1 cs 501 spring 2005 cs 501: software engineering lecture 10 requirements 4
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1 CS 501 Spring 2005
CS 501: Software Engineering
Lecture 10
Requirements 4
2 CS 501 Spring 2005
Course Administration
Presentations, March 9-10
Read the instructions on the Assignments web page
Reserve a time slot by sending email to anat@cs.cornell.edu. Time slots are listed on the home page of the web site. First-come-first-served.
3 CS 501 Spring 2005
Formal Specification
Why?
• Precise standard to define and validate software.
Why not?
• May be time consuming
• Methods are not suitable for all applications
4 CS 501 Spring 2005
Remember
Formal specification does not prescribe the implementation
With formal specification it is possible, at least theoretically, to generate code automatically from the specification, but this may not be the most effective way:
• Writing the generator may be a very large programming task.
• The resulting code may perform badly.
Formal specification does not guarantee correctness
• If the specification is wrong, the system will be wrong.
5 CS 501 Spring 2005
Formal Specification using Mathematical Notation
Mathematical requirements can be specified formally.
Example: requirements from a mathematical package:
B1, B2, ... Bk is a sequence of m x m matrices
1, 2, ... k is a sequence of m x m elementary matrices
B1-1 = 1
B2-1 = 21
Bk-1 = k ... 21
The numerical accuracy must be such that, for all k,
BkBk-1 - I <
6 CS 501 Spring 2005
Formal Specification Using Diagrams
digitunsigned integer
digit. E
+
-
unsigned integerunsigned integer
unsigned number
Example: Pascal number syntax
7 CS 501 Spring 2005
Formal Specification of Programming Languages
<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> ::= + | -
Example: Pascal number syntax
8 CS 501 Spring 2005
Formal Specification using Z ("Zed")
Z is a specification language developed by the Programming Research Group at Oxford University around 1980. Z is used for describing and modeling computing systems. It is based on axiomatic set theory and first order predicate logic.
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
9 CS 501 Spring 2005
Informal: The function intrt(a) returns the largest integer whose square is less than or equal to a.
Formal (Z):
intrt: N N
a : N •
intrt(a) * intrt(a) < a < (intrt(a) + 1) * (intrt(a) + 1)
Example: Specification using Z
10 CS 501 Spring 2005
Example: Implementation of intrt
1 + 3 + 5 + ... (2n - 1) = n2
Static specification does not describe the design of the system.
A possible algorithm uses the mathematical identity:
11 CS 501 Spring 2005
Example: Program for intrt
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 CS 501 Spring 2005
Formal Specification of Finite State Machine Using Z
A finite state machine is a broadly used method of formal specification:
• Event driven systems (e.g., games)
• User interfaces
• Protocol specification
etc., etc., ...
13 CS 501 Spring 2005
State Transition Diagram
Patients Fields Setup ReadyBeam
on
Enter Enter Start
Stop
Select field
Select patient(lock on)
(lock off)
14 CS 501 Spring 2005
State Transition Table
SelectPatient
SelectField
Enter lock off Start Stop lock on
Patients
Fields
Setup
Ready
Beamon
Fields
Fields
Fields
Patients
Patients
Patients
Setup
Setup
Setup
Ready
Beamon
Ready
15 CS 501 Spring 2005
Z Specification
STATE ::= patients | fields | setup | ready | beam_on
EVENT ::= select_patient | select_field | enter | start | stop | lock_off | lock_on
FSM == (STATE X EVENT) STATE
no_change, transitions, control : FSM
Continued on next slide
16 CS 501 Spring 2005
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, lock_off) ready,
(ready, select_patient) patients, (ready, select_field) fields, (ready, start) beam_on, (ready, lock_on) setup,
(beam_on, stop) ready, (beam_on, lock_on) setup }
17 CS 501 Spring 2005
Schemas
Schema:
• The basic unit of formal specification.
• Enables complex system to be specified as subsystems
• Describes admissible states and operations of a system.
18 CS 501 Spring 2005
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.
19 CS 501 Spring 2005
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.
20 CS 501 Spring 2005
LibSys: Modeling
Formal Specifications are models. As with all models, it is necessary to decide what should be included and what can be left out.
Level of detail
Assume given sets:
Copy, Book, Reader
Global constant:
maxloans
21 CS 501 Spring 2005
Domain and Range
dom mX Yx
ran my
m : X Y
dom m = { x X : y Y x y}
ran m = { y Y : x X x y}
m
domain:
range:
22 CS 501 Spring 2005
LibSys: Schema for Abstract States
Library
stock : Copy Bookissued : Copy Readershelved : F Copyreaders: F Reader
shelved dom issued = dom stockshelved dom issued = Øran issued readersr : readers • #(issued {r}) maxloans<
finite subset
Name
Declaration part
Predicate
23 CS 501 Spring 2005
Schema Inclusion
LibDB
stock : Copy Bookreaders: F Reader
LibLoansissued : Copy Readershelved : F Copy
r : Reader • #(issued {r}) maxloansshelved dom issued = Ø
<
24 CS 501 Spring 2005
Schema Inclusion (continued)
Library
LibDBLibLoans
dom stock = shelved dom issuedran issued readers
25 CS 501 Spring 2005
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!
26 CS 501 Spring 2005
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
27 CS 501 Spring 2005
Operation: Issue a Book
stock, stock' : Copy Book
issued, issued' : Copy Reader
shelved, shelved': F Copy
readers, readers' : F Reader
c?: Copy; r? :Reader
[See next slide]
Issue
28 CS 501 Spring 2005
Operation: Issue a Book (continued)
[See previous slide]
Issue
shelved dom issued = dom stockshelved' dom issued' = dom stock'shelved dom issued = Ø; shelved' dom issued' = Øran issued readers; ran issued' readers'r : readers #(issued {r}) maxloansr : readers' #(issued' {r}) maxloansc? shelved; r? readers; #(issued {r?}) < maxloansissued' = issued {c? r?}stock' = stock; readers' = readers
<<
29 CS 501 Spring 2005
Schema Decoration
Issue
LibraryLibrary'c? : Copy; r? : Reader
c? shelved; r? readers#(issued {r?}) < maxloansissued' = issued {c? r?}stock' = stock; readers' = readers
30 CS 501 Spring 2005
Schema Decoration
Issue
Libraryc? : Copy; r? : Reader
c? shelved; r? readers#(issued {r?}) < maxloansissued' = issued {c? r?}stock' = stock; readers' = readers
31 CS 501 Spring 2005
The Schema Calculus
Schema inclusion
Schema decoration
Schema disjunction:
AddCopy AddKnownTitle AddNewTitle
Schema conjunction:
AddCopy EnterNewCopy AddCopyAdmin
Schema negation
Schema composition
=̂
=̂
32 CS 501 Spring 2005
Z in Practice
In carefully monitored industrial use, Z has been shown to improve the timeliness and accuracy of software development, yet it is widely used in practice.
Complexity of notation makes communication with client difficult.
Few software developers are comfortable with the underlying axiomatic approach.
Heavy notation is awkward to manipulate with conventional tools, such as word processors.
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