![Recursion in specifications
Operations are often specified recursively.
Tail (Cons (L, v)) = if L = Create then Create
else Cons (Tail (L), v).
• Cons ([5, 7], 9) = [5, 7, 9]
• 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]](https://image.slidesharecdn.com/lecture3fm-241130081356-463ec1d5/85/formal-method-chapter-1-lecture_3_fm-pptlecture_3_fm-ppt-24-320.jpg)
formal method chapter 1 lecture_3_fm.pptlecture_3_fm.ppt
- 1. Formal Methods in Software Engineering Credit Hours: 3+0
- 3. Objectives To explain why formal specification techniques help discover problems in system requirements To describe the use of algebraic techniques for interface specification To describe the use of model-based techniques for behavioural specification
- 4. Topics covered Formal specification in the software process Sub-system interface specification Behavioural specification
- 5. 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.
- 6. 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 still hard to scale up to large systems.
- 7. Use of formal methods The principal benefits of formal methods are in reducing the number of faults in systems. Consequently, their main area of applicability is in critical systems engineering. There have been several successful projects where formal methods have been used in this area. In this area, the use of formal methods is most likely to be cost-effective because high system failure costs must be avoided.
- 8. Specification in the software process Specification and design are inextricably intermingled. Architectural design is essential to structure a specification and the specification process. Formal specifications are expressed in a mathematical notation with precisely defined vocabulary, syntax and semantics.
- 9. Specification and design Increasing contractor involvement Decreasing client involvement Specification Design User requirements definition System requirements specification Architectural design Formal specification High-level design
- 10. Specification in the software process System requirements specification Formal specification High-level design User requirements definition System modelling Architectural design
- 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. Cost profile The use of formal specification means that the cost profile of a project changes • There are greater up front costs as more time and effort are spent developing the specification; • However, implementation and validation costs should be reduced as the specification process reduces errors and ambiguities in the requirements.
- 13. Development costs with formal specification Specification Specification Design and implementation Design and implementation Validation Validation Cost
- 14. Specification techniques Algebraic specification • The system is specified in terms of its operations and their relationships. Model-based specification • 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.
- 16. 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 as it is focused on the defined operations in an object.
- 18. The structure of an algebraic specification sort < name > imports < LIST OF SPECIFICA TION NAMES > Inf ormal descr iption of the sor t and its oper ations Oper ation signatures setting out the names and the types of the parameters to the operations defined over the sor t Axioms defining the oper ations o ver the sor t < SP ECIFICATION NAM E >
- 19. 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.
- 20. Systematic algebraic specification Algebraic specifications of a system may be developed in a systematic way • Specification structuring; • Specification naming; • Operation selection; • Informal operation specification; • Syntax definition; • Axiom definition.
- 21. 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.
- 22. Operations on a list ADT Constructor operations which evaluate to sort List • Create, Cons and Tail. Inspection operations which take sort list as a parameter and return some other sort • Head and Length. Tail can be defined using the simpler constructors Create and Cons. No need to define Head and Length with Tail.
- 23. List specification Head (Create) = Undefinedexception(empty list) Head (Cons (L, v)) = if L = Create thenv else Head (L) Leng th (Create) = 0 Leng th (Cons (L, v)) = Leng th (L) + 1 Tail (Create ) = Create Tail (Cons (L, v)) = if L = Create thenCreate else Cons (Tail (L), v) sortList imports INTEGER Defines a list where elements are added at the end and remo ved from the front. The oper ations are Create , which br ings an empty list into e xistence , Cons , which creates a ne w list with an added member , Leng th, which e valuates the list siz e, Head, which e valuates the front element of the list, and Tail, which creates a list b y remo ving the head from its input list. Undefined represents an undefined value of type Elem. Create List Cons (List, Elem) List Head (List) Elem Leng th (List) Integer Tail (List) List LIST ( Elem )
- 24. Recursion in specifications Operations are often specified recursively. Tail (Cons (L, v)) = if L = Create then Create else Cons (Tail (L), v). • Cons ([5, 7], 9) = [5, 7, 9] • 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]
- 25. Interface specification in critical systems 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.
- 26. 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;
- 27. 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.
- 28. Sector specification (1) 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) sortSector 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) Sector Leave (Sector, Call-sign) Sector Move (Sector, Call-sign, Height) Sector Lookup (Sector, Call-sign) Height Create Sector Put (Sector, Call-sign, Height) Sector In-space (Sector , Call-sign) Boolean Occupied (Sector , Height) Boolean SECTOR