Lectures 9 10 Formal Specifications Software Engineering COMP

Lectures 9, 10 Formal Specifications Software Engineering, COMP 201 Slide 1

Formal Specification - Techniques for the unambiguous specification of software Objectives: l l To explain why formal specification techniques help discover problems in system requirements To describe the use of • • l algebraic techniques (for interface specification) and model-based techniques(for behavioural specification) To introduce Abstract State Machine Model Software Engineering, COMP 201 Slide 2

Formal methods l l Formal specification is part of a more general collection of techniques that are known as ‘formal methods’ COMP 313 “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 Software Engineering, COMP 201 Slide 3

Acceptance of formal methods l 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 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 Software Engineering, COMP 201 Slide 4

Use of formal methods l Their principal benefits are in reducing the number of errors in systems so their main area of applicability is critical systems: • • l l 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 Software Engineering, COMP 201 Slide 5

Specification in the software process l l l 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. Software Engineering, COMP 201 Slide 6

Specification and design Software Engineering, COMP 201 Slide 7

Specification in the software process Software Engineering, COMP 201 Slide 8

Specification techniques l Algebraic approach • l 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 Software Engineering, COMP 201 Slide 9

Formal specification languages ASML - Abstract State Machine Language Yuri. Gurevich, Microsoft Research, 2001 Software Engineering, COMP 201 Slide 10

Use of formal specification l l 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 Software Engineering, COMP 201 Slide 11

Development costs with formal specification Software Engineering, COMP 201 Slide 12

1. Interface specification l l l 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 Software Engineering, COMP 201 Slide 13

Sub-system interfaces Software Engineering, COMP 201 Slide 14

The structure of an algebraic specification < SPECIFICATION NAME > (Gener ic Parameter) sort < name > imports < LIST OF SPECIFICATION NAMES > Informal descr iption of the sor t and its operations introduction description Operation signatures setting out the names and the types of the parameters to the operations defined over the sort signature Axioms defining the operations over the sort Software Engineering, COMP 201 axioms Slide 15

Behavioural specification l l 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 Software Engineering, COMP 201 Slide 16

OSI reference model Application Model-based specification Algebraic specification Software Engineering, COMP 201 Slide 17

Abstract State Machine Language (Asm. L) l l Asm. L is a language for modelling the structure and behaviour of digital systems Asm. L 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 Software Engineering, COMP 201 Slide 18

Abstract State l l An Asm. L 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 Asm. L provides a variety of features that allow you to describe the relevant state of a system in a very economical, high-level way Software Engineering, COMP 201 Slide 19

Abstract State Machine and Turing Machine l l l 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 Software Engineering, COMP 201 Slide 20

State transitions l The behaviour of a machine (its run) can always be depicted as a sequence of states linked by state transitions paint in green A paint in red B • Moving from state A to state B is a state transition Software Engineering, COMP 201 Slide 21

Configurations l l l 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 Software Engineering, COMP 201 Slide 22

Evolution of state variables We can view any machine’s state as a dictionary of (Name, Value) pairs, called state variables paint in green A paint in red B (Colour, Red) is a variable, where “Colour” is the name of variable, “Red” is the value Software Engineering, COMP 201 Slide 23

Evolution of state variables l l 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 Software Engineering, COMP 201 Slide 24

Example Diagram shows the run of a machine that models how orders might be Initialise Process All Orders processed S 1 S 2 S 3 Mode = “Initial” Mode = “Active” Mode = “Final” Orders = 0 Orders = 2 Orders = 0 Balance = £ 200 Balance = £ 500 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 Software Engineering, COMP 201 Slide 25

Control Logic The machine’s 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 machine’s variables will be in the following step Software Engineering, COMP 201 Slide 26

Control Logic as a Black Box • The machine control logic is a black box that takes as input a state dictionary S 1 and gives as output a new dictionary S 2 mode “Initial” orders 0 balance £ 0 input The Machine’s Control Logic output … if mode = “Initial” then mode : = “Active” l Mode “Active” orders 2 balance £ 200 The two dictionaries S 1 and S 2 have the same set of keys, but the values associated with each variable name may differ between S 1 and S 2 Software Engineering, COMP 201 Slide 27

Run of the Machine l l 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 S 1 S 2 S 3 … S 1 is given to the black box yielding S 2, processing S 2 results in S 3, and so on … l When no more changes to state are possible, the run is complete Software Engineering, COMP 201 Slide 28

Update operations l l 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, …) l All changes happen simultaneously, when you moving from one step to another. Then, all updates happen at once. (atomic transaction) Software Engineering, COMP 201 Slide 29

Programs Example 1. Hello, world Main() step Write. Line(“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 ) Software Engineering, COMP 201 Slide 30

