Theory of programming language chapter 6

ISBN 0-321—49362-1
Chapter 6
Data Types

Copyright © 2018 Pearson. All rights reserved. 1-2
Chapter 6 Topics
• Introduction
• Primitive Data Types
• Character String Types
• Enumeration Types
• Array Types
• Associative Arrays
• Record Types
• Tuple Types
• List Types
• Union Types
• Pointer and Reference Types
• Optional Types
• Type Checking
• Strong Typing
• Type Equivalence
• Theory and Data Types

Introduction
• A data type defines a collection of data
objects and a set of predefined operations
on those objects
• A descriptor is the collection of the attributes
of a variable
• An object represents an instance of a user-
defined (abstract data) type
• One design issue for all data types: What
operations are defined and how are they
specified?

Primitive Data Types
• Almost all programming languages provide a
set of primitive data types
• Primitive data types: Those not defined in
terms of other data types
• Some primitive data types are merely
reflections of the hardware
• Others require only a little non-hardware
support for their implementation

Primitive Data Types: Integer
• Almost always an exact reflection of the
hardware so the mapping is trivial
• There may be as many as eight different
integer types in a language
• Java’s signed integer sizes: byte, short,
int, long

Primitive Data Types: Floating Point
• Model real numbers, but only as
approximations
• Languages for scientific use support at least
two floating-point types (e.g., float and
double; sometimes more
• Usually exactly like the hardware, but not
always
• IEEE Floating-Point
Standard 754

Primitive Data Types: Complex
• Some languages support a complex type,
e.g., C99, Fortran, and Python
• Each value consists of two floats, the real part
and the imaginary part
• Literal form (in Python):
(7 + 3j), where 7 is the real part and 3 is the
imaginary part

Primitive Data Types: Decimal
• For business applications (money)
– Essential to COBOL
– C# offers a decimal data type
• Store a fixed number of decimal digits, in
coded form (BCD)
• Advantage: accuracy
• Disadvantages: limited range, wastes memory

Primitive Data Types: Boolean
• Simplest of all
• Range of values: two elements, one for “true”
and one for “false”
• Could be implemented as bits, but often as
bytes
– Advantage: readability

Primitive Data Types: Character
• Stored as numeric codings
• Most commonly used coding: ASCII
• An alternative, 16-bit coding: Unicode (UCS-2)
– Includes characters from most natural languages
– Originally used in Java
– Now supported by many languages
• 32-bit Unicode (UCS-4)
– Supported by Fortran, starting with 2003

Character String Types
• Values are sequences of characters
• Design issues:
– Is it a primitive type or just a special kind of array?
– Should the length of strings be static or dynamic?

Character String Types Operations
• Typical operations:
– Assignment and copying
– Comparison (=, >, etc.)
– Catenation
– Substring reference
– Pattern matching

Character String Type in Certain
Languages
• C and C++
– Not primitive
– Use char arrays and a library of functions that provide operations
• SNOBOL4 (a string manipulation language)
– Primitive
– Many operations, including elaborate pattern matching
• Fortran and Python
– Primitive type with assignment and several operations
• Java (and C#, Ruby, and Swift)
– Primitive via the String class
• Perl, JavaScript, Ruby, and PHP
- Provide built-in pattern matching, using regular
expressions

Character String Length Options
• Static: COBOL, Java’s String class
• Limited Dynamic Length: C and C++
– In these languages, a special character is used to
indicate the end of a string’s characters, rather
than maintaining the length
• Dynamic (no maximum): SNOBOL4, Perl,
JavaScript

Character String Type Evaluation
• Aid to writability
• As a primitive type with static length, they are
inexpensive to provide--why not have them?
• Dynamic length is nice, but is it worth the
expense?

Character String Implementation
• Static length: compile-time descriptor
• Limited dynamic length: may need a run-time
descriptor for length (but not in C and C++)
• Dynamic length: need run-time descriptor;
allocation/deallocation is the biggest
implementation problem

Compile- and Run-Time Descriptors
Compile-time
descriptor for
static strings
Run-time
descriptor for
limited dynamic
strings

User-Defined Ordinal Types
• An ordinal type is one in which the range of
possible values can be easily associated with
the set of positive integers
• Examples of primitive ordinal types in Java
– integer
– char
– boolean

Enumeration Types
• All possible values, which are named
constants, are provided in the definition
• C# example
enum days {mon, tue, wed, thu, fri, sat, sun};
• Design issues
– Is an enumeration constant allowed to appear in
more than one type definition, and if so, how is
the type of an occurrence of that constant
checked?
– Are enumeration values coerced to integer?
– Any other type coerced to an enumeration type?

