Lectures 9,10 Formal Specifications Software Engineering, COMP201 Slide 1 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 Software Engineering, COMP201 Slide 2 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 Software Engineering, COMP201 Slide 3 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 Software Engineering, COMP201 Slide 4 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 Software Engineering, COMP201 Slide 5 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. Software Engineering, COMP201 Slide 6 Specification and design In creas in g co n tracto r in vol vemen t Decreas in g cl ien t i n vo lv emen t Requ ir em ent s d efi ni ti on Requ ir em ent s s pecifi cat io n Archi tect ur al d es ig n S o ftw are s pecifi cat io n Hi g h-lev el d es ig n S p eci ficat io n Des ig n Software Engineering, COMP201 Slide 7 Specification in the software process R equ irem ent s s pecifi cat io n Fo rm al s pecifi cat io n R equ irem ent s d efi ni ti on Hi g h-le vel d es ig n S y st em m o dell in g Ar chi tect ural d es ig n Software Engineering, COMP201 Slide 8 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 Software Engineering, COMP201 Slide 9 Formal specification languages A lg e b ra ic M o d e l-b a s e d S e q u e n tia l L a rc h (G u tta g , H o rn in g e t a l., 1 9 8 5 ; G u tta g , H o rn in g e t a l., 1 9 9 3 ) , O B J (F u ta tsu g i, G o g u e n e t a l., 1 9 8 5 ) Z (S p iv e y , 1 9 9 2 ) V D M (J o n e s, 1 9 8 0 ) B (W o rd sw o rth , 1 9 9 6 ) C o n c u rre n t L o to s (B o lo g n e si a n d B rin k sm a , 1 9 8 7 ) , C S P (H o a re , 1 9 8 5 ) P e tri N e ts (P e te rso n , 1981) ASML - Abstract State Machine Language Yuri. Gurevich, Microsoft Research, 2001 Software Engineering, COMP201 Slide 10 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 Software Engineering, COMP201 Slide 11 Development costs with formal specification C o st Vali dat io n Des ig n and Im pl em ent at io n Vali dat io n Des ig n and Im pl em ent at io n S p eci ficat io n S p eci ficat io n W i th ou t fo rm al s pecifi cat io n W i th fo rm al s pecifi cat io n Software Engineering, COMP201 Slide 12 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 Software Engineering, COMP201 Slide 13 Sub-system interfaces Int erface o bj ect s S u b-s ys tem A S u b-s ys tem B Software Engineering, COMP201 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, COMP201 axioms Slide 15 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 Software Engineering, COMP201 Slide 16 OSI reference model Model-based specification 7 Ap pl icat io n Application Ap pl icat io n 6 P resen tati on 5 S es si on 4 Trans po rt 3 Net wo rk Net wo rk Net wo rk 2 Dat a li nk Dat a li nk Data lin k 1 P hy si cal P hy si cal P hy si cal P resen tati on Algebraic specification S es si on Trans po rt C o m mu ni ca t io ns m edi um Software Engineering, COMP201 Slide 17 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 Software Engineering, COMP201 Slide 18 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 Software Engineering, COMP201 Slide 19 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 Software Engineering, COMP201 Slide 20 State transitions 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, COMP201 Slide 21 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 Software Engineering, COMP201 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, COMP201 Slide 23 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 Software Engineering, COMP201 Slide 24 Example Diagram shows the run of a machine that models how orders might be Initialise Process All Orders processed S1 S2 S3 Mode = “Initial” Mode = “Active” Mode = “Final” Orders = 0 Orders = 2 Orders = 0 Balance = £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, COMP201 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, COMP201 Slide 26 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 mode “Initial” orders 0 balance £0 input The Machine’s Control Logic output … Mode “Active” orders 2 balance £200 if mode = “Initial” then mode := “Active” 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 Software Engineering, COMP201 Slide 27 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 Software Engineering, COMP201 Slide 28 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) Software Engineering, COMP201 Slide 29 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 ) Software Engineering, COMP201 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 D:\> test.exe >output_file.txt Software Engineering, COMP201 Slide 31 I. Steps A step can be introduced independently or as part of sequence of steps in the form: step … step … 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 Software Engineering, COMP201 Slide 32 Stopping for fixed point “until fixed point” enum EnumMode 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, COMP201 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 WriteLine(x) x:= x + 1 until expression 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 Software Engineering, COMP201 Slide 34 Conditions eq ne lt gt in notin subset superset subseteq superseteq = < > Software Engineering, COMP201 Slide 35 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. Software Engineering, COMP201 Slide 36 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 Software Engineering, COMP201 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 ident1 in expr1, ident2 in expr2 … 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 myList = [1,2,3] Main() step foreach i in myList WriteLine (i) Software Engineering, COMP201 Slide 38 Guidelines for using steps You choose … Situation operations occur in a fixed order each operation must be done in order operations must be done in sequence, one after another operations can be done without order Repeat an operation until no more changes occur sequence of steps iterated steps with stopping condition “while”,“until” iteration over collection “foreach” iteration over collection “forall” fixed-point stopping condition “until fixed point” Software Engineering, COMP201 Slide 39 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 Software Engineering, COMP201 Slide 40 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 Software Engineering, COMP201 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 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 Software Engineering, COMP201 Slide 42 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 temp = x x=y y = temp in ASML step x:= y y:=x Software Engineering, COMP201 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, COMP201 Slide 44 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 Software Engineering, COMP201 Slide 45 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. 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, COMP201 Slide 46 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 Software Engineering, COMP201 Slide 47 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 Software Engineering, COMP201 Slide 48

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# Formal Specification - University of Liverpool