Domains, Relations, and Base Relvars

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Domains, Relations, and Base Relvars
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Introduction

• Structural Terminology

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Structural Terminology
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Domains

• A domain is a data type
• Ex) system-defined type INTEGER, CHAR
• User-defined type S, P,
• A Type
• All possible values of the type
• Ex) the type INTEGER the set of all possible
  integers
• S the set of all possible supplier
  numbers

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Operators

• For each type defined, there are valid operators
  that can be legally applied to the values of the
  type
• Ex) integer
• Comparison operators like , lt,
• Arithmetic operators like , ,
• Ex) S
• Only Comparison operators like , lt,

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Type and Physical Representation

• Types
• A model issue
• ? the operators for a given type will depend on
  the intended meaning or semantics of the type
• Physical representation
• An implementation issue
• Ex) S
• Physically represented as a character string
• But no character string operation

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Role of Types

• For every operation, there will be type checking
• Assures legal operations only
• Ex) P.WEIGHT SP.QTY
• Meaningless ? rejected
• Ex) P.WEIGHT SP.QTY
• Meaningful ? accepted

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Values are typed

• A value carries a type
• a kind of flag like
• I am an integer or I am a supplier number
• Possible operations between values are checked
  for every operation

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Type definition

• Tutorial D
• A hypothetical Pascal-like language to explain
  concepts in the textbook
• Format of type definition
• TYPE lttype namegt ltpossible representationgt
• Ex) the type definitions for the suppliers and
  parts database
• TYPE S POSSREP (CHAR)
• TYPE NAME POSSREP (CHAR)
• TYPE P POSSREP (CHAR)
• TYPE COLOR POSSREP (CHAR)
• TYPE WEIGHT POSSREP (RATIONAL)
• TYPE QTY POSSREP (INTEGER)

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Relation values

• relation for short
• Definition of relation
• Given a collection of n types or domains Ti
  (i1,2,,n), not necessarily all distinct, r is a
  relation on those types if it consists of 2
  parts, a heading and a body, where (see the next
  slide)

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Relation values (cont.)

• Definition of relation (cont.)
• The heading is a set of n attributes of the form
  AiTi, where Ai is attribute name and Ti is type
  name (i1, 2, , n)
• The body is a set of m tuples t, where t is a set
  of components of the form Aivi in which vi is a
  value of type Ti (i1, 2, , n)
• m cardinality, n degree

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Properties of Relations

• There are no duplicate tuples
• Tuples are unordered, top to bottom
• Attributes are unordered, left to right
• Each tuple contains exactly one value for each
  attribute ? first normal form(1NF)