1 CS 501 Spring 2002 CS 501: Software Engineering Lecture 10 Techniques for Requirements Definition...

1 CS 501 Spring 2002

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


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 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 <


Formal Specification Using Diagrams

digitunsigned integer

digit. E

+

-

unsigned integerunsigned integer

unsigned number

Pascal number syntax


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> ::= + | -

Pascal number syntax


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


Two Rules

Formal specification does not guarantee correctness

Formal specification does not prescribe the implementation


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 2002

Example: Algorithm

1 + 3 + 5 + ... (2n - 1) = n2

Static specification does not describe the design of the system.

A possible algorithm uses the mathematical identity:

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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;}

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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., ...

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Finite State Machine

Example:

Therapy control console

[informal description]

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State Transition Diagram

Patients Fields Setup ReadyBeam

on

Enter Enter Start

Stop

Select field

Select patient(interlock)

(ok)

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State Transition Table

SelectPatient

SelectField

Enter ok Start Stop interlock

Patients

Fields

Setup

Ready

Beamon

Fields

Fields

Fields

Patients

Patients

Patients

Setup

Setup

Setup

Ready

Beamon

Ready

17 CS 501 Spring 2002

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 }

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Schemas

Schema:

Enables complex system to be specifed as subsystems

The basic unit of formal specification.

Describes admissible states and operations of a system.

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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.

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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.

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LibSys

Level of Detail:

Assume given sets:

Copy, Book, Reader

Global constant:

maxloans

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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:

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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<

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Schema Inclusion

LibDB

stock : Copy Bookreaders: F Reader

LibLoansissued : Copy Readershelved : F Copy

r : Reader • #(issued {r}) maxloansshelved dom issued = Ø

<

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Schema Inclusion (continued)

Library

LibDBLibLoans

dom stock = shelved dom issuedran issued readers

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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!

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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

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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

29 CS 501 Spring 2002

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

<<

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Schema Decoration

Issue

LibraryLibrary'c? : Copy; r? : Reader

c? shelved; r? readers#(issued {r?}) < maxloansissued' = issued {c? r?}stock' = stock; readers' = readers

31 CS 501 Spring 2002

Schema Decoration

Issue

Libraryc? : Copy; r? : Reader

c? shelved; r? readers#(issued {r?}) < maxloansissued' = issued {c? r?}stock' = stock; readers' = readers

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The Schema Calculus

Schema inclusion

Schema decoration

Schema disjunction:

AddCopy AddKnownTitle AddNewTitle

Schema conjunction:

AddCopy EnterNewCopy AddCopyAdmin

Schema negation

Schema composition

=̂

=̂

1 CS 501 Spring 2002 CS 501: Software Engineering Lecture 10 Techniques for Requirements Definition...

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