bearers, joists and rafters 26 Specification 27 * he guarantee is provided by the chemical supplier for the benefit of T the property owner. It is a limited and ...
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Chapter 27 Formal Specification 2, In traditional engineering disciplines such as electrical and civil engineering. progress has usually involved the development of better mathematical techniques. The engineering industry has had no difficulty accepting the need for mathematical. analysis and in incorporating mathematical analysis into its processes. Mathematical analysis is a routine part of the process of developing and validating. a product design, However software engineering has not followed the same path Although. there has now been more than 30 years of research into the use of mathematical. techniques in the software process these techniques have had a limited impact So. called formal methods of software development are not widely used in industrial. software development Most software development companies do not consider it. cost effective to apply them in their software development processes. The term formal methods is used to refer to any activities that rely on. mathematical representations of software including formal system specification. specification analysis and proof transformational development and program. verification All of these activities are dependent on a formal specification of the. software A formal software specification is a specification expressed in a language. whose vocabulary syntax and semantics are formally defined This need for a. formal definition means that the specification languages must be based on. mathematical concepts whose properties are well understood The branch of. mathematics used is discrete mathematics and the mathematical concepts are drawn. from set theory logic and algebra, In the 1980s many software engineering researchers proposed that using. formal development methods was the best way to improve software quality They. argued that the rigour and detailed analysis that are an essential part of formal. methods would lead to programs with fewer errors and which were more suited to. users needs They predicted that by the 21st century a large proportion of. software would be developed using formal methods, Clearly this prediction has not come true There are four main reasons for. 1 Successful software engineering The use of other software engineering. methods such as structured methods configuration management and. information hiding in software design and development processes have. resulted in improvements in software quality People who suggested that the. only way to improve software quality was by using formal methods were. clearly wrong, 2 Market changes In the 1980s software quality was seen as the key software. engineering problem However since then the critical issue for many. classes of software development is not quality but time to market Software. must be developed quickly and customers are sometimes willing to accept. software with some faults if rapid delivery can be achieved Techniques for. rapid software development do not work effectively with formal. specifications Of course quality is still an important factor but it must be. achieved in the context of rapid delivery,Ian Sommerville 2009. 3 Chapter 27 Formal Specification, 3 Limited scope of formal methods Formal methods are not well suited to. specifying user interfaces and user interaction The user interface. component has become a greater and greater part of most systems so you. can only really use formal methods when developing the other parts of the. 4 Limited scalability of formal methods Formal methods still do not scale up. well Successful projects that have used these techniques have mostly been. concerned with relatively small critical kernel systems As systems increase. in size the time and effort required to develop a formal specification grows. disproportionately, These factors mean that most software development companies have been. unwilling to risk using formal methods in their development process However. formal specification is an excellent way of discovering specification errors and. presenting the system specification in an unambiguous way Organizations that. have made the investment in formal methods have reported fewer errors in the. delivered software without an increase in development costs It seems that formal. methods can be cost effective if their use is limited to core parts of the system and. if companies are willing to make the high initial investment in this technology. The use of formal methods is increasing in the area of critical systems. development where emergent system properties such as safety reliability and. security are very important The high cost of failure in these systems means that. companies are willing to accept the high introductory costs of formal methods to. ensure that their software is as dependable as possible As I discuss in Chapter 24. critical systems have very high validation costs and the costs of system failure are. large and increasing Formal methods can reduce these costs. Critical systems where formal methods have been applied successfully. include an air traffic control information system Hall 1996 railway signalling. systems Dehbonei and Mejia 1995 spacecraft systems Easterbrook et al 1998. and medical control systems Jacky 1995 Jacky et al 1997 They have also been. used for software tool specification Neil et al 1998 the specification of part of. IBM s CICS system Wordsworth 1991 and a real time system kernel Spivey. 