Data Types

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					   Data types

• Primitive data types
• Structured data types
• Strings
• Enumerated types
• Arrays
• Records
• Pointers

                CSI 3125, Data Types, page 1
Primitive data types


  • Numeric types

  • Booleans

  • Characters

                 CSI 3125, Data Types, page 2
   Data types: introduction

A data type is not just a set of objects.
We must consider all operations on
these objects. A complete definition of
a type must include a list of operations,
and their definitions.

Primitive data objects are close to
hardware, and are represented directly
(or almost directly) at the machine
level—usually word, byte, bit.

                         CSI 3125, Data Types, page 3
            Integer types

An integer type is a finite approximation
of the infinite set of integer numbers:
{0, 1, -1, 2, -2, ...}.

Various kinds of integers:
signed—unsigned, long—short—small.

Hardware implementations of integers:
one's complement, two's complement, ...

                          CSI 3125, Data Types, page 4
         Floating-point types

All "real" numbers in computers are finite
approximations of the non-denumerable
set of real numbers.
Precision and range of values are defined
by the language or by the programmer.
Hardware implementations (used by
floating-point processors): exponent and

                          CSI 3125, Data Types, page 5
              Boolean type

This type is not supported by all languages
(for example, it is not available in PL/, C,

The values are true and false. Operations
are as in classical two-valued propositional

Hardware implementation: a single bit or a
byte (this allows more efficient operations).

                            CSI 3125, Data Types, page 6
              Character types

This is usually ASCII, but extended character
(Unicode, ISO) sets are often used.
Accented characters é à ü etc. should fit within
ASCII, though there is no single standard.
Chinese or Japanese are examples of writing
systems that require character sets of many
more than 256 elements.
Hardware implementation: a byte (ASCII,
EBCDIC), two bytes (Unicode) or several bytes.
                             CSI 3125, Data Types, page 7
    Other primitive types

• word (for example, in Modula-2)

• byte, bit (for example, in PL/I)

• pointer (for example, in C)

                        CSI 3125, Data Types, page 8
Structured data types

  • Strings
  • Enumerated types
  • Arrays
  • Records

               CSI 3125, Data Types, page 9

A string is a sequence of characters. It may be:
• a special data type (its objects can be
  decomposed into characters)—Fortran, Basic;
• an array of characters—Pascal, Ada;
• a list of characters—Prolog;
• consecutively stored characters—C.
The syntax is the same: characters in quotes.
Pascal has one kind of quotes, Ada has two:
'A' is a character, "A" is a string.

                            CSI 3125, Data Types, page 10
       String operations

Typical operations on strings
string  string                string
string  int  int      string
string                  characters
   decompose into an array or list
characters              string
   convert an array or list into a string

                        CSI 3125, Data Types, page 11
   String operations (2)

string           integer

string           boolean
  is it empty?

string  string           boolean
  equality, ordering

                       CSI 3125, Data Types, page 12
     More string operations…

Specialized string manipulation languages
(Snobol, Icon) include built-in pattern
matching, sometimes very complicated,
with extremely elaborate backtracking.

Another language that works very well
with strings is, of course, Perl.

                       CSI 3125, Data Types, page 13
   Fixed- and variable-length strings
The allowed length of strings is a design
   fixed-length strings—Pascal, Ada, Fortran;
   variable-length strings—C, Java, Perl.
A character may be treated as a string of
length 1, or as a separate data structure.
Many languages (Pascal, Ada, C, Prolog)
treat strings as special cases of arrays or
Operations on strings are the same as on arrays or
lists of other types. For example, every character in
a character array is available at once, whereas a list
of characters must be searched linearly.

                                CSI 3125, Data Types, page 14
               Enumerated types

Also called: user-defined ordinal types
[read Section 6.4]
We can declare a list of symbolic constants that are
to be treated literally, just like in Prolog or Scheme.
We also specify the implicit ordering of those newly
introduced symbolic constants. In Pascal:
type day =
      (mo, tu, we, th, fr, sa, su);
Here, we have mo < tu < we < th < fr < sa < su.