Evaluation of Enumerated Type
• Aid to readability, e.g., no need to code a
color as a number
• Aid to reliability, e.g., compiler can check:
– operations (don’t allow colors to be added)
– No enumeration variable can be assigned a value
outside its defined range
– C#, F#, Swift, and Java 5.0 provide better support
for enumeration than C++ because enumeration
type variables in these languages are not coerced
into integer types

Array Types
• An array is a homogeneous aggregate of
data elements in which an individual element
is identified by its position in the aggregate,
relative to the first element.

Array Design Issues
• What types are legal for subscripts?
• Are subscripting expressions in element references
range checked?
• When are subscript ranges bound?
• When does allocation take place?
• Are ragged or rectangular multidimensional arrays
allowed, or both?
• What is the maximum number of subscripts?
• Can array objects be initialized?
• Are any kind of slices supported?

Array Indexing
• Indexing (or subscripting) is a mapping from
indices to elements
array_name (index_value_list)  an element
• Index Syntax
– Fortran and Ada use parentheses
• Ada explicitly uses parentheses to show uniformity
between array references and function calls because
both are mappings
– Most other languages use brackets

Arrays Index (Subscript) Types
• FORTRAN, C: integer only
• Java: integer types only
• Index range checking
- C, C++, Perl, and Fortran do not specify
range checking
- Java, ML, C# specify range checking

Subscript Binding and Array Categories
• Static: subscript ranges are statically bound
and storage allocation is static (before run-
time)
– Advantage: efficiency (no dynamic allocation)
• Fixed stack-dynamic: subscript ranges are
statically bound, but the allocation is done at
declaration time
– Advantage: space efficiency

(continued)
• Fixed heap-dynamic: similar to fixed stack-
dynamic: storage binding is dynamic but
fixed after allocation (i.e., binding is done
when requested and storage is allocated
from heap, not stack)

(continued)
• Heap-dynamic: binding of subscript ranges
and storage allocation is dynamic and can
change any number of times
– Advantage: flexibility (arrays can grow or shrink
during program execution)

(continued)
• C and C++ arrays that include static modifier
are static
• C and C++ arrays without static modifier are
fixed stack-dynamic
• C and C++ provide fixed heap-dynamic arrays
• C# includes a second array class ArrayList that
provides fixed heap-dynamic
• Perl, JavaScript, Python, and Ruby support
heap-dynamic arrays

Array Initialization
• Some language allow initialization at the time
of storage allocation
– C, C++, Java, Swift, and C#
– C# example:
int list [] = {4, 5, 7, 83}
– Character strings in C and C++
char name [] = ″freddie″;
– Arrays of strings in C and C++
char *names [] = {″Bob″, ″Jake″, ″Joe″];
– Java initialization of String objects
String[] names = {″Bob″, ″Jake″, ″Joe″};

Heterogeneous Arrays
• A heterogeneous array is one in which the
elements need not be of the same type
• Supported by Perl, Python, JavaScript, and
Ruby

Array Initialization
• C-based languages
– int list [] = {1, 3, 5, 7}
– char *names [] = {″Mike″, ″Fred″, ″Mary Lou″};
• Python
– List comprehensions
list = [x ** 2 for x in range(12) if x % 3 == 0]
puts [0, 9, 36, 81] in list

Arrays Operations
• APL provides the most powerful array processing
operations for vectors and matrixes as well as unary
operators (for example, to reverse column elements)
• Python’s array assignments, but they are only
reference changes. Python also supports array
catenation and element membership operations
• Ruby also provides array catenation

Rectangular and Jagged Arrays
• A rectangular array is a multi-dimensioned
array in which all of the rows have the same
number of elements and all columns have
the same number of elements
• A jagged matrix has rows with varying
number of elements
– Possible when multi-dimensioned arrays actually
appear as arrays of arrays
• C, C++, and Java support jagged arrays
• F# and C# support rectangular arrays and
jagged arrays

Slices
• A slice is some substructure of an array;
nothing more than a referencing mechanism
• Slices are only useful in languages that have
array operations