1990 The Cleanroom method of software development Prowell et al 1999. relies on formally based arguments that code conforms to its specification Because. reasoning about the security of a system is also possible if a formal specification is. developed it is likely that secure systems will be an important area for formal. methods use Hall and Chapman 2002,27 1 Formal specification in the software process. Critical systems development usually involves a plan based software process that is. based on the waterfall model of development discussed in Chapter 4 Both the. system requirements and the system design are expressed in detail and carefully. analysed and checked before implementation begins If a formal specification of. Ian Sommerville 2009,Chapter 27 Formal Specification 4. Increasing contractor involvement,Decreasing client involvement. User System,Architectural Formal High level,requirements requirements. design specification design,definition specification. Figure 27 1,Specification Specification,and design. the software is developed this usually comes after the system requirements have. been specified but before the detailed system design There is a tight feedback loop. between the detailed requirements specification and the formal specification As I. discuss later one of the main benefits of formal specification is its ability to. uncover problems and ambiguities in the system requirements. The involvement of the client decreases and the involvement of the. contractor increases as more detail is added to the system specification In the early. stages of the process the specification should be customer oriented You should. write the specification so that the client can understand it and you should make as. few assumptions as possible about the software design However the final stage of. the process which is the construction of a complete consistent and precise. specification is principally intended for the software contractor It precisely. specifies the details of the system implementation You may use a formal language. at this stage to avoid ambiguity in the software specification. Figure 27 1 shows the stages of software specification and its interface with. the design process The specification stages shown in Figure 27 1 are not. independent nor are they necessarily developed in the sequence shown Figure 27 2. shows specification and design activities may be carried out in parallel streams. There is a two way relationship between each stage in the process Information is. fed from the specification to the design process and vice versa. As you develop the specification in detail your understanding of that. specification increases Creating a formal specification forces you to make a. detailed systems analysis that usually reveals errors and inconsistencies in the. informal requirements specification This error detection is probably the most. requirements,specification,specification,High level. requirements,definition,Figure 27 2,specification in the. System Architectural,software process modelling design. Ian Sommerville 2009,5 Chapter 27 Formal Specification. Validation,Design and,implementation Validation,Design and. implementation,Specification,Specification,Figure 27 3. development costs,with formal,specification, potent argument for developing a formal specification Hall 1990 It helps you. discover requirements problems that can be very expensive to correct later. Depending on the process used specification problems discovered during. formal analysis might influence changes to the requirements specification if this. has not already been agreed If the requirements specification has been agreed and. is included in the system development contract you should raise the problems that. you have found with the customer It is then up to the customer to decide how they. should be resolved before you start the system design process. Developing and analysing a formal specification front loads software. development costs Figure 27 3 shows how software process costs are likely to be. affected by the use of formal specification When a conventional process is used. validation costs are about 50 of development costs and implementation and. design costs are about twice the costs of specification With formal specification. specification and implementation costs are comparable and system validation costs. are significantly reduced As the development of the formal specification uncovers. requirements problems rework to correct these problems after the system has been. designed is avoided, Two fundamental approaches to formal specification have been used to. write detailed specifications for industrial software systems These are. 1 An algebraic approach where the system is described in terms of operations. and their relationships, 2 A model based approach where a model of the system is built using. mathematical constructs such as sets and sequences and the system. operations are defined by how they modify the system state. Different languages in these families have been developed to specify. sequential and concurrent systems Figure 27 4 shows examples of the languages in. Ian Sommerville 2009,Chapter 27 Formal Specification 6. Sequential Concurrent, Algebraic Larch Guttag et al 1993 Lotos Bolognesi and Brinksma. OBJ Futatsugi et al 1985 1987,Model based Z Spivey 1992 CSP Hoare 1985. Figure 27 4,Formal VDM Jones 1980 Petri Nets Peterson 1981. specification B Wordsworth 1996, each of these classes You can see from this table that most of these languages were. developed in the 1980s It takes several years to refine a formal specification. language so most formal specification research is now based on these languages. and is not concerned with inventing new notations, In this chapter my aim is to introduce both algebraic and model based. approaches The examples here should give you an idea of how formal. specification results in a precise detailed specification but I don t discuss. specification language details specification techniques or methods of program. verification You can download a more detailed description of both algebraic and. model based techniques from the book s website,27 2 Sub system interface specification. Large systems are usually decomposed into sub systems that are developed. independently Sub systems make use of other sub systems so an essential part of. the specification process is to define sub system interfaces Once the interfaces are. agreed and defined the sub systems can be developed independently. Sub system interfaces are often defined as a set of objects or components. Figure 27 5 These describe the data and operations that can be accessed through. the sub system interface You can therefore define a sub system interface. specification by combining the specifications of the objects that make up the. Precise sub system interface specifications are important because sub. system developers must write code that uses the services of other sub systems. Sub system Sub system,Figure 27 5 A B,Sub system,Ian Sommerville 2009. 