Types
Aaron Bloomfield
CS 415
Fall 2005
1
Why have Types?
• Types provide context for operations
– a+b  what kind of addition?
– pointer p = new object  how much space?
• Limit valid set of operations
– int a = “string”  know error before run time
2
Computer Hardware & Types
• Remember CS216?
– Bits in data are generally untyped
– Bits interpreted as having a type, such as:
• Instruction
• Address
• Floating-point number
• Character
• High-level language interprets bits
3
Type assignment
• Language-dependent
• a+b example again:
– Ada: a and b declared with static types
– Perl: $a and $b are dynamically typed
– Scheme: checked at run-time
– Smalltalk: checked at run-time
– Bliss: completely untyped
4
Static vs. Dynamic Typing
• First, what does strongly typed mean?
– Prevents invalid operations on a type
• Statically typed: strongly typed and type
checks can be performed at compile time
– Ada, Pascal: almost all type checking done at
compile time, with just a few exceptions
– C, C++, Java, Ocaml
• Dynamically typed: type checking is
delayed until run time
– Scheme, Smalltalk, Perl
5
Defining/Declaring a Type
• Fortran: variable’s type known from name
– Letters I-N = integer type
– Otherwise = real (floating-point) type
• Scheme, Smalltalk: run-time typing
• Most languages (such as C++): user
explicitly declares type
– int a, char b
6
Classifying types
• A type is either one of a small group of built-in
types or a user-defined composite
• Built-in types include:
–
–
–
–
–
Integers
Characters: ASCII, Unicode
Boolean (not in C/C++)
Floating points (double, real, float, etc.)
Rarer types:
• Complex (Scheme, Fortran)
• Rational (Scheme)
• Fixed point (Ada)
7
Number precision
• Is the precision specified by the type in the
language implementation?
– Java, C, C++ Fortran: user specifies precision
• Java: byte, short, int, long
– Most other languages: implementation
– Is the precision consistent across platforms?
• Java: Yes
• C/C++: No
8
Number precision
• If user doesn’t specify type, code can lose
portability due to differences in precision
– In C/C++, precision is platform-dependent
• Neat example in Haskell
–
2 ^ 200 
1606938044258990275541962092341162602522202993782792835301376
– Support for infinite precision types
– Java provides BigInteger and BigDecimal for this
purpose
9
Type Equivalence
• Determining when the types of two
values are the same
struct student { string name; string
address;}
struct school { string name; string
address;}
• Are these the same?
be?
Should they
10
Structural Equivalence
• The same components, put together the same
way = same type
• Algol-68, early Pascal, C (with exceptions)
– And ML, somewhat
• Straightforward and easy to implement
• Definition varies from lang to lang
– eg. Does the ORDER of the fields matter?
• Back to example: are they the same?
struct student { string name; string address;}
struct school { string name; string address;}
• Yes, they are (with structural equivalence)
11
Name Equivalence
•
•
•
•
More popular recently
A new name or definition = a new type
Java, current Pascal, Ada
Assume that: if programmer wrote two different
definitions, then wanted two types
– Is this a good or bad assumption to make?
• Back to example: are they the same?
struct student { string name; string address;}
struct school { string name; string address;}
• No, they are not (with name equivalence)
12
Problem! Aliases
• Modula-2 example:
TYPE celsius_temp = REAL;
TYPE fahren_temp = REAL;
VAR c : celsius_temp;
f : fahren_temp;
…
f := c;
• Modula has loose name equivalence, so this is
okay
– But normally it probably should be an error
13
Types of Name Equivalence
• Strict: aliases are distinct types
• Loose: aliases are equivalent types
• Ada has both:
– type test_score is integer;
– type celsius_temp is new integer;
type fahren_temp is new integer;
• A derived type is incompatible with its parent type
• now f := c will generate an error
14
Type Conversion
• Conversion needed when certain types
are expected but not received
• a+b  expecting either 2 ints or 2 floats
• Switching between types may result in
overflow
– example: floating-point  integer
15
Coercion
• Can automatically force values to another
type for the given context
• a+b revisited:
– Without coercion, if both aren’t the same type
then there’s a compile-time error
– With coercion, if either is floating-point, then
addition is floating-point; otherwise int addition
• Issue: Things are happening without you
asking them to occur! Good/Bad?
16
Data Types
Records (Structures)
Variants (Unions)
Arrays
Sets
17
Records
• Also known as ‘structs’ and ‘types’.
–C
struct resident {
char initials[2];
int ss_number;
bool married;
};
• fields – the components of a record,
usually referred to using dot notation.
18
Nesting Records
• Most languages allow records to be
nested within each other.
– Pascal
type two_chars = array [1..2] of char;
type married_resident = record
initials: two_chars;
ss_number: integer;
incomes: record
husband_income: integer;
wife_income: integer;
end;
end;
19
Memory Layout of Records
• Fields are stored adjacently in memory.
• Memory is allocated for records based on
the order the fields are created.
• Variables are aligned for easy reference.
