Lectures 9,10

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Lectures 9,10

• Formal Specifications

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Formal Specification - Techniques for the
unambiguous specification of software

• Objectives
• To explain why formal specification techniques
  help discover problems in system requirements
• To describe the use of
• algebraic techniques (for interface
  specification) and
• model-based techniques(for behavioural
  specification)
• To introduce Abstract State Machine Model

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Formal methods

• Formal specification is part of a more general
  collection of techniques that are known as
  formal methods COMP313 Formal Methods
• These are all based on mathematical
  representation and analysis of software
• Formal methods include
• Formal specification
• Specification analysis and proof
• Transformational development
• Program verification

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Acceptance of formal methods

• Formal methods have not become mainstream
  software development techniques as was once
  predicted
• Other software engineering techniques have been
  successful at increasing system quality. Hence
  the need for formal methods has been reduced
• Market changes have made time-to-market rather
  than software with a low error count the key
  factor. Formal methods do not reduce time to
  market
• The scope of formal methods is limited. They are
  not well-suited to specifying and analysing user
  interfaces and user interaction
• Formal methods are hard to scale up to large
  systems

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Use of formal methods

• Their principal benefits are in reducing the
  number of errors in systems so their main area of
  applicability is critical systems
• Air traffic control information systems,
• Railway signalling systems
• Spacecraft systems
• Medical control systems
• In this area, the use of formal methods is most
  likely to be cost-effective
• Formal methods have limited practical
  applicability

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Specification in the software process

• Specification and design are inextricably mixed.
• Architectural design is essential to structure a
  specification.
• Formal specifications are expressed in a
  mathematical notation with precisely defined
  vocabulary, syntax and semantics.

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Specification and design
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Specification in the software process
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Specification techniques

• Algebraic approach
• The system is specified in terms of its
  operations and their relationships
• Model-based approach
• The system is specified in terms of a state model
  that is constructed using mathematical constructs
  such as sets and sequences.
• Operations are defined by modifications to the
  systems state

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Formal specification languages
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Use of formal specification

• Formal specification involves investing more
  effort in the early phases of software
  development
• This reduces requirements errors as it forces
  a detailed analysis of the requirements
• Incompleteness and inconsistencies can be
  discovered and resolved !!!
• Hence, savings as made as the amount of rework
  due to requirements problems is reduced

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Development costs with formal specification
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1. Interface specification

• Large systems are decomposed into subsystems with
  well-defined interfaces between these subsystems
• Specification of subsystem interfaces allows
  independent development of the different
  subsystems
• Interfaces may be defined as abstract data types
  or object classes
• The algebraic approach to formal specification
  is particularly well-suited to interface
  specification

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Sub-system interfaces
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The structure of an algebraic specification
lt SPECIFICA
TION NAME gt (Gener
ic P
ar
ameter)
sort
lt name gt
introduction
imports
lt LIST
OF SPECIFICA
TION NAMES gt
description
Inf
or
mal descr
iption of the sor
t and its oper
ations
Oper
ation signatures setting out the names and the
types of
signature
the parameters to the operations defined over the
sort
Axioms defining the oper
ations o
v
er the sor
t
axioms
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Behavioural specification

• Algebraic specification can be cumbersome when
  the object operations are not independent of the
  object state
• Model-based specification exposes the system
  state and defines the operations in terms of
  changes to that state

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OSI reference model
Model-based specification
Application
Algebraic specification
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Abstract State Machine Language (AsmL)

• AsmL is a language for modelling the structure
  and behaviour of digital systems
• AsmL can be used to faithfully capture the
  abstract structure and step-wise behaviour of any
  discrete systems, including very complex ones
  such as
• Integrated circuits, software components, and
  devices that combine both hardware and software

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Abstract State

• An AsmL model is said to be abstract because it
  encodes only those aspects of the systems
  structure that affect the behaviour being
  modelled
• The goal is to use the minimum amount of detail
  that accurately reproduces (or predicts) the
  behaviour of the system
• Abstraction helps us reduce complex problems into
  manageable units and prevents us from getting
  lost in a sea of details
• AsmL provides a variety of features that allow
  you to describe the relevant state of a system in
  a very economical, high-level way

