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Chapter 6
Relations
Prof. Yin-Fu Huang
CSIE, NYUST
6.1 Introduction
 Relation types, values, and variables
6.2 Tuples
 A set of ordered triples of the form <Ai, Ti, vi>
 Degree, attribute, heading
Major_P# : P#
Minor_P# : P#
P2
P4
Qty : Qty
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6.2 Tuples (Cont.)
 Properties of tuples
 Every tuple contains exactly one value for each of
its attributes.
 There is no left-to–right ordering to the components
of a tuple.
 Every subset of a tuple is a tuple.
 The tuple type generator
e.g.
Var Addr Tuple { Street
City
State
Zip
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Char,
Char,
Char,
Char};
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6.2 Tuples (Cont.)
 Operators on tuples
 the tuple selector, assignment, equality comparison
 tuple projection, tuple join
 Wrap, Unwrap
e.g. Naddr1:= Naddr2 Wrap {Street, City, State, Zip} As Addr;
Naddr2:= Naddr1 Unwrap Addr;
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6.3 Relation Types
 A relation value consists of a heading and a body.
Relation [<heading>] {<tuple exp commalist>}
 The relation type generator
e.g.
Var Part_Structure …
Relation {Major_P# P#, Minor_P# P#,
Qty Qty} … ;
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6.4 Relation Values
 Properties of relations (See Fig. 6.1)
 Relations are normalized. ⇒ first normal form
 Attributes are unordered, left to right.
 Tuples are unordered, top to bottom.
 There are no duplicate tuples.
 Relations vs. Tables
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6.4 Relation Values (Cont.)
 Relation-valued attributes (See Fig. 6.2)
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6.4 Relation Values (Cont.)
 Relations with no attributes
 There are precisely two relations of degree zero-one
that contains just one tuple, and one that contains no
tuples at all.
i.e. Table_Dee: Relation { } { Tuple{ } }
Table_Dum: Relation { } { }
 Operators on relations
 Relational comparisons
 Other operators: 
 Order By
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6.5 Relation Variables
 Base Relvar definition
 Var <relvar name> Base <relation type>
<candidate key def list>
[<foreign key def list>];
e.g. Var SP Base Relation
{S# S#,
P# P#,
Qty Qty}
Primary key {S#, P#}
Foreign key {S#} References S
Foreign key {P#} References P;
 Drop Var <relvar name>;
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6.5 Relation Variables (Cont.)
 Updating Relvars
<relation assignment>::=<relation assign commalist>;
<relation assign>::= <relvar name>:=<relation exp>;
e.g. S’:=S Where Not (City=’Paris’);
Insert <relvar name> <relation exp>;
Delete <relvar name> [Where <bool exp>];
Update <relvar name> [Where <bool exp>]
{attribute update commalist>};
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6.6 SQL Facilities
 Rows
 A left-to-right ordering
[Row] (<exp commalist>)
 Table Types
 A left-to-right ordering
 Duplicated rows
Values <row value constructor commalist>
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6.6 SQL Facilities (Cont.)
 Table values and variables
 Create Table <base table name>
(<base table element commalist>);
• <base table element>: 1. <column definition>
2. <constraint>
• <column definition>:
<column name> <type name> [<default spec>]
 Drop Table <base table name> <behavior>
• <behavior>: Restrict or Cascade
 Alter Table
e.g. Alter Table S Add Column Discount Integer Default -1;
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6.6 SQL Facilities (Cont.)
 Structured Types
e.g. Create Type Point As (X Float, Y Float) Not Final
Ref Is System Generated;
Create Table Points Of Point
(Ref Is Point# System Generated …);
In the example, base table Points actually has three columns
(Point#, X, and Y, in that order).
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The End.
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