Course Project
CpSc 828: LightWeight Formal Methods
Computer Science Department
Clemson University
Brian Malloy
Writing Specifications using Z April 4, 2002

In order to receive credit for this assignment, you must submit your latex source file by email by 9 AM on Thursday, Apr 18th, 2002. Presentations of the projects will begin on Thursday, April 18th and will likely continue through April 23rd. You must choose one of the projects below. I would like to have the choices somewhat evenly distributed; so please send me an email once you have made your selection and I will let you know if it's okay.

You must write a Z specification that has been checked by fuzz and found to be syntactically correct. Your spec should be in latex format and you must submit the latex source. Your specification must include proper comments, explaining each Z specification, Your spec should begin by providing an overview of your specification, including the kinds of items in the system and the operations that will be permitted on the items. This overview should be an introduction to your spec and should be understandable to a reader who has never met you and does not know what you're doing. I would like to make your specifications available on my web page so that newcomers to Z might find your work helpful.

Your specifiation should begin by specifying the types and free variables that you will use in your specification. You should also describe the state of the system and, where applicable, the initial state of the system.

You may work in groups of size one or two. You must either choose one of the projects listed below, or suggest a project of your own and have it approved by me. Simply email me with your suggestion and I will get back to you asap. I have tried to express the projects below as unuequivocally as possible; if you have questions, please send me email.

Please choose one of the following:

1. On my web page for this course, you will find a Z specification for a Stack, expressed from first principles. That is, the specification for Stack uses the notion of a function or mapping from the natural numbers to Elements, rather than a data structure from the Z Math Toolkit, such as sequence or bag. Study the Z specification and notice that the operations IsEmpty, Leave and Join provide a common interface that may be applied to a Stack, a Queue, or a PriorityQueue. Please provide a Z specification for Queue and PriorityQueue from first principles, so that the interface is the same for all three data structures. You may use the Stack specification as a model for the Queue and PriorityQueue. Using a common interface for all three data structures will provide an opportunity for you to compare and contrast the three structures.

2. Provide a Z specification for Stack, Queue and PriorityQueue using a sequence from the Z Math Toolkit. Use the same interface for each data structure, including operations for IsEmpty, Leave and Join to provide a common interface. Be sure to specify, in your narrative, whether or not the structures are generic or work on Element.

3. We have discussed a Z specification for a FishGame that included operations to CatchAFish, FreeSomeFish, StockThePond and GetFishCount. Modify this specification to allow upto three players in the game. Your FishGame should maintain a ``list'' of the players ordered by the number of fish that each player has caught; use either a sequence to implement your list, or implement the list from first principles, as in #1 above. Include an operation in your game that returns the player who has caught the most fish.

4. Write a Z specification for a movie store that rents movies in DVD format. Your specification should maintain a ``list'' of customers, and should permit operations such as renting a movie, returning a movie, and finding the number of movies that are currently being rented as well as the number of movies available for rental. Since a movie store can have more than one copy of a movie, you should use a bag from the Math Toolkit.

5. Write a Z specification for a binary tree, including operations IsEmpty, Leave, Join and find. You may either use first principles, or one of the structures in the Z toolkit. (Note: there is a Z specification for a binary tree in the Spivey reference manual in section 3.9).