Chapter 5

1. Chapter 5 Types

2. Topics in this Chapter • Values vs. Variables • Types vs. Representations • Type Definition • Operators • Type Generators • SQL Facilities

3. Types • The relational model • The relational model as described with Tutorial D • SQL 92 • SQL 99 • MySQL • SQL– other

4. Types • A type is a set of values • Sometimes called domains in the relational context • Types can be system-defined or user-defined • All types have associated operators • Formally, this means that the operator can take the given type as a parameter • For example integers can be passed to an addition operator but not a sub-string operator

5. Enumerated Data Types • Syntax: enum <User type name> < Constant_list> • enum WeekDay {Mon, Tue, Wed, Thu, Fri}; • WeekDay workday; • workday = Tue; • Enumerated data type variables can only assume values which have been previously declared.

6. Values vs. Variables - Values • A value is an individual constant • It has no location in time or space • A value is represented by encoding, which generates its appearance, which is spatial and temporal • Appearances can occur in different times and spaces: they are manifold • A value cannot be updated, for then it would be some other value: a value is immutable

7. Values vs. Variables - Variables • A variable is a holder for an appearance of a value • It has location in time or space • A variable can be updated, that is, it can hold another value • A variable maintains its identity during the update: it is still the same variable

8. Values vs. Variables • Values can be simple or complex • Simple: integer, char • Complex: a document, a relation • A value per se can have multiple appearances • An appearance can have multiple encodings • When we refer to a “value,” we often mean “an appearance of an encoding of a value”

9. Values and Variables are Typed • Every value has its immutable type • Every variable has its immutable type, so that all its values will be of that type • Every attribute of every relvar has its immutable type • Operators have a type when operating, but this can be polymorphic in different contexts • e.g. = can operate on integers or characters, but not both at the same time

10. Types and their Representations • A type per se is idealized, conceptual, a model • A representation (appearance) of the type is its implementation • Sometimes a type is called an ADT – Abstract Data Type, but this is inherently redundant • This logical and physical distinction is an aspect of data independence

11. Abstract Data Types • Definition: A mathematically specified collection of data-storing entities with operations to create, access, change, etc. instances. • Also known as ADT. • Note: Since the collection is defined mathematically, rather than as an implementation in a computer language, we may reason about effects of the operations, relations to other abstract data types, whether a program implements the data type, etc. • National Institute of Standards and Technology

12. /** * This class represents complex numbers, * and defines methods for performing * arithmetic on complex numbers. **/ public class ComplexNumber { // These are the instance variables. Each // ComplexNumber object holds two double values, // known as x and y. They are private, so they are // not accessible from outside this class. // Instead, they are available // through the real() and imaginary() methods below. private double x, y; /** * This is the constructor. * It initializes the x and y variables **/ public ComplexNumber(double real, double imaginary) { this.x = real; this.y = imaginary; }

13. ComplexNumber compP = new ComplexNumber(PRealPart, PImaginaryPart); ComplexNumber compQ = new ComplexNumber(QRealPart, QImaginaryPart);

14. /** * An accessor method. Returns the real part * of the complex number. * Note that there is no setReal() method to set * the real part. This means * that the ComplexNumber class is "immutable". **/ public double real() { return x; } /** * An accessor method. Returns the imaginary part * of the complex number */ public double imaginary() { return y; }

15. /** * This is a static class method. It takes two complex * numbers, adds them, and returns the result as a third * number. Because it is static, there is no "current * instance" or "this" object. Use it like this: * ComplexNumber c = ComplexNumber.add(a, b); **/ public static ComplexNumber add(ComplexNumber a, ComplexNumber b) { return new ComplexNumber(a.x + b.x, a.y + b.y); } ComplexNumber compT = ComplexNumber.add(compP, compQ);

16. /** * A static class method to multiply complex * numbers */ public static ComplexNumber multiply(ComplexNumber a, ComplexNumber b) { return new ComplexNumber (a.x*b.x - a.y*b.y, a.x*b.y + a.y*b.x); }

17. Types and their Representations - Scalar vs. Non-Scalar • A scalar type is atomic and encapsulated • Integer, char, bool • A non-scalar type is complex and user-visible • Name, address, employee, radiology image • Values, variables, attributes, operators, parameters, expressions: all can be scalar or not

18. Types and their Representations - Possible Representations • Let T be a scalar type • The physical representation is hidden from the user • Values of type T must have at least one possible representation, which is not hidden from the user • The possible representation of a scalar type may have components, and if so, then at least one set of these must be visible to the user

19. Types and their Representations - Possible Representations • Each type has at least one POSSREP visible to the user in its declaration • Each POSSREP includes two operators • Selector to specify a value for each representation • Ex.: QTY (100), QTY(N1 – N2) • THE_ to access each representation • Ex.: THE_QTY (Q), THE_QTY (Q1 – Q2), • QTY cannot equal 100, because quantity is not an integer, if it has been declared as a type • QTY can equal QTY(100)

