1 CS 501 Spring 2002

CS 501: Software Engineering

Lecture 10

Techniques for Requirements Definition and Specification II

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Administration

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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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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 <

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Formal Specification Using Diagrams

digitunsigned integer

digit. E

+

-

unsigned integerunsigned integer

unsigned number

Pascal number syntax

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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

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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

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Two Rules

Formal specification does not guarantee correctness

Formal specification does not prescribe the implementation

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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

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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

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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

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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

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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

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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

=̂

=̂