int) # State Condition Length Instructions Input 1 Length = length(Input) ‘ AB ‘ 5 0 2 if Length > 0 true 3 repeat(until State=3 or Length=0) 4 if Input[Length-1] = ‘ ‘ true 5 Length = Length - 1 4 6 if State < 2 State=State+1 1 true 7 else State = 3 false until State=3 or Length=0

35. Execution Table Example - 2 • 3 cycles are required before the until condition is satisfied. • Just as with a test case, the execution table will only prove the case for this specific variable combination. • Carefully check the initial conditions to ensure they are set by the program. • Double check the execution table for errors and omissions.

36. Proof by Induction • This method applies to Boolean functions with integer parameters. • It states • if f(n) is true for n = k • and if • when n = z where z > k • and f(z) is true • you can show that f(z+1) is true • then f(n) is true for all values of n larger than k

37. Simplified Proof by Induction • Goal: Prove that some statement f(n) which depends on a non-negative integer variable n is true for all values of n. • Typical goal statement: This loop terminates and gives the correct result when the body has been executed n times. • Proof by induction says that we have reached our goal if we can do two things: • Demonstrate f(0); and • Demonstrate f(k+1), where we are allowed to assume f(k).

38. Proof by Induction Example • Example: • for i=1 to Limit • do xyz • If • you can show that this loop works for Limit = 0 and • assuming it is true for some Limit = z, you can then show it is true for Limit = z+1* then you have shown that the loop works for all non-negative values of Limit. *The form of reasoning here: assuming the loop has worked so far, show it works this time.

39. A Proof by Induction Technique • If • you have a design element using variable x • you verify that it works for x = k (x = 0 frequently the simplest choice) • Next • assume it works for some larger value x = z • try to find a value of z where program behavior would be improper at z + 1 • If you cannot, the proof is completed.

40. Factorial Example - 1 • Prove that the following program produces N! • Factorial(N) • F = 1 • for i = 1 to N • F = F*i • return = F • N! (“N factorial”) = 1 * 2 * ... * N • 0! = 1

41. Factorial Example - 2 • Show that when N=0, F = N! • since 0 factorial is 1, this is correct • Next, assume that when N = z, F = z! • Finally, find any value of z where • F(z) = z! and F(z+1) <> (z+1)! • Such cases would only occur when • the computing number system was exceeded • computing capacity was exceeded

42. Assignment • Previous reading: • Chapter 10 • Appendix B • New reading: • Chapter 12

43. The Messages to Remember from Lecture 12 • 1. Your design review yield will significantly • improve if you use disciplined design • review methods. • 2. The time spent verifying designs will be • more than repaid by the testing time saved. • 3. Practice verification techniques and select • the most effective for finding the defects • you most comonly find in testing.