7 Chapter 27 Formal Specification,SPECIFICATION NAME. imports LIST OF SPECIFICATION NAMES, Informal description of the sort and its operations. Figure 27 6 The Operation signatures setting out the names and the types of. structure of an the parameters to the operations defined over the sort. specification Axioms defining the operations over the sort. before these have been implemented The interface specification provides. information for sub system developers so that they know what services will be. available in other sub systems and how these can be accessed Clear and. unambiguous sub system interface specifications reduce the chances of. misunderstandings between a sub system providing some service and the sub. systems using that service, The algebraic approach was originally designed for the definition of abstract. data type interfaces In an abstract data type the type is defined by specifying the. type operations rather than the type representation Therefore it is similar to an. object class The algebraic method of formal specification defines the abstract data. type in terms of the relationships between the type operations. Guttag Guttag 1977 first discussed this approach in the specification of. abstract data types Cohen et al Cohen et al 1986 show how the technique can. be extended to complete system specification using an example of a document. retrieval system Liskov and Guttag Liskov and Guttag 1986 also cover the. algebraic specification of abstract data types, The structure of an object specification is shown in Figure 27 6 The body of. the specification has four components, 1 An introduction that declares the sort the type name of the entity being. specified A sort is the name of a set of objects with common characteristics. It is similar to a type in a programming language The introduction may also. include an imports declaration where the names of specifications defining. other sorts are declared Importing a specification makes these sorts. available for use, 2 A description part where the operations are described informally This. makes the formal specification easier to understand The formal. specification complements this description by providing an unambiguous. syntax and semantics for the type operations, 3 The signature part defines the syntax of the interface to the object class or. abstract data type The names of the operations that are defined the number. and sorts of their parameters and the sort of operation results are described. in the signature,Ian Sommerville 2009,Chapter 27 Formal Specification 8. 4 The axioms part defines the semantics of the operations by defining a set of. axioms that characterize the behavior of the abstract data type These. axioms relate the operations used to construct entities of the defined sort. with operations used to inspect its values, The process of developing a formal specification of a sub system interface. includes the following activities, 1 Specification structuring Organize the informal interface specification into a. set of abstract data types or object classes You should informally define the. operations associated with each class, 2 Specification naming Establish a name for each abstract type specification. decide whether or not they require generic parameters and decide on names. for the sorts identified, 3 Operation selection Choose a set of operations for each specification based. on the identified interface functionality You should include operations to. create instances of the sort to modify the value of instances and to inspect. the instance values You may have to add functions to those initially. identified in the informal interface definition, 4 Informal operation specification Write an informal specification of each. operation You should describe how the operations affect the defined sort. 5 Syntax definition Define the syntax of the operations and the parameters to. each operation This is the signature part of the formal specification You. should update the informal specification at this stage if necessary. 6 Axiom definition Define the semantics of the operations by describing what. conditions are always true for different operation combinations. To explain the technique of algebraic specification I use an example of a. simple data structure a linked list as shown in Figure 27 7 Linked lists are. ordered data structures where each element includes a link to the following element. in the structure I have used a simple list with only a few associated operations so. that the discussion here is not too long In practice object classes defining a list. would probably have more operations, Assume that the first stage of the specification process namely specification. structuring has been carried out and that the need for a list has been identified The. name of the specification and the name of the sort can be the same although it is. useful to distinguish between these by using some convention I use uppercase for. the specification name LIST and lowercase with an initial capital for the sort name. List As lists