Slice Examples
• Python
vector = [2, 4, 6, 8, 10, 12, 14, 16]
mat = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
vector (3:6) is a three-element array
mat[0][0:2] is the first and second element of the
first row of mat
• Ruby supports slices with the slice method
list.slice(2, 2) returns the third and fourth
elements of list

Implementation of Arrays
• Access function maps subscript expressions to
an address in the array
• Access function for single-dimensioned arrays:
address(list[k]) = address (list[lower_bound])
+ ((k-lower_bound) * element_size)

Accessing Multi-dimensioned Arrays
• Two common ways:
– Row major order (by rows) – used in most
languages
– Column major order (by columns) – used in
Fortran
– A compile-time descriptor
for a multidimensional
array

Locating an Element in a Multi-
dimensioned Array
•General format
Location (a[I,j]) = address of a [row_lb,col_lb] + (((I -
row_lb) * n) + (j - col_lb)) * element_size

Compile-Time Descriptors
Single-dimensioned array Multidimensional array

Associative Arrays
• An associative array is an unordered
collection of data elements that are indexed
by an equal number of values called keys
– User-defined keys must be stored
• Design issues:
- What is the form of references to elements?
- Is the size static or dynamic?
• Built-in type in Perl, Python, Ruby, and Swift

Associative Arrays in Perl
• Names begin with %; literals are delimited
by parentheses
%hi_temps = ("Mon" => 77, "Tue" => 79, "Wed" =>
65, …);
• Subscripting is done using braces and keys
$hi_temps{"Wed"} = 83;
– Elements can be removed with delete
delete $hi_temps{"Tue"};

Record Types
• A record is a possibly heterogeneous
aggregate of data elements in which the
individual elements are identified by names
• Design issues:
– What is the syntactic form of references to the
field?
– Are elliptical references allowed

Definition of Records in COBOL
• COBOL uses level numbers to show nested
records; others use recursive definition
01 EMP-REC.
02 EMP-NAME.
05 FIRST PIC X(20).
05 MID PIC X(10).
05 LAST PIC X(20).
02 HOURLY-RATE PIC 99V99.

References to Records
• Record field references
1. COBOL
field_name OF record_name_1 OF ... OF record_name_n
2. Others (dot notation)
record_name_1.record_name_2. ... record_name_n.field_name
• Fully qualified references must include all record names
• Elliptical references allow leaving out record names as long as
the reference is unambiguous, for example in COBOL
FIRST, FIRST OF EMP-NAME, and FIRST of EMP-REC are
elliptical references to the employee’s first name

Evaluation and Comparison to Arrays
• Records are used when collection of data
values is heterogeneous
• Access to array elements is much slower than
access to record fields, because subscripts
are dynamic (field names are static)
• Dynamic subscripts could be used with
record field access, but it would disallow type
checking and it would be much slower

Implementation of Record Type
Offset address relative to the
beginning of the records is
associated with each field

Tuple Types
• A tuple is a data type that is similar to a record,
except that the elements are not named
• Used in Python, ML, and F# to allow functions
to return multiple values
– Python
• Closely related to its lists, but immutable
• Create with a tuple literal
myTuple = (3, 5.8, ′apple′)
Referenced with subscripts (begin at 1)
Catenation with + and deleted with del

Tuple Types (continued)
• ML
val myTuple = (3, 5.8, ′apple′);
- Access as follows:
#1(myTuple) is the first element
- A new tuple type can be defined
type intReal = int * real;
(The asterisk is just a separator)
• F#
let tup = (3, 5, 7)
let a, b, c = tup
This assigns a tuple to a tuple pattern (a, b, c)

List Types
• Lists in Lisp and Scheme are delimited by
parentheses and use no commas
(A B C D) and (A (B C) D)
• Data and code have the same form
As data, (A B C) is literally what it is
As code, (A B C) is the function A applied to the
parameters B and C
• The interpreter needs to know which a list is,
so if it is data, we quote it with an apostrophe
′(A B C) is data

List Types (continued)
• List Operations in Scheme
– CAR returns the first element of its list parameter
(CAR ′(A B C)) returns A
– CDR returns the remainder of its list parameter
after the first element has been removed
(CDR ′(A B C)) returns (B C)
- CONS puts its first parameter into its second
parameter, a list, to make a new list
(CONS ′A (B C)) returns (A B C)
- LIST returns a new list of its parameters
(LIST ′A ′B ′(C D)) returns (A B (C D))

