Slide 1 Formal Specification - Techniques for the unambiguous specification of software Objectives:...

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

Formal methods

Formal specification is part of a more general collection of techniques that are known as ‘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

Notations For Formal Specification

Any notation with precise semantics can be used Formalism typically applied to just part of a

specification Notations use discrete mathematics, some with

graphics Several notations are sometimes used in the

same specification:• Z or VDM for data manipulation• Statecharts for system states and transitions• Natural language for non-functional specifications

Formal Specification

Goals of formal specification:• Complete• Consistent• Concise• Unambiguous• Valid—state exactly what the user wants

Specifications based on formal semantic model What is/are semantics? What is a formal semantic model?

Formal Semantics

Semantics means “meaning” Formal semantics:

• Meaning expressed in mathematics

Formal semantic model:• Complete semantic definition of a language in mathematics

What mathematics?• Discrete mathematics!

Formal semantics permit dependable communication between all parties

Types Of Languages

Procedural:• Computation defined by desired sequence of actions computer is to

perform

• Most high-level languages are procedural

Declarative:• Computation defined by desired state that computer should be in

• Many specification languages are declarative

Functional:• Computation defined as desired function computer is to evaluate

• Most functional languages derive from LISP

Types Of Languages

High-level language programs are actually specifications!• Compilers write the program for you• So you have been specifying programs, not writing them

The big difference in languages is:• Declarative:

» Says nothing about HOW, just WHAT

• Procedural:» Says nothing about WHAT, just HOW

Types Of Languages—Examples

Procedural:

read (x);

y := x;

while y**2 > x loop

y := y – 1;

end loop;

print (y); Declarative:

y**2 <= x AND (y+1)**2 > x

Formal Methods Activities

Write a specification using a formal notation Validate the specification

• Inspect it with domain experts• Perform automated analysis to prove theorems

Refine the specification to an implementation• Semantics-preserving transformations to code

Verify that the implementation matches the spec• Mathematical argument

Library Example: Informal Statement

A book can either be in the stacks, on reserve, or loaned out

If a book is in the stacks or on reserve, then it can be requested

We want to • formalize the concepts and the statements• prove some theorems to gain confidence that the spec is

correct

Library Example: Formalization (1/2)

First let’s formalize some concepts

S: the book is in the stacks R: the book is on reserve L: the book is on loan Q: the book is requested

Library Example: Formalization (2/2)

If a book is requested, then it is on the shelf or on reserve

Library Example: Proof of a Theorem

Library Example: Proof By Contradiction

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

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

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 as 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

Two 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 system’s state

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

Sub-system interfaces

Sub-systemA

Sub-systemB

Interfaceobjects

The structure of an algebraic specification

sort < name >imports < LIST OF SPECIFICATION NAMES >

Informal descr iption of the sor t and its operations

Operation signatures setting out the names and the types ofthe parameters to the operations defined over the sort

Axioms defining the operations over the sort. Axioms relatethe operations used to construct entities with operations usedto inspect their values.

< SPECIFICATION NAME > (Generic Parameter)

Specification components Introduction

• Defines the sort (the type name) and declares other specifications that are used

Description• Informally describes the operations on the type

Signature• Defines the syntax of the operations in the interface and

their parameters

Axioms• Defines the operation semantics by defining axioms which

characterise behaviour

Specification operations

Constructor operations. Operations which create entities of the type being specified

Inspection operations. Operations which evaluate entities of the type being specified

To specify behaviour, define the inspector operations for each constructor operation

Interface specification in criticalsystems

Consider an air traffic control system where aircraft fly through managed sectors of airspace

Each sector may include a number of aircraft but, for safety reasons, these must be separated

In this example, a simple vertical separation of 300m is proposed

The system should warn the controller if aircraft are instructed to move so that the separation rule is breached

A sector object

Critical operations on an object representing a controlled sector are• Enter. Add an aircraft to the controlled airspace• Leave. Remove an aircraft from the controlled airspace• Move. Move an aircraft from one height to another• Lookup. Given an aircraft identifier, return its current

height

Primitive operations

It is sometimes necessary to introduce additional operations to simplify the specification

The other operations can then be defined using these more primitive operations

Primitive operations• Create. Bring an instance of a sector into existence

• Put. Add an aircraft without safety checks

• In-space. Determine if a given aircraft is in the sector

• Occupied. Given a height, determine if there is an aircraft within 300m of that height

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

Abstract State Machine Language (AsmL)

AsmL is an executable specification 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

Abstract State An AsmL model is said to be abstract because it

encodes only those aspects of the system’s 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

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

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

paint in green

paint in redA B

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 machine’s operation can be seen as a well-defined transition from one particular state to another

Evolution of state variables

paint in green

paint in redA B

We can view any machine’s 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

Evolution of state variables Names are given by the machine’s 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

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

S1

Mode = “Initial”

Orders = 0

Balance = £0

Initialise Process All Orders

S3

Mode = “Final”

Orders = 0

Balance = £500

S2

Mode = “Active”

Orders = 2

Balance = £200

Each transition operation: • can be seen as the result of invoking the machine’s

control logic on the current state • calculates the subsequence state as output

Control LogicThe machine’s control logic

behaves like a fix set of transition rules that say how state may evolve

We can think of the control logic as a text that precisely specifies, for any given state, what the values of the machine’s variables will be in the following step

Typical form of the operational text is:

“ if condition then update ”

Control Logic as a Black Box

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

The Machine’s Control Logic

…

if mode = “Initial”

then mode := “Active”

mode “Initial”

orders 0

balance £0

Mode “Active”

orders 2

balance £200

input

output

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

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

Update operations We use the symbol

“: =” (reads as “gets”) to indicate the value that a name will have in the resulting state

For example: mode:=“Active”

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)

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 !!!!!!!

Main() is like main() in Java and C

Example 2. Reading a filevar F as File? = undefvar Fcontents as String = “”var Mode as String = “Initial”Main() step until fixpoint if Mode = “Initial” then F :=open(“mfile.txt”) Mode :=“Reading”

if Mode = “Reading” and length(FContents) =0 then FContents :=fread (F,1)

if Mode = “Reading” and length(FContents) =1 then FContents := FContents + fread (F,1)

if Mode = “Reading” and length(FContents) >1 then WriteLine (FContents) Mode :=“Finished”

Example 2. Graph representation

S1

F= undef

Fcontents =“”

Mode = Initial

Step 1 Step 2

S3

F= <open file 1>

Fcontents =“a”

Mode = Reading

S2

F= <open file 1>

Fcontents =“”

Mode = Reading

S4

F= <open file 1>

Fcontents =“ab”

Mode = Reading Step 4Step5

S5

F= <open file 1>

Fcontents =“ab”

Mode = Finished

Step 3

Key points

Formal system specification complements informal specification techniques

Formal specifications are precise and unambiguous. They remove areas of doubt in a specification

Formal specification forces an analysis of the system requirements at an early stage. Correcting errors at this stage is cheaper than modifying a delivered system

Key points

Formal specification techniques are most applicable in the development of critical systems and standards.

Algebraic techniques are suited to interface specification where the interface is defined as a set of object classes

Model-based techniques model the system using sets and functions. This simplifies some types of behavioural specification

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