are collections of other types the specification has a generic. parameter Elem The name Elem can represent any type integer string list and. In general for each abstract data type the required operations should. include an operation to bring instances of the type into existence Create and to. construct the type from its basic elements Cons In the case of lists there should. be an operation to evaluate the first list element Head an operation that returns. Ian Sommerville 2009,9 Chapter 27 Formal Specification. imports INTEGER, Defines a list where elements are added at the end and removed. from the front The operations are Create which brings an empty list. into existence Cons which creates a new list with an added member. Length which evaluates the list size Head which evaluates the front. element of the list and Tail which creates a list by removing the head from. its input list Undefined represents an undefined value of type Elem. Create A List,Cons List Elem A List,Head List A Elem. Length List A Integer,Tail List A List,Head Create Undefined exception empty list. Head Cons L v if L Create then v else Head L,Length Create 0. Figure 27 7 A Length Cons L v Length L 1,simple list Tail Create Create. specification Tail Cons L v if L Create then Create else Cons Tail L v. the list created by removing the first element Tail and an operation to count the. number of list elements Length, To define the syntax of each of these operations you must decide which. parameters are required for the operation and the results of the operation In. general input parameters are either the sort being defined List or the generic sort. Elem The results of operations may be either of those sorts or some other sort. such as Integer or Boolean In the list example the Length operation returns an. integer Therefore you must include an imports declaration declaring that the. specification of integer is used in the specification. To create the specification you define a set of axioms that apply to the. abstract type and these specify its semantics You define the axioms using the. operations defined in the signature part These axioms specify the semantics by. setting out what is always true about the behavior of entities with that abstract type. Operations on an abstract data type usually fall into two classes. 1 Constructor operations that create or modify entities of the sort defined in. the specification Typically these are given names such as Create Update. Add or in this case Cons meaning construct, 2 Inspection operations that evaluate attributes of the sort defined in the. specification Typically these are given names such as Eval or Get. A good rule of thumb for writing an algebraic specification is to establish. the constructor operations and write down an axiom for each inspection operation. over each constructor This suggests that if there are m constructor operations and n. inspection operations there should be m n axioms defined. Ian Sommerville 2009,Chapter 27 Formal Specification 10. However the constructor operations associated with an abstract type may. not all be primitive constructors That is it may be possible to define them using. other constructors and inspection operations If you define a constructor operation. using other constructors then you only need to define the inspection operations. using the primitive constructors, In the list specification the constructor operations that build lists are Create. Cons and Tail The inspection operations are Head return the value of the first. element in the list and Length return the number of elements in the list which are. used to discover list attributes The Tail operation however is not a primitive. constructor There is therefore no need to define axioms over the Tail operation for. Head and Length operations but you do have to define Tail using the primitive. constructor operations, Evaluating the head of an empty list results in an undefined value The. specifications of Head and Tail show that Head evaluates the front of the list and. Tail evaluates to the input list with its head removed The specification of Head. states that the head of a list created using Cons is either the value added to the list. if the initial list is empty or is the same as the head of the initial list parameter to. Cons Adding an element to a list does not affect its head unless the list is empty. Recursion is commonly used when writing algebraic specifications The. value of the Tail operation is the list that is formed by taking the input list and. removing its head The definition of Tail shows how recursion is used in. constructing algebraic specifications The operation is defined on empty lists then. recursively on non empty lists with the recursion terminating when the empty list. It is sometimes easier to understand recursive specifications by developing a. short example Say we have a list 5 7 where 5 is the front of the list and 7 the end. of the list The operation Cons 5 7 9 should return a list 5 7 9 and a Tail. operation applied to this should return the list 7 9 The sequence of equations. which results from substituting the parameters in the above specification with these. Tail 5 7 9,Tail Cons 5 7 9 Cons Tail 5 7 9,Cons Tail Cons 5 7 9 Cons Cons Tail 5 7 9. Cons Cons Tail Cons 5 7 9 Cons Cons Create 7 9,Cons 7 9 7 9. The systematic rewriting of the axiom for Tail illustrates that it does indeed. produce the anticipated result You can check that axiom for Head is correct using. the same rewriting technique, Now let us look at how you can use algebraic specification of an interface in. a critical system specification Assume that in an air traffic control system an. object has been designed to represent a controlled sector of airspace Each. controlled sector may include a number of aircraft each of which has a unique. aircraft identifier For safety reasons all aircraft must be separated by at least 300. metres in height The system warns the controller if an attempt is made to position. an aircraft so that this constraint is breached,Ian Sommerville 2009. 