Z notation
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Z - Notation. Presented By: Adam Attinello CMSC 445. Z – Notation? HUH?!?. First off – its pronounced Zed After the Zermelo-Fränkel set theory It is a set of conventions for presenting mathematical text, chosen to make it convenient to use simple mathematics to describe computing systems.

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Z - Notation

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Z notation

Z - Notation

Presented By:Adam Attinello

CMSC 445


Z notation huh

Z – Notation? HUH?!?

  • First off – its pronounced Zed

    • After the Zermelo-Fränkel set theory

  • It is a set of conventions for presenting mathematical text, chosen to make it convenient to use simple mathematics to describe computing systems.

  • It is targeted to clarify and streamline the specification and requirement process


Boring facts about z notation

Boring Facts About Z – Notation

  • Based on the standard mathematical notation

    • The mathematical notation of Z consists of a small core

      • Supplemented by a larger collection of useful objects and operators called the Z mathematical tool-kit.

  • Some Problems with Z notation

    • Z notation uses many non-ASCII symbols

    • The specification includes suggestions for rendering the Z notation symbols in ASCII as well as LaTeX.


How to model a system

How To Model A System

  • Z decomposes specifications into manageably sized module’s, called schemas:

    • Schemas are divided into 3 parts:

      • A State

      • A collection of state variables and their values

      • There are also some operations that can change its state

  • Z is also a natural fit to object-oriented programming.

    • You can also use Z in a functional style, among others

    • There are some object oriented languages that extend Z


Z notation formulas

Z operators are defined by formulas.

These are done through symbols

These symbols hold most of the same meanings as they do in an of our math classes

Z – Notation Formulas


The birthday book example

The Birthday Book Example

  • This is the “Hello World of Z Notation”

    • This is a shorter version of the true example

  • My example will allow you too do 3 things:

    • Add a person’s name and birthday

    • Store that information

    • Then find it again


Notation example

Name

Some variables are declared. As well as state transitions.

Relationship between the values of the variables

Init Birthday Book

Birthday Book

Known = 

Notation Example

[NAME; DATE]:


Notation example ii

Birthday book

known: NAME

birthday: NAME DATE

Known : dom birthday

Notation Example II

  • One possible state of the system has three people in the set known, with their birthdays recorded by the function birthday:

    known = { John; Mike; Susan }

    birthday = { John 25-Mar,

    Mike 20-Dec,

    Susan 20-Dec }


How the system might look

Add Birthday

Birthday Book

name?: NAME

date?: DATE

How the system might look

name? known

birthday’ = birthday U { name? date}


Notation example iii

Notation Example III

Find Birthday

Birthday book

name?: NAME

Date! : DATE

name? Known

date != birthday(name?)


References

REFERENCES

  • http://spivey.oriel.ox.ac.uk/mike/zrm/zrm.pdf

  • http://staff.washington.edu/jon/z-lectures/z-lectures.html

  • Software Engineering Theory and Practice, 3rd Edition


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