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CS 501: Software Engineering

CS 501: Software Engineering. Lecture 10 Techniques for Requirements Definition and Specification II . Administration. Formal Specification. Why?  Precise standard to define and validate software. Why not?  May be time consuming  Methods are not suitable for all applications.

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CS 501: Software Engineering

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  1. CS 501: Software Engineering Lecture 10 Techniques for Requirements Definition and Specification II

  2. Administration

  3. Formal Specification Why?  Precise standard to define and validate software. Why not?  May be time consuming  Methods are not suitable for all applications

  4. Formal Specification using Mathematical Notation Example: B1, B2, ... Bk is a sequence of m x m matrices 1, 2, ... k is a sequence of m x m elementarymatrices B1-1 = 1 B2-1 = 21 Bk-1 = k ... 21 The numerical accuracy must be such that, for all k, BkBk-1 - I<

  5. digit digit + . E - Formal Specification Using Diagrams Pascal number syntax unsigned integer unsigned number unsigned integer unsigned integer

  6. Formal Specification of Programming Languages Pascal number syntax <unsigned number> ::= <unsigned integer> | <unsigned real> <unsigned integer> ::= <digit> {<digit>} <unsigned real> ::= <unsigned integer> . <digit> {<digit>} | <unsigned integer> . <digit> {<digit>} E <scale factor> | <unsigned integer> E <scale factor> <scale factor> ::= <unsigned integer> | <sign> <unsigned integer> <sign> ::= + | -

  7. Formal Specification using Z ("Zed") Ben Potter, Jane Sinclair, David Till, An Introduction to Formal Specification and Z (Prentice Hall) 1991 Jonathan Jacky The Way of Z (Cambridge University Press) 1997

  8. Two Rules  Formal specification does not guarantee correctness  Formal specification does not prescribe the implementation

  9. Example: Specification using Z Informal: The function intrt(a) returns the largest integer whose square is less than or equal to a. Formal (Z): intrt: NN a : N • intrt(a) * intrt(a) < a < (intrt(a) + 1) * (intrt(a) + 1)

  10. Example: Algorithm Static specification does not describe the design of the system. A possible algorithm uses the mathematical identity: 1 + 3 + 5 + ... (2n - 1) = n2

  11. Example: Program int intrt (int a) /* Calculate integer square root */ { int i, term, sum; term = 1; sum = 1; for (i = 0; sum <= a; i++) { term = term + 2; sum = sum + term; } return i; }

  12. Formal Specification Using Finite State Machine A broadly used method of formal specification:  Event driven systems (e.g., games)  User interfaces  Protocol specification etc., etc., ...

  13. Finite State Machine Example: Therapy control console [informal description]

  14. State Transition Diagram Select field Start Enter Enter (ok) Beam on Patients Fields Setup Ready Stop (interlock) Select patient

  15. State Transition Table Select Patient Select Field interlock ok Enter Start Stop Patients Fields Setup Patients Fields Setup Fields Ready Patients Beam on Patients Ready Fields Setup Beam on Ready Setup

  16. Z Specification STATE ::= patients | fields | setup | ready | beam_on EVENT ::= select_patient | select_field | enter | start | stop | ok | interlock FSM == (STATE X EVENT) STATE no_change, transitions, control : FSM Continued on next slide

  17. Z Specification (continued) control = no_change transitions no_change = { s : STATE; e : EVENT • (s, e) s } transitions = { (patients, enter)fields, (fields, select_patient) patients, (fields, enter) setup, (setup, select_patient) patients, (setup, select_field) fields, (setup, ok) ready, (ready, select_patient) patients, (ready, select_field) fields, (ready, start) beam_on, (ready, interlock) setup, (beam_on, stop) ready, (beam_on, interlock) setup }

  18. Schemas Schema:  Enables complex system to be specifed as subsystems  The basic unit of formal specification.  Describes admissible states and operations of a system.

  19. LibSys: An Example of Z Library system:  Stock of books  Registered users.  Each copy of a book has a unique identifier.  Some books on loan; other books on shelves available for loan.  Maximum number of books that any user may have on loan.

  20. LibSys: Operations  Issue a copy of a book to a reader.  Reader returns a book.  Add a copy to the stock.  Remove a copy from the stock.  Inquire which books are on loan to a reader.  Inquire which readers has a particular copy of a book.  Register a new reader.  Cancel a reader's registration.

  21. LibSys Level of Detail: Assume given sets: Copy, Book, Reader Global constant: maxloans

  22. Domain and Range ran m X dom m Y m y x m : XY dom m = { x X :  y  Y  xy} ran m = { y Y :  x  X  xy} domain: range:

  23. < LibSys: Schema for Abstract States Library stock : CopyBook issued : CopyReader shelved : FCopy readers: FReader shelved dom issued = dom stock shelved dom issued = Ø ran issued readers r : readers• #(issued {r}) maxloans

  24. < Schema Inclusion LibDB stock : Copy Book readers: FReader LibLoans issued : Copy Reader shelved : FCopy r : Reader• #(issued {r}) maxloans shelved dom issued = Ø

  25. Schema Inclusion (continued) Library LibDB LibLoans dom stock = shelved dom issued ran issued  readers

  26. Schemas Describing Operations Naming conventions for objects: Before: plain variables, e.g., r After: with appended dash, e.g., r' Input: with appended ?, e.g., r? Output: with appended !, e.g., r!

  27. Operation: Issue a Book  Inputs: copy c?, reader r?  Copy must be shelved initially: c?  shelved  Reader must be registered: r?  readers  Reader must have less than maximum number of books on loan: #(issued {r?}) < maxloans  Copy must be recorded as issued to the reader: issued' = issued {c? r?}  The stock and the set of registered readers are unchanged: stock' = stock; readers' = readers

  28. Operation: Issue a Book stock, stock' : Copy Book issued, issued' : Copy Reader shelved, shelved': FCopy readers, readers' : FReader c?: Copy; r? :Reader [See next slide] Issue

  29. < < Operation: Issue a Book (continued) Issue [See previous slide] shelved dom issued = dom stock shelved' dom issued' = dom stock' shelved  dom issued = Ø; shelved'  dom issued' = Ø ran issued  readers; ran issued'  readers' r : readers  #(issued {r}) maxloans r : readers'  #(issued' {r}) maxloans c? shelved; r?  readers; #(issued  {r?}) < maxloans issued' = issued  {c? r?} stock' = stock; readers' = readers

  30. Schema Decoration Issue Library Library' c? : Copy; r? : Reader c? shelved; r?  readers #(issued {r?}) < maxloans issued' = issued  {c? r?} stock' = stock; readers' = readers

  31. Schema Decoration Issue Library c? : Copy; r? : Reader c? shelved; r?  readers #(issued {r?}) < maxloans issued' = issued  {c? r?} stock' = stock; readers' = readers

  32. ^ ^ = = The Schema Calculus Schema inclusion Schema decoration Schema disjunction: AddCopy AddKnownTitle  AddNewTitle Schema conjunction: AddCopyEnterNewCopy  AddCopyAdmin Schema negation Schema composition

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