                                CSI 3125, Data Types, page 15
     Operators for enumerated types

Pascal supplies the programmer with three generic
operations for every new enumerated type T:
succ: successor, for example, succ(tu) = we
pred: predecessor, for example, pred(su) = sa
                      (each is undefined at one end)
ord: (ordinal) position in the type, starting at 0,so for
example ord(th) = 3
For characters, Pascal also has chr, producing the
character at a given position, so for example
chr(65) returns ‘A’.

                                   CSI 3125, Data Types, page 16
         Enumerated types in Ada

Ada makes these generic operations complete:
  succ:    successor,
  pred:    predecessor,
  pos:     position,
  val:     constant at position.

Ada also supplies type attributes, among them

day'FIRST = mo, day'LAST = su

                              CSI 3125, Data Types, page 17
       Reuse of symbolic constants
A design issue: is the symbolic constant allowed in
more than one type? In Pascal, no. In Ada, yes:
  type stoplight is
     (red, amber, green);
  type rainbow is
     (violet, indigo, blue, green,
      yellow, orange, red);
Qualified descriptions—similar to type casts—prevent
any confusion: we can write stoplight'(red) or
                                CSI 3125, Data Types, page 18
Implementation of enumerated types

Map the constants c1, ..., ck into
small integers 0, ..., k-1.

Enumerated types help increase clarity
and readability of programs by separating
concepts from their numeric codes.

                         CSI 3125, Data Types, page 19
An array represents a mapping:
  index_type  component_type

The index type must be a discrete type (integer,
character, enumeration etc). In some languages this
type is specified implicitly:
  an array of size N is indexed 0…N-1 in C++ / Java /
  Perl, but in Fortran it is 1…N. In Algol, Pascal, Ada
  the lower and upper bound must be both given.

There are normally few restrictions on the component
type (in some languages we can even have arrays of
procedures or files).

                                 CSI 3125, Data Types, page 20
         Multidimensional arrays

Multidimensional arrays can be defined in two
ways (for simplicity, we show only dimension 2):
index_type1  index_type2  component_type
This corresponds to references such as A[I,J].
Algol, Pascal, Ada work like this.
index_type1 (index_type2  component_type)
This corresponds to references such as A[I][J].
Java works like this.
Perl sticks to one dimension

                             CSI 3125, Data Types, page 21
       Operations on arrays (1)

select an element (get or change its value):

select a slice of an array:
  (read the textbook, Section 6.5.7)

assign a complete array to a complete array:
  A := B;

There is an implicit loop here.

                              CSI 3125, Data Types, page 22
        Operations on arrays (2)

Compute an expression with complete arrays
(this is possible in extendible or specialized
languages, for example in Ada):
  V := W + U;

If V, W, U are arrays, this may denote array
addition. All three arrays must be compatible
(the same index and component type), and
addition is probably carried out element by

                           CSI 3125, Data Types, page 23
              Subscript binding

static:               fixed size, static allocation
   this is done in older Fortran.
semistatic:           fixed size, dynamic allocation
semidynamic:          size determined at run time,
                      dynamic allocation
dynamic:              size fluctuates during execution,
                      flexible allocation required
   Algol 68, APL—both little used...

                                CSI 3125, Data Types, page 24
Array-type constants and initialization
Many languages allow initialization of arrays to be
specified together with declarations:
     C        int vector [] = {10,20,30};
     Ada      vector: array(0..2)
                     of integer := (10,20,30);
Array constants in Ada
  temp is array( -40..40;
  T: temp;
  T := (15,12,18,22,22,30,22);
  T := (mo=>15, we=>18, tu=>12,
            sa=>30, others=>22);
  T := (15,12,18, sa=>30, others=>22);

                              CSI 3125, Data Types, page 25
          Implementing arrays (1)

The only issue is how to store arrays and access their
elements—operations on the component type decide
how the elements are manipulated.