The Executable Specification Language - ASML Compiler asmlc [name of the program] !!! Use D drive at the University Laboratories !!! Example D: >asmlc test. asml D: > test. exe >output_file. txt Software Engineering, COMP 201 Slide 31

I. Steps A step can be introduced independently or as part of sequence of steps in the form: step … The general syntax for steps is Step [label] [stopping-condition] statement block l a statement block consists of indented statement that follow l a label is an optional string, number of identifier followed by a colon (“: ”) l stopping condition is any these forms: until fixpoint until expression while expression Software Engineering, COMP 201 Slide 32

Stopping for fixed point “until fixed point” enum Enum. Mode Initial Started Finished var mode = Initial var count = 0 Initial if count < 10 then count: = count+1 count: = 1 Main() step until fixpoint if mode = Initial then mode : =Started count: =1 if mode = Started and count < 10 then count: = count+1 if mode = Started and count >=10 then mode: = Finished Software Engineering, COMP 201 Started count 10 Finished Slide 33

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 var x as Integer = 1 Main() step while x < 10 Write. Line(x) x: = x + 1 until expression var x as Integer = 1 Main() step until x > 9 Write. Line(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 Software Engineering, COMP 201 Slide 34

Conditions eq ne lt gt in notin subset superset subseteq superseteq = < > Software Engineering, COMP 201 Slide 35

Sequences of steps l The syntax step … indicates a sequence of steps that will be performed in order • Labels after the “step” keyword are optional but helpful as documentation. Software Engineering, COMP 201 Slide 36

Be wary ! l l l 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 Software Engineering, COMP 201 Slide 37

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 ident 1 in expr 1, ident 2 in expr 2 … statement-block Sequential, step-based iteration is available for sets as well as sequences, but in the case of sets, the order is not specified my. List = [1, 2, 3] Main() step foreach i in my. List Write. Line (i) Software Engineering, COMP 201 Slide 38

Guidelines for using steps Situation You choose … operations occur in a fixed order each operation must be done in order operations must be done in sequence, one after another sequence of steps iterated steps with stopping condition “while”, “until” iteration over collection “foreach” operations can be done iteration over collection without order “forall” Repeat an operation until no fixed-point stopping condition more changes occur “until fixed point” Software Engineering, COMP 201 Slide 39

II. Updates “How are variables updated? ” l l l 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 Software Engineering, COMP 201 Slide 40

The update statement Update symbol “: =” (reads as “gets”) var x = 0 var y = 1 Main() step Write. Line(“In the first step, x =” + x) // x is 0 Write. Line (“In the first step, y =” + y) // y is 1 x: =2 step // updates occur here Write. Line(“In the second step, x =” + x)//x is 2 Write. Line(“In the second step, y =” + y)//y is 1 Software Engineering, COMP 201 Slide 41

Delayed effect of updates Updates don’t actually occur until the step following the one in which they are written var x = 0 var y = 1 Main() step Write. Line(“In the first step, x =” + x) // x is 0 Write. Line(“In the first step, y =” + y) // y is 1 step x: =2 Write. Line (“In the second step, x =” + x) // x is 0 step Write. Line (“In the third step, x =” + x) // x is 2 Software Engineering, COMP 201 Slide 42

When updates occur l l 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 temp = x x=y y = temp in ASML step x: = y y: =x Software Engineering, COMP 201 Slide 43

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 step x: =1 x: =2 Error: CLASH in the update set we don’t know which of the two should take effect Software Engineering, COMP 201 Slide 44

Total and partial updates l l An update of the variable can either be total or partial Total update is a simple replacement of variable’s 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 Software Engineering, COMP 201 Slide 45

Total update of a set-valued variable var Students as Set of String = {} Main() step Write. Line (“The initial roster is = ” + Students) Students : = {“Bill”, “Carol”, “Ted”, “Alice”} step Write. Line (“The final roster is = ” + Students) 1. 2. 3. The variable Students was, initially, an empty set It was then updated to contain the names of the four students Update became visible in the second step as the finial roster Software Engineering, COMP 201 Slide 46

Partial update of a set-valued variable var Students as Set of String = {} Main() step Write. Line (“The initial roster is = ” + Students) Students(“Bill”) : = true Students(“Carol”) : = true Students(“Ted”) : = true Students(“Alice”) : = true step Write. Line (“The final roster is = ” + Students) l l l “ 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 Software Engineering, COMP 201 Slide 47

Updating a set-valued variable var Students as Set of String = {} Main() step Write. Line (“The initial roster is = ” + Students) Students : = {“Bill”, “Carol”, “Ted”, “Alice”} step Write. Line (“The current roster is = ” + Students) Students ( “Bill”) : = false // ( * ) step Write. Line (“The final roster is = ” + Students) l l 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 Software Engineering, COMP 201 Slide 48