• List Operations in ML
– Lists are written in brackets and the elements are
separated by commas
– List elements must be of the same type
– The Scheme CONS function is a binary operator in
ML, ::
3 :: [5, 7, 9] evaluates to [3, 5, 7, 9]
– The Scheme CAR and CDR functions are named hd
and tl, respectively

• F# Lists
– Like those of ML, except elements are separated
by semicolons and hd and tl are methods of the
List class
• Python Lists
– The list data type also serves as Python’s arrays
– Unlike Scheme, Common Lisp, ML, and F#,
Python’s lists are mutable
– Elements can be of any type
– Create a list with an assignment
myList = [3, 5.8, "grape"]

• Python Lists (continued)
– List elements are referenced with subscripting,
with indices beginning at zero
x = myList[1] Sets x to 5.8
– List elements can be deleted with del
del myList[1]
– List Comprehensions – derived from set notation
[x * x for x in range(6) if x % 3 == 0]
range(12) creates [0, 1, 2, 3, 4, 5, 6]
Constructed list: [0, 9, 36]

Unions Types
• A union is a type whose variables are allowed
to store different type values at different
times during execution
• Design issue
– Should type checking be required?

Discriminated vs. Free Unions
• C and C++ provide union constructs in which
there is no language support for type
checking; the union in these languages is
called free union
• Type checking of unions require that each
union include a type indicator called a
discriminant
– Supported by ML, Haskell, and F#

Unions in F#
• Defined with a type statement using OR
type intReal =
| IntValue of int
| RealValue of float;;
intReal is the new type
IntValue and RealValue are constructors
To create a value of type intReal:
let ir1 = IntValue 17;;
let ir2 = RealValue 3.4;;

Variant Records in Ada
type Payment is (Cash, Check, Credit);
type Transaction (pay : Payment := Cash) is record
amount : Real;
case pay is
when Cash => discount : Boolean;
when Check => checknum : Positive;
when Credit =>
cardnum : String (1..16);
expiration : String (1..8);
end case;
end record;

Evaluation of Unions
• Free unions are unsafe
– Do not allow type checking
• Java and C# do not support unions
– Reflective of growing concerns for safety in
programming language

Pointer and Reference Types
• A pointer type variable has a range of values
that consists of memory addresses and a
special value, nil
• Provide the power of indirect addressing
• Provide a way to manage dynamic memory
• A pointer can be used to access a location in
the area where storage is dynamically
created (usually called a heap)

Design Issues of Pointers
• What are the scope of and lifetime of a
pointer variable?
• What is the lifetime of a heap-dynamic
variable?
• Are pointers restricted as to the type of value
to which they can point?
• Are pointers used for dynamic storage
management, indirect addressing, or both?
• Should the language support pointer types,
reference types, or both?

Pointer Operations
• Two fundamental operations: assignment
and dereferencing
• Assignment is used to set a pointer variable’s
value to some useful address
• Dereferencing yields the value stored at the
location represented by the pointer’s value
– Dereferencing can be explicit or implicit
– C++ uses an explicit operation via *
j = *ptr
sets j to the value located at ptr

Pointer Assignment Illustrated
The assignment operation j = *ptr

Problems with Pointers
• Dangling pointers (dangerous)
– A pointer points to a heap-dynamic variable that has been
deallocated
• Lost heap-dynamic variable
– An allocated heap-dynamic variable that is no longer
accessible to the user program (often called garbage)
• Pointer p1 is set to point to a newly created heap-dynamic
variable
• Pointer p1 is later set to point to another newly created
heap-dynamic variable
• The process of losing heap-dynamic variables is called
memory leakage

Pointers in C and C++
• Extremely flexible but must be used with care
• Pointers can point at any variable regardless of when
or where it was allocated
• Used for dynamic storage management and
addressing
• Pointer arithmetic is possible
• Explicit dereferencing and address-of operators
• Domain type need not be fixed (void *)
void * can point to any type and can be type
checked (cannot be de-referenced)

Pointer Arithmetic in C and C++
float stuff[100];
float *p;
p = stuff;
*(p+5) is equivalent to stuff[5] and p[5]
*(p+i) is equivalent to stuff[i] and p[i]