20. Type Definition • TYPE WEIGHT POSSREP { D DECIMAL (5,1) CONSTRAINT D > 0.0 AND D < 5000.0 }; • TYPE WEIGHT POSSREP LBS { L DECIMAL (5,1) CONSTRAINT L > 0.0 AND L < 5000.0 }; POSSREP GMS { G DECIMAL (7,1) CONSTRAINT G > 0.0 AND G < 2270000.0 AND MOD (G, 45.4) = 0.0 };

21. Operators • OPERATOR ABS (Z RATIONAL) RETURNS RATIONAL; RETURN (CASE WHEN Z > 0.0 THEN +Z WHEN Z < 0.0 THEN –Z END CASE); END OPERATOR;

22. Operators To define an operator: OPERATOR REFLECT (P POINT) UPDATES P; BEGIN; THE_X (P) := - THE_X (P) ; THE_Y (P) := - THE_Y (P) ; RETURN; END; END OPERATOR; To remove the operator: DROP OPERATOR REFLECT;

23. Type Conversions In Java: float x = 2.0; int y = 17; x = y; // coercion x = (float)y; // explicit type conversion // (casting)

24. Type Conversions • QTY(100) converts an integer to a quantity • THE_QTY (Q1) converts a quantity to an integer • P# = ‘P2’ violates the rule that both sides of an assignment must be of the same type • Compiler uses the P# selector implicitly to convert ‘P2’ from Char to P# • a/k/a “Coercion” • Coercion is not permitted

25. Type Conversions • Coercion is not permitted • Explicit casting is permitted CAST_AS_CHAR (530.00) • This is called strong typing: • i.e., every value has a type, • and the compiler checks to verify that operands are of the correct type for an operation • Can’t add weight to quantity, but can multiply them

26. Type and Domain • All types are known to the system • The types in a database are a closed set • Assignments and comparisons, ditto • In a database system, a domain is a type, and thereby is an object class • Hence we can speak about relations and objects simultaneously

27. Type Generators • a/k/a parameterized types, or templates • ARRAY is a classic invocation of a type generator • ARRAY can take in all sorts of types, and can return all sorts of other types VAR SALES ARRAY INTEGER [12]; • ARRAY operators such as assignment, equality, THE_ work equally well with any valid type, i.e., a type known to the system

28. SQL Facilities Built-in types: Numeric, Decimal, Integer, Smallint, Float Date, Time, Timestamp, Interval Boolean, Bit, Character Binary Large Object (BLOB) Character Large Object (CLOB)

29. SQL Facilities Binary Large Object (BLOB) not really binary, not really an “object” long string of octets an image, sound file, etc. SQL provides a locator construct to enable handling piecemeal Character Large Object (CLOB)

30. SQL Facilities • Mostly strong typing, but SQL will coerce FLOAT to NUMERIC, for example • Supports two kinds of user-defined types: distinct types and structured types • SQL does not support POSSREP – only one representation per type • SQL does not support CONSTRAINTs

31. SQL Facilities – DISTINCT Types • CREATE TYPE WEIGHT AS DECIMAL (5,1) FINAL; • For DISTINCT types, SQL supports Selector and THE_ • DISTINCT types are strong, so you cannot use a comparison operator between the type and its underlying representation WHERE PART_WEIGHT = WEIGHT(14.0) selector (cast)

32. SQL Facilities – Structured Types • CREATE TYPE POINT AS (X FLOAT,Y FLOAT) NOT FINAL; • Uses operators in place of Select and THE_ • Observe and mutate methods • Structured types can be ALTERed or DROPped • Tuples and relations are structured types

33. SQL Facilities –Type Generators • SQL includes type generators (called type constructors): • ROW generates a set of fields • ARRAY generates an array

34. CREATE TABLE CUST (CUST# CHAR(3), ADDR ROW ( STREET CHAR(50), CITY CHAR(25), STATE CHAR(2), ZIP CHAR(5) ) PRIMARY KEY (CUST#) ); SELECT CX.CUST# FROM CUST AS CX WHERE CX.ADDR.STATE = ‘CA’;

35. CREATE TABLE ITEM_SALES (ITEM# CHAR(5), SALES INTEGER ARRAY[12], PRIMARY KEY (ITEM#) ); SELECT ITEM# FROM ITEM_SALES WHERE SALES[3] > 10;

36. type abstract data type (ADT) enumerated data type type coercion type conversion (casting) strong typing type constraint DISTINCT types structured types SQL built-in types

37. variable vs. value scalar vs. non-scalar system defined type vs. user defined type type vs. representation representation vs. implementation