1. Introduction to the Z Example Two

2. 2 Write Z specifications for the Birthday Book Problem  The Birthday Book system keeps track of people’s birthdays. It allows you to add and search for birthdays. Also, it issues reminders.

3. 3 The Z specification should include:  Given Sets  State Schema  Initial State  Operations

4. 4 The Birthday Book Z Specification 1. Given Sets [NAME,DATE]

5. 5 The Birthday Book Z Specification 2. State definition BirthDayBook known: ℙ NAME Birthday: NAME DATE known = dom birthday Notation: D R ↦ Ξ ∀   × → Δ ≠ ∧ ∨ ∉ ∈ ∅ ∃ ℤ ℕ ℙ ℝ ≙   

6. Birthday Function: Example  known = {Ahmed, Zaid, Qais}  birthday = {Ahmed ↦ 17-Ram, Zaid ↦ 27-Sha, Qais ↦ 10-Raj}  The notation x ↦ y

7. 7 The Birthday Book Z Specification 3. Initial State BirthDayInit BirthdayBook known = Ø

8. 8 The Birthday Book Z Specification Operations 1. Add birthday 2. Find birthday 3. Remind

9. 9 The Birthday Book Z Specification 4. Operations (AddBirthday) AddBirthday  BirthdayBook name? : NAME date?: DATE name?  known known’= known  {name?} birthday’ = birthday  {name? ↦ date?}

10. 10 The Birthday Book Z Specification 4. Operations (FindBirthday) FindBirthday BirthdayBook name? : NAME date!: DATE name?  known date! = birthday(name?) 

11. 11 The Birthday Book Z Specification 4. Operations (Remind) Remind BirthdayBook cards! : ℙ NAME today?: DATE cards!= {n: known | birthday (n) = today!} 