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Definitions

Definitions. Given sets. 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 ]. Declaration of variables.

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Definitions

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  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 : pBook --- 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

  9. Consistency

  10. Consistency : example

  11. Generic Definitions

  12. Generic Abbreviations

  13. Generic Axiomatic Definitions

  14. Generic Axiomatic Definitions

  15. Generic Axiomatic Definitions

  16. Generic Axiomatic Definitions

  17. Characteristic set

  18. Characteristic set

  19. Characteristic set

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