Optimized for space
Optimized for memory alignment
4 bytes / 32 bits
4 bytes / 32 bits
initials
(2 bytes)
married
(1 byte)
initials
(2 bytes)
ss_number
(4 bytes)
ss_number
(4 bytes)
married
(1 byte)
20
Simplifying Deep Nesting
• Modifying records with
become bothersome.
deep
nesting
can
book[3].volume[7].issue[11].name := ‘Title’;
book[3].volume[7].issue[11].cost := 199;
book[3].volume[7].issue[11].in_print := TRUE;
• Fortunately, this problem can be simplified.
• In Pascal, keyword with “opens” a record.
with book[3].volume[7].issue[11] do
begin
name := ‘Title’;
cost := 199;
in_print := TRUE;
end;
21
Simplifying Deep Nesting
• Modula-3 and C provide better methods
for manipulation of deeply nested records.
– Modula-3 assigns aliases to allow multiple openings
with var1 =
var2 =
DO
var1.name
var2.cost
END;
book[1].volume[6].issue[12],
book[5].volume[2].issue[8]
= var2.name;
= var1.cost;
– C allows pointers to types
• What could you write in C to mimic the code above?
22
Variant Records
• variant records – provide two or more
alternative fields.
• discriminant – the field that determines
which alternative fields to use.
• Useful for when only one type of record
can be valid at a given time.
23
Variant Records – Pascal Example
type resident = record
initials: array [1..2] of char;
initials
(2 bytes)
married
(1 byte)
husband_income (4 bytes)
case married: boolean of
true: (
husband_income: integer;
wife_income: integer;
);
false: (
income: real;
);
id_number: integer;
end;
wife_income (4 bytes)
Case is TRUE
initials
(2 bytes)
married
(1 byte)
income (4 bytes)
Case is FALSE
24
Unions
• A union is like a record
– But the different fields take up the same space within
memory
union foo {
int i;
float f;
char c[4];
}
• Union size is 4 bytes!
25
Union example (from an assembler)
union DisasmInst {
#ifdef BIG_ENDIAN
struct { unsigned char a, b, c, d; } chars;
#else
struct { unsigned char d, c, b, a; } chars;
#endif
int intv;
unsigned unsv;
struct { unsigned offset:16, rt:5, rs:5, op:6; } itype;
struct { unsigned offset:26, op:6; } jtype;
struct { unsigned function:6, sa:5, rd:5, rt:5, rs:5,
op:6; } rtype;
};
26
void CheckEndian() {
union {
char charword[4];
unsigned int intword;
} check;
check.charword[0]
check.charword[1]
check.charword[2]
check.charword[3]
=
=
=
=
Another union example
1;
2;
3;
4;
#ifdef BIG_ENDIAN
if (check.intword != 0x01020304) {
/* big */
cout << "ERROR: Host machine is not Big Endian.\nExiting.\n";
exit (1);
}
#else
#ifdef LITTLE_ENDIAN
if (check.intword != 0x04030201) {
/* little */
cout << "ERROR: Host machine is not Little Endian.\nExiting.\n";
exit (1);
}
#else
cout << "ERROR: Host machine not defined as Big or Little Endian.\n";
cout << "Exiting.\n";
exit (1);
#endif // LITTLE_ENDIAN
#endif // BIG_ENDIAN
}
27
Arrays
• Group a homogenous type into indexed
memory.
• Language differences: A(3) vs. A[3].
– Brackets are preferred since parenthesis are
typically used for functions/subroutines.
• Subscripts are usually integers, though
most languages support any discrete type.
28
Array Dimensions
• C uses 0 -> (n-1) as the array bounds.
– float values[10];
// ‘values’ goes from 0 -> 9
• Fortran uses 1 -> n as the array bounds.
– real(10) values
! ‘values’ goes from 1 -> 10
• Some languages let the
define the array bounds.
programmer
– var values: array [3..12] of real;
(* ‘values’ goes from 3 -> 12 *)
29
Multidimensional Arrays
• Two ways to make multidimensional arrays
– Both examples from Ada
– Construct specifically as multidimensional.
matrix: array (1..10, 1..10) of real;
-- Reference example: matrix(7, 2)
• Looks nice, but has limited functionality.
– Construct as being an array of arrays.
matrix: array (1..10) of array (1..10) of real;
-- Reference example: matrix(7)(2)
• Allows us to take ‘slices’ of data.
30
Array Memory Allocation
• An array’s “shape” (dimensions and
bounds) determines how its memory is
allocated.
– The time at which the shape is determined also
plays a role in determining allocation.
• At least 5 different cases for determining
memory allocation:
31
Array Memory Allocation
• Global lifetime, static shape:
– The array’s shape is known at compile time,
and exists throughout the entire program.
• Array can be allocated in static global memory.
• int global_var[30]; void main() { };
• Local lifetime, static shape:
– The array’s shape is known at compile time,
but exists only as locally needed.
• Array is allocated in subroutine’s stack frame.
• void main() { int local_var[30]; }
32
Array Memory Allocation
• Local lifetime, bound at elaboration time:
– Array’s shape is not known at compile time, and
exists only as locally needed.