An array is represented during execution by an array
descriptor. It tells us about:
  the index type,
  the component type,
  the address of the array, that is, the data.

                                  CSI 3125, Data Types, page 26
          Implementing arrays (2)

Specifically, we need:
   the lower and upper bound (for subscript checking),
   the base address of the array,
   the size of an element.

We also need the subscript—it gives us the offset (from
the base) in the memory area allocated to the array.

A multi-dimensional array will be represented by a
descriptor with more lower-upper bound pairs.

                                CSI 3125, Data Types, page 27
 Implementing multidimensional arrays

                    11   12 13 14 15
                    21 22 23 24 25
                    31 32 33 34 35

 Row major order (second subscript increases faster)

11    12 13 14 15 21 22 23 24 25 31 32 33 34 35

     Column major order (first subscript increases faster)

11    21 31 12 22 32 13 23 33 14 24 34 15 25 35

                                    CSI 3125, Data Types, page 28
                              Implementing multidimensional arrays (2)

Suppose that we have this array:
   A: array [LOW1..HIGH1,
                LOW2..HIGH2] of ELT;
where the size of each entity of type ELT is
This calculation is done for row-major
(calculations for column-major are quite
similar). We need the base—for example,
the address LOC of A[LOW1, LOW2].

                          CSI 3125, Data Types, page 29
                                Implementing multidimensional arrays (3)

We can calculate the address of A[I,J] in the
row-major order, given the base.
Let the length of each row in the array be:
The address of A[I,J] is:
  (J - LOW2) * SIZE + LOC

                            CSI 3125, Data Types, page 30
                                 Implementing multidimensional arrays (4)
Here is an example.
VEC: array [1..10, 5..24] of integer;
The length of each row in the array is:
  ROWLENGTH = 24 - 5 + 1 = 20
Let the base address be 1000, and let the size of
an integer be 4.
The address of VEC[i,j] is:
(i - 1) * 20 * 4 + (j - 5) * 4 + 1000
For example, VEC[7,16] is located in 4 bytes at
1524 = (7 - 1) * 20 * 4 +
          (16 - 5) * 4 + 1000

                             CSI 3125, Data Types, page 31
       Languages without arrays

A final word on arrays: they are not supported
by standard Prolog and pure Scheme. An array
can be simulated by a list, which is the basic
data structure in Scheme and a very important
data structure in Prolog.
Assume that the index type is always 1..N.
Treat a list of N elements:
  [x1, x2, ..., xN] (Prolog)
  (x1 x2 ... xN) (Scheme)
as the (structured) value of an array

                           CSI 3125, Data Types, page 32

A record is a heterogeneous collection of fields
(components)—this differs from homogenous

Records are supported by a majority of
important languages, beginning with Cobol,
through Pascal, PL/I, Ada, C (where they are
called structures), Prolog (!) to C++.

There are no records in Java, but classes
replace them. There are no records in Perl.

                            CSI 3125, Data Types, page 33
      Ada records—syntax
type date is record
   day: 1..31;
   month: 1..12;
   year: 1000..9999;
 end record;

type person is record
  name: record
          fname: string(1..20);
          lname: string(1..20);
        end record;
  born: date;
  gender: (F, M);
end record;

                       CSI 3125, Data Types, page 34

A field is distinguished by a name rather than an
index. Iteration on elements of an array is natural
and very useful, but iteration on fields of a record is
not possible (why?).

A field is indicated by a qualified name. In Ada:
      X, Y: person; := 15;
      X.born.month := 11;
      X.born.year := 1964;
      Y.born := (23, 9, 1949); := "Smithson";

                                CSI 3125, Data Types, page 35
          Operations on records (1)
Selection of a component is done by field name.
Construction of a record from components—either from
separate fields, or as a complete record in a structured
  D := (month => 10, day => 15, year => 1994);
  D := (day => 15, month => 10, year => 1994);
  D := (15, 10, 1994);
  D := (15, 10, year => 1994);
Note that an array can also be assigned such a constant.
Interpretation depends on context.
  A: array(1..3)of integer;
  A := (15, 10, 1994);

                               CSI 3125, Data Types, page 36
       Operations on records (2)

Assignment of complete records is allowed in
Ada, and is done field by field.