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Abstract State Machine and Turing Machine

• An abstract state machine is a particular kind of
  mathematical machine, like the Turing machine
  (TM)
• But unlike a TM, ASMs may be defined a very high
  level of abstraction
• An easy way to understand ASMs is to see them as
  defining a succession of states that may follow
  an initial state

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State transitions

• The behaviour of a machine (its run) can always
  be depicted as a sequence of states linked by
  state transitions

• Moving from state A to state B is a state
  transition

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Configurations

• Each state is a particular configuration of the
  machine
• The state may be simple or it may be very large,
  with complex structure
• But no matter how complex the state might be,
  each step of the machines operation can be seen
  as a well-defined transition from one particular
  state to another

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Evolution of state variables

• We can view any machines state as a dictionary
  of
• (Name, Value)
• pairs, called state variables

(Colour, Red) is a variable, where Colour is
the name of variable, Red is the value
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Evolution of state variables

• Names are given by the machines symbolic
  vocabulary
• Values are fixed elements, like numbers and
  strings of characters

The run of a machine is a series of states and
state transitions that results form applying
operations to each state in succession
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Example

• Diagram shows the run of a machine that models
  how orders might be
• processed

• Each transition operation
• can be seen as the result of invoking the
  machines control logic on the current state
• calculates the subsequence state as output

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Control Logic

• The machines control logic
• behaves like a fix set of transition
• rules that say how state may evolve

Typical form of the operational text is if
condition then update
We can think of the control logic as a text
that precisely specifies, for any given state,
what the values of the machines variables will
be in the following step
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Control Logic as a Black Box

• The machine control logic is a black box that
  takes as input a state dictionary S1 and gives as
  output a new dictionary S2

input
mode Initial
orders 0
balance 0
output
Mode Active
orders 2
balance 200

• The two dictionaries S1 and S2 have the same set
  of keys, but the values associated with each
  variable name may differ between S1 and S2

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Run of the Machine

• The run of the machine can be seen as what
  happens when the control logic is applied to each
  state in turn
• The run starts form initial state
• S1 ? S2 ? S3 ?
• S1 is given to the black box yielding S2,
  processing S2 results in S3,
• and so on
• When no more changes to state are possible, the
  run is complete

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Update operations

• We use the symbol
• (reads as gets)
• to indicate the value that a name will have in
  the resulting state
• For example modeActive
• Update can be seen only during the following step
  (this is in contrast to Java, C, Pascal, )
• All changes happen simultaneously, when you
  moving from one step to another. Then, all
  updates happen at once.(atomic transaction)

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Programs

• Example 1. Hello, world
• Main()
• step WriteLine(hello, world!)

ASML uses indentations to denote block structure,
and blocks can be places inside other
blocks Statement block affect the scope of
variables Whitespace includes blanks and new-line
character, ASML does not recognize tab character
for indentation !!!!!!! An operation names Main()
gives the top-level operational definition of the
model (Main() is like main() in Java and C )
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The Executable Specification Language - ASML
Compiler asmlc name of the program !!!
Use D drive at the University Laboratories
!!! Example D\gtasmlc test.asml D\gt
test.exe D\gt test.exe gtoutput_file.txt
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I. Steps

• The general syntax for steps is
• Step label stopping-condition
• statement block
• a statement block consists of indented statement
  that follow
• a label is an optional string, number of
  identifier followed by a colon ()
• stopping condition is any these forms
• until fixpoint
• until expression
• while expression

A step can be introduced independently or as part
of sequence of steps in the form step step
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Stopping for fixed point until fixed point
enum EnumMode Initial Started
Finished var mode Initial var count
0 Main() step until fixpoint if mode
Initial then mode Started
count1 if mode Started and count lt 10 then
count count1 if mode Started
and count gt10 then mode Finished
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Stopping for conditions while until
Either while or until may be used to give an
explicit stopping condition for iterated
sequential steps of the machine.
while expression until expression
var x as Integer 1 Main() step while x lt 10
WriteLine(x) x x 1
var x as Integer 1 Main() step until x gt 9
WriteLine(x) x x 1
Running each of these examples produces nine
steps. It will print numbers 1,2,3,4,5,6,7,8
and 9 as output
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Conditions
eq ne ? lt lt gt gt in ? notin ?
subset ? superset ? subseteq ? superseteq ?
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Sequences of steps

• The syntax step step indicates a sequence
  of steps that will be performed in order

• Labels after the step keyword are optional but
  helpful as documentation.

