1. Definitions

2. Given sets

3. Given sets : examples To introduce declaration of a set of student ; [ student ] In a library management system, the type Book and Person can be introduced as given sets : [ Book, Person ]

4. Declaration of variables A name is assigned a type when it is declared. Once a given set is declared, we can declare variables. Example stud1 : Student --- declaring a student library1 : p Book --- declaring a set of books primes : p  --- declaring primes to be a set of integers newestbook : Book   --- what the book is and a number showing the copy library : p (Book   ) --- declaring a library as a set of copies of books

5. Abbreviations Syntactic equivalence Example basic_ref == {math, intro_to_computers} Is equivalent to the declaration basic_ref : p Book together with the predicate basic_ref = {math, intro_to_computers}

6. Enumerated types Use data type definition to introduce a type with a small number of members Name ::= list of elements separated by | Example YesNo ::= yes | no

7. Axiomatic description To introduce variables along with predicates giving further information

8. Consistency

10. Consistency : example

11. Generic Definitions

12. Generic Abbreviations

13. Generic Axiomatic Definitions

17. Characteristic set