Records can be compared for equality or
inequality, regardless of their structure or type
of components. No generic standard ordering
of records exists, but specific ordering can be
defined by the programmer.

                            CSI 3125, Data Types, page 37
             More on records
Ada allows default values for fields:
    type date is record
       day: 1..31; month: 1..12;
       year: 1000..9999 := 2002;
    end record;
    D: date;       -- D.year is now 2002
There are almost no restrictions on field types.
Any combination of records and arrays (any
depth) is usually possible. A field could also be
a file or even a procedure!
                             CSI 3125, Data Types, page 38
       The Prolog equivalent of records
Records—or rather terms—in Prolog can carry their type and
their components around:
date(day(15), month(10), year(1994))
      name(fname("Jim"), lname("Berry")),
      born(date(day(15), month(10), year(1994))),
If we can assure correct use, this can be simplified by dropping
one-argument "type" functors:
date(15, 10, 1994)
person(name("Jim", "Berry"),
          born(date(15, 10, 1994)),
                                   CSI 3125, Data Types, page 39
                  Back to pointers
[Note: We’re skipping 6.9.9]

A pointer variable has addresses as values (and a
special address nil or null for "no value"). They are used
primarily to build structures with unpredictable shapes
and sizes—lists, trees, graphs—from small fragments
allocated dynamically at run time.

A pointer to a procedure is possible, but normally we
have pointers to data (simple and composite). An
address, a value and usually a type of a data item
together make up a variable. We call it an anonymous
variable: no name is bound to it. Its value is accessed
by dereferencing the pointer.

                                 CSI 3125, Data Types, page 40
                                             Back to pointers (2)

Pointers in Pascal are quite well designed.

    p                             value(p) = 

                    17            value(p^) = 17

 Note that, as with normal named variables, in this:
     p^ := 23;
 we mean the address of p^ (the value of p).
 In this:
     m := p^;
 we mean the value of p^.

                                CSI 3125, Data Types, page 41
          Pointer variable creation

A pointer variable is declared explicitly and has the
scope and lifetime as usual.
An anonymous variable has no scope (because it has
no name) and its lifetime is determined by the
programmer. It is created (in a special memory area
called heap) by the programmer, for example:
  new(p);                          in Pascal
  p = malloc(4);                   in C
       and destroyed by the programmer:
  dispose(p);                      in Pascal
  free(p);                         in C

                                CSI 3125, Data Types, page 42
                                      Pointer variable creation (2)

If an anonymous variable exists outside
the scope of the explicit pointer variable,
we have "garbage" (a lost object). If an
anonymous variable has been destroyed
inside the scope of the explicit pointer
variable, we have a dangling reference.
       p^ := 23;
       if p^ > 0 {???}

                           CSI 3125, Data Types, page 43
                                      Pointer variable creation (2)

Producing garbage, an example in Pascal:
    new(p); p^ := 23; new(p);
{the anonymous variable with the value 23
becomes inaccessible}
Garbage collection is the process of
reclaiming inaccessible storage. It is usually
complex and costly. It is essential in
languages whose implementation relies on
pointers: Lisp, Prolog.

                           CSI 3125, Data Types, page 44
   Pointers: types and operators

Pointers in PL/I are typeless. In Pascal, Ada,
C they are declared as pointers to types, so
that a dereferenced pointer (p^, *p) has a
fixed type.
Operations on pointers in C are quite rich:
   char b, c;
   c = '\007';
   b = *((&c - 1) + 1);

                          CSI 3125, Data Types, page 45

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