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Be wary !

• Be wary of introducing unnecessary steps
• This can occur if two operations are really not
  order-dependent but are given as two sequential
  steps, regardless
• It is very easy to fall into this trap, since
  most people are used to the sequential structures
  used by other programming languages

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Iteration over collections
Another common idiom for iteration is to do one
step per element in some finite collection such
as a set or sequence
step foreach ident1 in expr1, ident2 in expr2

statement-block
myList 1,2,3 Main() step foreach i in
myList WriteLine (i)
Sequential, step-based iteration is available for
sets as well as sequences, but in the case of
sets, the order is not specified
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Guidelines for using steps
Situation You choose
operations occur in a fixed order sequence of steps
each operation must be done in order iterated steps with stopping condition while,until
operations must be done in sequence, one after another iteration over collection foreach
operations can be done without order iteration over collection forall
Repeat an operation until no more changes occur fixed-point stopping condition until fixed point
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II. Updates How are variables updated?

• A program defines state variables and operations
• The most important concept is that state is a
  dictionary of (name,value) pairs
• Each name identifies an occurrence for state
  variables

• Operations may propose new values for state
  variables
• But effect of these changes is only visible in
  subsequent step

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The update statement

• Update symbol (reads as gets)

var x 0 var y 1 Main() step
WriteLine(In the first step, x x) // x is
0 WriteLine (In the first step, y y)
// y is 1 x2 step // updates occur here
WriteLine(In the second step, x x)//x
is 2 WriteLine(In the second step, y
y)//y is 1
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Delayed effect of updates
Updates dont actually occur until the step
following the one in which they are written
var x 0 var y 1 Main() step
WriteLine(In the first step, x x) // x is
0 WriteLine(In the first step, y y) //
y is 1 step x2 WriteLine (In the
second step, x x) // x is 0 step
WriteLine (In the third step, x x) // x
is 2
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When updates occur

• All updates given within a single step occur
  simultaneously at the end of the step.
• Conceptually, the updates are applied in
  between the steps.

Swapping values
in C, Java in ASML
temp x x y y temp step x y yx
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Consistency of updates

• The order within a step does not matter, but all
  of updates in the step must be consistent
• None of the updates given within a step may
  contradict each other
• If updates do contradict, then they are called
  inconsistent updates and an error occur

Inconsistent update Error CLASH in the update set
step x1 x2 we dont know which of the two should take effect
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Total and partial updates

• An update of the variable can either be total or
  partial
• Total update is a simple replacement of
  variables value with a new value
• Partial updates apply to variables that have
  structure
• The left hand side of the update operation
• X val
• indicates whether the update is total or
  partial

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Total update of a set-valued variable
var Students as Set of String Main() step
WriteLine (The initial roster is
Students) Students Bill, Carol,
Ted, Alice step WriteLine (The final
roster is Students)

1. The variable Students was, initially, an empty
   set
2. It was then updated to contain the names of the
   four students
3. Update became visible in the second step as the
   finial roster

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Partial update of a set-valued variable
var Students as Set of String Main() step
WriteLine (The initial roster is
Students) Students(Bill) true
Students(Carol) true Students(Ted)
true Students(Alice) true step
WriteLine (The final roster is Students)

• X val is update operation
• If X ends with an index form, then the update is
  partial
• If X ends with a variable name, then the update
  is total

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Updating a set-valued variable
var Students as Set of String Main() step
WriteLine (The initial roster is
Students) Students Bill, Carol, Ted,
Alice step WriteLine (The current roster
is Students) Students ( Bill)
false // ( ) step WriteLine
(The final roster is Students)

• Updating the set Students with updating statement
  () removes Bill from the set
• The update is partial in the sense that other
  students may be added to the set Students in the
  same step without contradiction