1. (State) Model-Based Approaches II Software Specification Lecture 36
Prepared by
Stephen M. Thebaut, Ph.D.
University of Florida

2. Specification using “Z”
Z is a mature and expressive notation for model-based specification. It combines formal and informal descriptions and incorporates graphical highlighting.
The basic building blocks of Z-based specifications are schemas.
Schemas identify state variables and define constraints and operations in terms of those variables.
Software Engineering, 5th Edition. Chapter 11

3. Software Engineering, 5th Edition. Chapter 11
Schemas
Schemas are comprised of three parts: name, signature, and predicate.
The signature declares (state) entities introduced in a schema and their type.
Signature declarations are given in the form identifier: type.
The predicate defines logical relationships between entities in the declaration.
Z is based on the predicate calculus + typed sets.
Software Engineering, 5th Edition. Chapter 11

4. Graphical Layout of a Schema
Schema Name
Signature
Predicate
Software Engineering, 5th Edition. Chapter 11

5. Software Engineering, 5th Edition. Chapter 11
Schemas (cont’d)
Schemas describe state entities or operations on state entities.
To describe state entities, declared variables comprise the entities while predicates specify their invariant properties.
To describe operations, declarations consist of initial and final state variables, inputs, and outputs, while predicates specify the relations among them.
Software Engineering, 5th Edition. Chapter 11

6. Software Engineering, 5th Edition. Chapter 11
Example 1
Specification of a generic container entity:
Container
contents: N
capacity: N
contents  capacity
modeled as natural numbers
invariant property
Software Engineering, 5th Edition. Chapter 11

7. Software Engineering, 5th Edition. Chapter 11
Example 1 (cont’d)
Specification of a generic indicator entity:
Indicator
light: {off, on}
reading: N
danger_level: N
light = on  reading  danger_level
Software Engineering, 5th Edition. Chapter 11

8. Software Engineering, 5th Edition. Chapter 11
Example 1 (cont’d)
Specification of a storage tank entity:
Storage_tank
Container
Indicator
reading = contents
capacity = 500
danger_level = 50
Predicates on separate lines are separated by an implicit “AND”.
Software Engineering, 5th Edition. Chapter 11

9. Software Engineering, 5th Edition. Chapter 11
Example 1 (cont’d)
Expanded specification of a storage tank entity:
Storage_tank
contents: N
capacity: N
light: {off, on}
reading: N
danger_level: N
contents  capacity
light = on  reading  danger_level
reading = contents
capacity = 500
danger_level = 50
Software Engineering, 5th Edition. Chapter 11

10. Software Engineering, 5th Edition. Chapter 11
Example 1 (cont’d)
Specification of a nominal storage tank fill operation:
Fill-OK
 Storage-tank
amount?: N
contents + amount?  capacity
contents’ = contents + amount?
“dash” indicates the value of contents AFTER the operation
“?” indicates that amount is an INPUT.
“Delta” indicates that values of one or more variables will be changed.
Software Engineering, 5th Edition. Chapter 11

11. Software Engineering, 5th Edition. Chapter 11
Example 1 (cont’d)
Specification of an exceptional storage tank fill operation:
OverFill
 Storage-tank
amount?: N
r!: seq CHAR
capacity < contents + amount?
r! = “Insufficient tank capacity – Fill cancelled”
“Xi” indicates that NO variables will be changed by the operation.
“!” indicates that r is an OUTPUT.
Software Engineering, 5th Edition. Chapter 11

12. Software Engineering, 5th Edition. Chapter 11
Example 1 (cont’d)
Complete specification of the storage tank fill operation:
Fill
Fill-OK V OverFill
Software Engineering, 5th Edition. Chapter 11

13. G Kontoya and I. Sommerville 1998
Example 2
Specification of a simple Library system:
Library
stock:  Book
onLoan: Book  Borrower
dom onLoan  stock
“Powerset Book”: the set of sets of books
set of books held by library
books on loan are a subset of existing stock
set of (book, borrower) pairs
Each book on loan is mapped to a borrower.
Note use of typed sets.
G Kontoya and I. Sommerville 1998

14. G Kontoya and I. Sommerville 1998
Example 2 (cont’d)
Specification of the borrow operation:
Borrow
 Library
book?: Book
reader?: Borrower
book?  stock
book?  dom onLoan
onLoan’ = onLoan  {(book?, reader?)}
stock’ = stock
G Kontoya and I. Sommerville 1998

15. G Kontoya and I. Sommerville 1998
Example 2 (cont’d)
Operation for adding a new book to current stock:
New
 Library
book?: Book
stock’ = stock  {book?}
onLoan’ = onLoan
G Kontoya and I. Sommerville 1998

16. G Kontoya and I. Sommerville 1998
Example 2 (cont’d)
Operation for returning a book to the library:
Return
 Library
book?: Book
book?  dom onLoan
dom onLoan’ = dom onLoan  book?
stock’ = stock
“Overriding” operator
G Kontoya and I. Sommerville 1998

17. Software Engineering, 5th Edition. Chapter 11
Exercise 4
Modify the storage tank specification by adding a fill warning light which indicates when the tank is close to capacity. This should be switched on when the contents are some high percentage of the capacity.
Software Engineering, 5th Edition. Chapter 11

18. Software Engineering, 5th Edition. Chapter 11
Key Points
Model-based specification relies on a state model of the system using mathematical entities such as the predicate calculus and typed sets.
Functions / operations may be specified by defining their effect on system state.
Software Engineering, 5th Edition. Chapter 11

19. Software Engineering, 5th Edition. Chapter 11
Key Points (cont’d)
It is normal to specify functions / operations incrementally and then combine the fragments to produce a complete specification.
Z specifications are comprised of a number of schemas that introduce typed names and define predicates over those names. They are distinguished from surrounding text by graphical highlighting.
Software Engineering, 5th Edition. Chapter 11

20. Software Engineering, 5th Edition. Chapter 11
Key Points (cont’d)
Schemas are building blocks which may be combined and used in other schemas. The effect of including schema A in schema B is that schema B inherits the names and predicates of schema A.
Software Engineering, 5th Edition. Chapter 11

21. (State) Model-Based Approaches II Software Specification Lecture 36
Prepared by
Stephen M. Thebaut, Ph.D.
University of Florida