Couples, Relations and Functions

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1 Couples, and Lecture 7 Tony Mullins Griffith College Dublin 1 Selector Given and Couples Tony Mullins Griffith College Dublin 3 Couples Tony Mullins Griffith College Dublin 5 Couples A couple is a pair of values. Couples are enclosed by round brackets and separated by a comma. Examples are,,,. Constructor: Tony Mullins Griffith College Dublin 2 Couples Tony Mullins Griffith College Dublin 4 id :: collection expression id :: collection :- predicate expression for.. yield The collection must be a set, bag or sequence and the result is a set, bag or sequence whose type is the same as the expression. In the second form only those values that satisfy the predicate are chosen. Tony Mullins Griffith College Dublin 6

2 Example Given a set for..yield returns the set returns the set Tony Mullins Griffith College Dublin 7 A relation is a set of couples. Domain of A Range of A Tony Mullins Griffith College Dublin 9 Example Specify a class called that models a relation of couples. The class should have functions that retrieve the domain, range, and cardinality of the relation. to check if a given couple is an element of the relation and check if a given set of couples are contained in the relation should be given. The class should also have functions that specify domain subtraction, domain restriction and range subtraction and restriction. Tony Mullins Griffith College Dublin 11 for.. yield Question 2 Worksheet 5 Calculate total occupancy in hotel could be written as follows: Tony Mullins Griffith College Dublin 8 Constructor Given Tony Mullins Griffith College Dublin 10 Tony Mullins Griffith College Dublin 12

3 The domain is the set of ordinates The range is the set of ordinates Tony Mullins Griffith College Dublin 13 returns ifis an element of the relation;otherwise returns if is a sub set of the relation;otherwise Tony Mullins Griffith College Dublin 15 Given such that Tony Mullins Griffith College Dublin 17 Given such that Cardinality is given by Tony Mullins Griffith College Dublin 14 Given a relation and a set, domain restriction equals the set of couples such that Tony Mullins Griffith College Dublin 16 Given a relation and a set, range restriction equals the set of couples such that Tony Mullins Griffith College Dublin 18

4 Given such that Tony Mullins Griffith College Dublin 19 Given such that Tony Mullins Griffith College Dublin 21 Given such that Tony Mullins Griffith College Dublin 23 Given a relation and a set, domain subtraction equals the set of couples such that Tony Mullins Griffith College Dublin 20 Given a relation and a set, range subtraction equals the set of couples such that Tony Mullins Griffith College Dublin 22 Schemas to add a new couple and a set of couples. Tony Mullins Griffith College Dublin 24

5 Schemas to remove a set of couples and remove a set of domain values. Tony Mullins Griffith College Dublin 25 A class of students can take any combination of the followng subjects: English, Maths, History, French, German. There are no restrictions on the number of subjects each student can take and there is no limit to the class size. Specify a class called that models students and the subjects they are studying. Tony Mullins Griffith College Dublin 27 Tony Mullins Griffith College Dublin 29 Schema to remove a set of values from the range. Tony Mullins Griffith College Dublin 26 Studies is a couple mapping a student to a subject Tony Mullins Griffith College Dublin 28 The list of students in the year is given by: The list of subjects currently being taken by students is given by: Tony Mullins Griffith College Dublin 30

6 List the subjects taken by a given student. Tony Mullins Griffith College Dublin 31 Add a student together with a single subject Alternative Tony Mullins Griffith College Dublin 33 A function is a relation where each element in the domain has at most one image in the range and are functions but violates the rule because it contains the couples and Tony Mullins Griffith College Dublin 35 List students taking a particular subject Tony Mullins Griffith College Dublin 32 Add a student together with a list of subjects Tony Mullins Griffith College Dublin 34 are modelled in Perfect by the class Constructors Tony Mullins Griffith College Dublin 36

7 Tony Mullins Griffith College Dublin 37 returns true if is an element of the domain of ; otherwise false returns the set of couples in Tony Mullins Griffith College Dublin 39, where of type and returns a map with couple appended to Tony Mullins Griffith College Dublin 41 and Schemas returns cardinality of the set of couples, where and of type p, returns the union of both maps, where of type and a set, returns those couples in that are not contained in., where of type and a set, returns those couples in that are contained in Tony Mullins Griffith College Dublin 38 returns the set of domain elements in returns the set of range elements in, duplicates removed returns the bag of range elements in returns true if is the empty otherwise Tony Mullins Griffith College Dublin 40 Note the pre-condition in both functions Tony Mullins Griffith College Dublin 42

8 The selector means that it is possible to reference a range value using the domain value as an index Tony Mullins Griffith College Dublin 43 Tony Mullins Griffith College Dublin 45 Tony Mullins Griffith College Dublin 47 It is also possible to use indexing to modify an element of a mapping. For example, given a map A of integer couples such that then Tony Mullins Griffith College Dublin 44 Tony Mullins Griffith College Dublin 46 Tony Mullins Griffith College Dublin 48

9 Tony Mullins Griffith College Dublin 49 Specify a simple database of books where each book has an associated unique key. A book has a single attribute title. Tony Mullins Griffith College Dublin 51 Tony Mullins Griffith College Dublin 53 Tony Mullins Griffith College Dublin 50 Tony Mullins Griffith College Dublin 52 Tony Mullins Griffith College Dublin 54

10 Tony Mullins Griffith College Dublin 55 Tony Mullins Griffith College Dublin 57 Tony Mullins Griffith College Dublin 56

Comp115: Databases. Relational Algebra

Comp115: Databases. Relational Algebra Comp115: Databases Relational Algebra Instructor: Manos Athanassoulis Up to now we have been discussing how to: (i) model the requirements (ii) translate them into relational schema (iii) refine the schema