Each of the following requires the construction of an Event-B model. For each model, an appropriate invariants should be provided and proved that your model satisfies these invariants. All the proff of obligations need to be discharged. The project was conducted in rodin, which enables to design and prove formal specifications.
A primary school class contains a number of children and a variety of books. Write a model which keeps track of the books that the children have read. It should maintain a relation hasread between children and books. It should also handle the following events:
record: adds the fact that the given child has read the given book
newbook: outputs a book that the given child has not already read
books_query: outputs the number of books the given child has read
A club membership department maintains a set of members, and a set of people that are in the waiting list to become members. No member can also be waiting for membership. The club allows a maximum of 500 members at any one time.
Using the set NAMES, and the variables member and waiting to maintain the required information, write suitable invariants that capture the constraints on these variables.
The model should handle the following events:
join: the given name, which must be in the waiting list, is made a member and removed from the waiting list
join_queue: the given name, which must not be in the waiting or membership lists, is added to the waiting list
remove: the given name, which must be in the membership list, is removed from the membership list
remove_queue: the given name, which must be in the waiting list, is removed from the waiting list
jump_queue: the given name, which must not be in the waiting or membership lists, is made a member
query_membership: outputs the number of members
query_queue: outputs the number of people in the waiting list.
A parking permit management system keeps track of people that have had parking permits registered to them. Each person with a permit must have exactly one car registered, and different people must register different cars. Write a model which maintains this information. It should handle the following events:
register: registers the given vehicle for the given person, provided they do not already have a vehicle registered
deregister: deregisters the vehicle for the given person
registered: outputs yes if the given person has a car registered and no otherwise
vehicle: outputs the vehicle that the given person has registered
owner: outputs the owner of the given vehicle
change_register: changes the vehicle that the given person has registered to the given vehicle
drugs_check: outputs a random registered vehicle to search for drugs.
In order to provide outputs for registered, you will need to provide a set RESPONSE which contains at least the elements yes and no.
Students are examined in a particular course with a pass mark of pass_mark, where marks are between 0 and 100. They may resit the exam up to twice more if they fail. In such cases the maximum mark allowed is the pass mark.
Write a model which tracks the examination results associated with the particular course. It will maintain a set registered which contains all of the students who have ever been registered for the course, and three functions: exam, resit1, and resit2. These contain the results of registered students. They should maintain information in a sensible way: for example, only registered students should have any marks; a student cannot have a resit1 mark unless they also have an exam mark; and if a student has a pass mark on the exam then they cannot have a resit1 mark. Write suitable invariants that express these constraints.
The model should handle the following events:
register: registers the given unregistered student for the course
exam_mark: enters the given exam mark for the given student
resit1_mark: enters the given first resit mark for the given student
resit2_mark: enters the given second resit mark for the given student
studentquery: outputs how many times the given student has sat the exam
markquery: outputs the top mark that the given student has achieved in any of the sittings of the exam