Reference Types
• C++ includes a special kind of pointer type
called a reference type that is used primarily
for formal parameters
– Advantages of both pass-by-reference and pass-
by-value
• Java extends C++’s reference variables and
allows them to replace pointers entirely
– References are references to objects, rather than
being addresses
• C# includes both the references of Java and
the pointers of C++

Evaluation of Pointers
• Dangling pointers and dangling objects are
problems as is heap management
• Pointers are like goto's--they widen the
range of cells that can be accessed by a
variable
• Pointers or references are necessary for
dynamic data structures--so we can't design a
language without them

Dangling Pointer Problem
• Tombstone: extra heap cell that is a pointer to the
heap-dynamic variable
– The actual pointer variable points only at tombstones
– When heap-dynamic variable de-allocated, tombstone
remains but set to nil
– Costly in time and space
. Locks-and-keys: Pointer values are represented as (key,
address) pairs
– Heap-dynamic variables are represented as variable plus
cell for integer lock value
– When heap-dynamic variable allocated, lock value is created
and placed in lock cell and key cell of pointer

Heap Management
• A very complex run-time process
• Single-size cells vs. variable-size cells
• Two approaches to reclaim garbage
– Reference counters (eager approach): reclamation
is gradual
– Mark-sweep (lazy approach): reclamation occurs
when the list of variable space becomes empty

Variable-Size Cells
• All the difficulties of single-size cells plus
more
• Required by most programming languages
• If mark-sweep is used, additional problems
occur
– The initial setting of the indicators of all cells in
the heap is difficult
– The marking process in nontrivial
– Maintaining the list of available space is another
source of overhead

Type Checking
• Generalize the concept of operands and operators to include
subprograms and assignments
• Type checking is the activity of ensuring that the operands of an
operator are of compatible types
• A compatible type is one that is either legal for the operator, or
is allowed under language rules to be implicitly converted, by
compiler- generated code, to a legal type
– This automatic conversion is called a coercion.
• A type error is the application of an operator to an operand of
an inappropriate type

Type Checking (continued)
• If all type bindings are static, nearly all type
checking can be static
• If type bindings are dynamic, type checking
must be dynamic
• A programming language is strongly typed if
type errors are always detected
• Advantage of strong typing: allows the
detection of the misuses of variables that
result in type errors

Strong Typing
Language examples:
– C and C++ are not: parameter type checking can
be avoided; unions are not type checked
– Java and C# are, almost (because of explicit type
casting)
- ML and F# are

Strong Typing (continued)
• Coercion rules strongly affect strong typing--
they can weaken it considerably (C++ versus
ML and F#)
• Although Java has just half the assignment
coercions of C++, its strong typing is still far
less effective than that of Ada

Name Type Equivalence
• Name type equivalence means the two
variables have equivalent types if they are in
either the same declaration or in declarations
that use the same type name
• Easy to implement but highly restrictive:
– Subranges of integer types are not equivalent
with integer types
– Formal parameters must be the same type as
their corresponding actual parameters

Structure Type Equivalence
• Structure type equivalence means that two
variables have equivalent types if their types
have identical structures
• More flexible, but harder to implement

Type Equivalence (continued)
• Consider the problem of two structured types:
– Are two record types equivalent if they are
structurally the same but use different field
names?
– Are two array types equivalent if they are the
same except that the subscripts are different?
(e.g. [1..10] and [0..9])
– Are two enumeration types equivalent if their
components are spelled differently?
– With structural type equivalence, you cannot
differentiate between types of the same structure
(e.g. different units of speed, both float)

Theory and Data Types
• Type theory is a broad area of study in
mathematics, logic, computer science, and
philosophy
• Two branches of type theory in computer
science:
– Practical – data types in commercial languages
– Abstract – typed lambda calculus
• A type system is a set of types and the rules
that govern their use in programs

Theory and Data Types (continued)
• Formal model of a type system is a set of
types and a collection of functions that define
the type rules
– Either an attribute grammar or a type map could
be used for the functions
– Finite mappings – model arrays and functions
– Cartesian products – model tuples and records
– Set unions – model union types
– Subsets – model subtypes

Summary
• The data types of a language are a large part of what
determines that language’s style and usefulness
• The primitive data types of most imperative
languages include numeric, character, and Boolean
types
• The user-defined enumeration and subrange types
are convenient and add to the readability and
reliability of programs
• Arrays and records are included in most languages
• Pointers are used for addressing flexibility and to
control dynamic storage management

Theory of programming language chapter 6

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