11 Chapter 27 Formal Specification, To simplify the description I have only defined a limited number of. operations on the sector object In a practical system there are likely to be many. more operations and more complex safety conditions related to the horizontal. separation of the aircraft The critical operations on the object are. 1 Enter This operation adds an aircraft represented by an identifier to the. airspace at a specified height There must not be other aircraft at that height. or within 300 metres of it, 2 Leave This operation removes the specified aircraft from the controlled. sector This operation is used when the aircraft moves to an adjacent sector. 3 Move This operation moves an aircraft from one height to another Again. the safety constraint that vertical separation of aircraft must be at least 300. metres is checked, 4 Lookup Given an aircraft identifier this operation returns the current height. of that aircraft in the sector, It makes it easier to specify these operations if some other interface. operations are defined These are, 1 Create This is a standard operation for an abstract data type It causes an. empty instance of the type to be created In this case it represents a sector. that has no aircraft in it, 2 Put This is a simpler version of the Enter operation It adds an aircraft to the. sector without any associated constraint checking, 3 In space Given an aircraft call sign this Boolean operation returns true if the. aircraft is in the controlled sector false otherwise. 4 Occupied Given a height this Boolean operation returns true if there is an. aircraft within 300 metres of that height false otherwise. The advantage of defining these simpler operations is that you can then use. them as building blocks to define the more complex operations on the Sector sort. The algebraic specification of this sort is shown in Figure 27 8. Essentially the basic constructor operations are Create and Put and I use. these in the specification of the other operations Occupied and In space are. checking operations that I have defined using Create and Put and I then use them. in other specifications I don t have space to explain all operations in detail here but. I discuss two of them Occupied and Move With this information you should be. able to understand the other operation specifications. 1 The Occupied operation takes a sector and a parameter representing the. height and checks if any aircraft have been assigned to that height Its. specification states that, In an empty sector one that has been create by a Create operation every. level is vacant The operation returns false irrespective of the value of the. height parameter,Ian Sommerville 2009,Chapter 27 Formal Specification 12. sort Sector,imports INTEGER BOOLEAN, Enter adds an aircraft to the sector if safety conditions are satisfed. Leave removes an aircraft from the sector, Move moves an aircraft from one height to another if safe to do so. Lookup Finds the height of an aircraft in the sector. Create creates an empty sector, Put adds an aircraft to a sector with no constraint checks. In space checks if an aircraft is already in a sector. Occupied checks if a specified height is available. Enter Sector Call sign Height A Sector,Leave Sector Call sign A Sector. Move Sector Call sign Height A Sector,Lookup Sector Call sign A Height. Create A Sector,Put Sector Call sign Height A Sector. In space Sector Call sign A Boolean,Occupied Sector Height A Boolean. Enter S CS H, if In space S CS then S exception Aircraft already in sector. elsif Occupied S H then S exception Height conflict. else Put S CS H, Leave Create CS Create exception Aircraft not in sector. Leave Put S CS1 H1 CS,if CS CS1 then S else Put Leave S CS CS1 H1. Move S CS H, if S Create then Create exception No aircraft in sector. elsif not In space S CS then S exception Aircraft not in sector. elsif Occupied S H then S exception Height conflict. else Put Leave S CS CS H, NO HEIGHT is a constant indicating that a valid height cannot be returned. Lookup Create CS NO HEIGHT exception Aircraft not in sector. Lookup Put S CS1 H1 CS,if CS CS1 then H1 else Lookup S CS. Occupied Create H false,Occupied Put S CS1 H1 H, if H1 H and H1 H 300 or H H1 and H H1 300 then true. else Occupied S H,Figure 27 8 The,specification of a In space Create CS false. In space Put S CS1 H1 CS, controlled sector if CS CS1 then true else In space S CS. In a non empty sector one where there has been previous Put operations. the Occupied operation checks whether the specified height parameter H. is within 300 metres of the height of aircraft that was last added to the. sector by a Put operation If so that height is already occupied so the. value of Occupied is true,Ian Sommerville 2009,13 Chapter 27 Formal Specification. If it is not occupied the operation checks the sector recursively You can. think of this check being carried out on the last aircraft put into the sector. If the height is not within range of the height of that aircraft the operation. then checks against the previous aircraft that has been put into the sector. and so on Eventually if there are no aircraft within range of the specified. height the check is carried out against an empty sector so returns false. 