CP2003 Lecture Notes - Primitive Types

See ``The Anatomy of Programming Languages'' by Fischer and Grodzinsky (Chapter 5) or ``Programming Language Concepts and Paradigms'' by David Watt (Chapter 2).

Values

A value is anything that may be evaluated, stored, incorporated in a data structure or object, passed as an argument, returned, etc. For examples, what kinds of values exist in C++?

primitive values (int, char, float etc.)
composite values (int array[30], classes, unions)
pointers/addresses (int *, &x, int *function())

Types

What is a type?

a set of values, e.g., the type integer might correspond to the set
{..., -1, 0, 1, ...}
NOTATION: v is a value of type T is represented by $v \epsilon T$
it must exhibit uniform behaviour under some set of operations like addition, multiplication, comparison, e.g., the Type {23, red, 'J'} would be an unusual type since it might be difficult to define operations such as a comparison of values (is red less than 23?)

type examples:

    boolean = {false, true}
    integer = {..., -1, 0, 1, ...}
    float = {..., -1.0, ..., 0.0, ..., 1.0, ...}
    character = {'\0', ..., 'a', ..., 'z', ..., '\255'}
    enumerated = {jan, feb, ..., dec}
      such as from a Pascal type definition like `type month = (jan, ...,
      dec);'
    subrange = {28, 29, 30, 31}
      such as from a Pascal definition like `var day : integer[28..31];'

NOTATION: the cardinality of a set S will be represented as #S. The cardinality is just the number of elements in the set:

    #boolean = 2
    #integer = MAXINT - MININT (in Pascal)
    #character = 255
    #{jan, feb, ..., dec} = 12
    #{28, 29, 30, 31} = 4

Basically, a type is an abstraction (i.e. don't know or care how they work) consisting of a type name (name of the type in your program, e.g. IDNumber), a type declaration (associates a name with a description, e.g. typedef int IDNumber) and a type description (including a physical description and set of supported operations, e.g. integer class)

Primitive Hardware Types

These are basic types, often supported at the `hardware' level.

byte - 8 bits (most computers are byte-addressable)
words - 32 bits (or 16 bits)
long words - 64 bits

Some logical operations on these entities are possible, such as:

hardware operations on `uninterpreted' bits

logical-or

        10101101    a byte
        00101011    another byte
        --------
        10101111    result of logical-or

logical-and

        10101101    a byte
        00101011    another byte
        --------
        00101001    result of logical-and

Some groups of bits, however, have `interpretations':

binary integers
- unsigned - 32 bits long, can represent a number in the range 0 to 2^(32) - 1
- signed - 32 bits long but 1 bit is the sign bit. If the sign bit is 'on' then the number is negative, if it is 'off', it is a positive number. Can represent a number in the range -2^(31) to 2^(31)-1.

Other encodings include floating point, packed decimal, 4 bit digits and character codes such as:

EBCIDIC - 7 bit characters (IBM generated, dying a slow death), not orderly
ASCII - 8 bit characters, current international standard, much more orderly
Unicode - 16 bit representation of a character (enabling approx. 64,000 characters). Supports non-English characters.