Lectures 9,10

1. Lectures 9,10 Formal Specifications

2. Formal Specification - Techniques for the unambiguous specification of software Objectives: • To explainwhy 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

3. 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

4. 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

5. 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

6. Specification in the software process • Specification and designare inextricably mixed. • Architectural designis essential to structure a specification. • Formal specifications are expressed in a mathematical notation with precisely definedvocabulary, syntax and semantics.

7. Specification and design

8. Specification in the software process

9. 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

10. ASML - Abstract State Machine Language Yuri. Gurevich, Microsoft Research, 2001 Formal specification languages

11. 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

12. Development costs with formal specification

13. 1. Interface specification • Large systems are decomposed into subsystems with well-defined interfaces between these subsystems • Specification of subsystem interfacesallows 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

14. Sub-system interfaces

15. The structure of an algebraic specification < SPECIFICA TION NAME > (Gener ic P ar ameter) sort < name > introduction imports < LIST OF SPECIFICA TION NAMES > 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

16. Behavioural specification • Algebraic specificationcan be cumbersome when the object operations are not independent of the object state • Model-based specificationexposes the system state and defines the operations in terms of changes to that state

17. OSI reference model Model-based specification Application Algebraic specification

18. 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

19. Abstract State • An AsmL modelis said to be abstractbecause 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 • Abstractionhelps 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

20. 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

21. paint in green A B paint in red 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

22. 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

23. paint in green A B paint in red Evolution of state variables 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

24. Evolution of state variables • Names are given by the machine’s symbolic vocabulary • Valuesare 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

25. S1 Mode = “Initial” Orders = 0 Balance = £0 S3 Mode = “Final” Orders = 0 Balance = £500 S2 Mode = “Active” Orders = 2 Balance = £200 Initialise Process All Orders 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 machine’s control logicon the current state • calculates the subsequence state as output

26. 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

27. The Machine’s Control Logic … if mode = “Initial” then mode := “Active” 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 • 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 input output

28. 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

29. 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)

30. 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 )

31. 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 D:\> test.exe >output_file.txt

32. 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 untilexpression whileexpression A step can be introduced independently or as part of sequence of steps in the form: step … step …

33. Initial if count < 10 then count:= count+1 count:= 1 Started count  10 Finished 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 count:=1 if mode = Started and count < 10 then count:= count+1 if mode = Started and count >=10 then mode:= Finished

34. 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. whileexpression untilexpression var x as Integer = 1 Main() step while x < 10 WriteLine(x) x:= x + 1 var x as Integer = 1 Main() step until x > 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

35. Conditions eq = ne  lt < gt > in  notin  subset  superset  subseteq  superseteq 

36. 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.

37. Be wary ! • Be wary of introducing unnecessary steps • This can occur if two operations are reallynot order-dependentbut are given as two sequential steps, regardless • It is very easy to fall into this trap, sincemost people are used to the sequential structures used by other programming languages

38. 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 foreachident1in expr1, ident2in 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

39. Guidelines for using steps

40. 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

41. 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 x:=2 step // updates occur here WriteLine(“In the second step, x =” + x)//x is 2 WriteLine(“In the second step, y =” + y)//y is 1

42. 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 WriteLine(“In the first step, x =” + x) // x is 0 WriteLine(“In the first step, y =” + y) // y is 1 step x:=2 WriteLine (“In the second step, x =” + x) // x is 0 step WriteLine (“In the third step, x =” + x) // x is 2

43. 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

44. 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

45. Total and partial updates • 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

46. 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) • 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

47. Partial update of a set-valued variable • “ 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 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)

48. 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