2 The Move operation moves an aircraft in a sector from one height to. another Its specification states that, If a Move operation is applied to an empty airspace the result of Create. the airspace is unchanged and an exception is raised to indicate that the. specified aircraft is not in the airspace, In a non empty sector the operation first checks using In space whether. the given aircraft is in the sector If it is not an exception is raised If it is. in the sector the operation checks that the specified height is available. using Occupied raising an exception if there is already an aircraft at that. If the specified height is available the Move operation is equivalent to the. specified aircraft leaving the airspace so the operation Leave is used and. being put into the sector at the new height,27 3 Behavioural specification. The simple algebraic techniques described in the previous section can be used to. describe interfaces where the object operations are independent of the object state. That is the results of applying an operation should not depend on the results of. previous operations Where this condition does not hold algebraic techniques can. become cumbersome Furthermore as they increase in size I find that algebraic. descriptions of system behavior become increasingly difficult to understand. An alternative approach to formal specification that has been more widely. used in industrial projects is model based specification Model based specification. is an approach to formal specification where the system specification is expressed. as a system state model You can specify the system operations by defining how. they affect the state of the system model The combination of these specifications. defines the overall behavior of the system, Mature notations for developing model based specifications are VDM. Jones 1980 Jones 1986 B Wordsworth 1996 and Z Hayes 1987 Spivey. 1992 I use Z pronounced Zed not Zee here In Z systems are modelled using. sets and relations between sets However Z has augmented these mathematical. concepts with constructs that specifically support software specification. In an introduction to model based specification I can only give an overview. of how a specification can be developed A complete description of the Z notation. would be longer than this chapter Rather I present some small examples to. Ian Sommerville 2009,Chapter 27 Formal Specification 14. Schema name Schema signature Schema predicate,contents N. Figure 27 9 The capacity N,structure of a Z,schema contents capacity. illustrate the technique and introduce notation as it is required A full description of. the Z notation is given in textbooks such as those by Diller Potter et al 1996 and. Jacky Jacky 1997, Formal specifications can be difficult and tedious to read especially when. they are presented as large mathematical formulae The designers of Z have paid. particular attention to this problem Specifications are presented as informal text. supplemented with formal descriptions The formal description is included as. small easy to read chunks called schemas that are distinguished from associated. text using graphical highlighting Schemas are used to introduce state variables and. to define constraints and operations on the state Schemas can themselves be. manipulated using operations such as schema composition schema renaming and. schema hiding, To be most effective a formal specification must be supplemented by. supporting informal description The Z schema presentation has been designed so. that it stands out from surrounding text Figure 27 9. The schema signature defines the entities that make up the state of the. system and the schema predicate sets out conditions that must always be true for. these entities Where a schema defines an operation the predicate may set out pre. and post conditions These define the state before and after the operation The. difference between these pre and post conditions defines the action specified in. the operation schema, To illustrate the use of Z in the specification of a critical system I have. developed a formal specification of the control system of the insulin pump that I. introduced in Chapter 3, Recall that this system monitors the blood glucose level of diabetics and. automatically injects insulin as required Even for a small system like the insulin. pump the formal specification is fairly long Although the basic operation of the. system is simple there are many possible alarm conditions that have to be. considered I only include some of the schemas defining the system here the. complete specification can be downloaded from the book s website. To develop a model based specification you have to define state variables. and predicates that model the state of the system that you are specifying and define. invariants conditions that are always true over these state variables. The Z state schema that models the insulin pump state is shown in Figure. 27 10 You can see how the two basic parts of the schema are used In the top part. names and types are declared and in the bottom part of the schema the invariants. Ian Sommerville 2009,15 Chapter 27 Formal Specification. INSULIN PUMP STATE,Input device definition,switch off manual auto. ManualDeliveryButton N, HardwareTest OK batterylow pumpfail sensorfail deliveryfail. InsulinReservoir present notpresent,Needle present notpresent. clock TIME,Output device definition,alarm on off,display1 string. display2 string,clock TIME,State variables used for dose computation. status running warning error,r0 r1 r2 N,capacity insulin available N. max daily dose max single dose minimum dose N,safemin safemax N. CompDose cumulative dose N,r2 Reading,dose insulin available. insulin available capacity, The cumulative dose of insulin delivered is set to zero once every 24 hours. clock 000000 cumulative dose 0, If the cumulative dose exceeds the limit then operation is suspended. cumulative dose max daily dose status error,display1 Daily dose exceeded. Pump configuration parameters,capacity 100 safemin 6 safemax 14. max daily dose 25 max single dose 4 minimum dose 1. Figure 27 10 State,schema for the display2 nat to string dose. insulin pump clock clock, The names declared in the schema are used to represent system inputs. system outputs and internal state variables,Ian Sommerville 2009.
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