• Array is allocated in subroutine’s stack frame and divided into
fixed-size and variable-sized parts.
• main() { var_ptr = new int[size]; }
• Arbitrary lifetime, bound at elaboration time:
– Array is just references to objects.
• Java does not allocate space; just makes a reference to
either new or existing objects.
• var_ptr = new int[size];
33
Array Memory Allocation
• Arbitrary lifetime, dynamic shape
– The array may shrink or grow as a result of program
execution.
• The array must be allocated from the heap.
• Increasing size usually requires allocating new memory,
copying from old memory, then de-allocating the old memory.
34
Memory Layout Options
• Ordering of array elements
accomplished in two ways:
can
be
– row-major order – Elements travel across
rows, then across columns.
– column-major order – Elements travel
across columns, then across rows.
Row-major
Column-major
35
Row Pointers vs.
Contiguous Allocation
• Row pointers – an array of pointers to an
array. Creates a new dimension out of
allocated memory.
• Avoids allocating holes in memory.
day[0]
day[1]
day[2]
day[3]
day[4]
day[5]
day[6]
S
u
n
d
a
y
d
a
y
T
u
M
o
n
e
s
d
a
y
W
e
d
n
e
s
d
a
y
T
h
u
r
s
d
a
y
F
r
i
d
a
y
S
a
u
r
d
a
y
t
Array =
57 bytes
Pointers =
28 bytes
Total Space =
85 bytes
36
Row Pointers vs.
Contiguous Allocation
• Contiguous allocation - array where each
element has a row of allocated space.
• This is a true multi-dimensional array.
– It is also a ragged array
S
u
n
d
a
y
M
o
n
d
a
y
T
u
e
s
d
a
y
W e
d
n
e
s
d
a
T
h
u
r
s
d
a
y
F
r
i
d
a
y
S
a
t
u
r
d
a
y
y
Array = 70 bytes
37
Array Address Calculation
• Calculate the size of an element (1D)
• Calculate the size of a row (2D)
– row = element_size * (Uelement - Lelement + 1)
• Calculate the size of a plane (3D)
– plane = row_size * (Urows - Lrows + 1)
• Calculate the size of a cube (4D)
:
:
38
Array Address Calculation
• Address of a 3-dimenional array A(i, j, k) is:
address of A
+ ((i - Lplane) * size of plane)
+ ((j - Lrow)
* size of row)
+ ((k - Lelement) * size of element)
A
A(i)
A(i, j)
A(i, j, k)
Memory
39
Sets
• Introduced by Pascal, found in most recent
languages as well.
• Common implementation uses a bit vector
to denote “is a member of”.
– Example:
U = {‘a’, ‘b’, …, ‘g’}
A = {‘a’, ‘c’, ‘e’, ‘g’} = 1010101
• Hash
tables
needed
implementations.
for
larger
– Set of integers = (232 values) / 8 = 536,870,912 bytes40
Enumerations
41
Enumerations
• enumeration – set of named elements
– Values are usually ordered, can compare
enum weekday {sun,mon,tue,wed,thu,fri,sat}
if (myVarToday > mon) { . . . }
• Advantages
– More readable code
– Compiler can catch some errors
• Is sun==0 and mon==1?
– C/C++: yes; Pascal: no
• Can also choose ordering in C
enum weekday {mon=0,tue=1,wed=2…}
42
Lists
43
Lists
• list – the empty list or a pair consisting of an
object (list or atom) and another list
(a . (b . (c . (d . nil))))
• improper list – list whose final pair contains two
elements, as opposed to the empty list
(a . (b . (c . d)))
• basic operations: cons, car, cdr, append
• list comprehensions (e.g. Miranda and Haskell)
[i * i
|
i <- [1..100]; i mod 2 = 1]
44
Recursive Types
45
Recursive Types
• recursive type - type whose objects may
contain references to other objects of the
same type
– Most are records (consisting of reference
objects and other “data” objects)
– Used for linked data structures: lists, trees
struct Node {
Node *left, *right;
int data;
}
46
Recursive Types
• In reference model of variables (e.g. Lisp,
Java), recursive type needs no special
support. Every variable is a reference
anyway.
• In value model of variables (e.g. Pascal,
C), need pointers.
47
Value vs. Reference
• Functional languages
– almost always reference model
• Imperative languages
– value model (e.g. C)
– reference model (e.g. Smalltalk)
• implementation approach: use actual values for
immutable objects
– combination (e.g. Java)
48
Pointers
• pointer – a variable whose value is a
reference to some object
– pointer use may be restricted or not
• only allow pointers to point to heap (e.g. Pascal)
• allow “address of” operator (e.g. ampersand in C)
– pointers not equivalent to addresses!
– how reclaim heap space?
• explicit (programmer’s duty)
• garbage collection (language implementation’s
duty)
49
Value Model – More on C
• Pointers and single dimensional arrays interchangeable,
though space allocation at declaration different
int a[10]; int *b;
• For subroutines, pointer to array is passed, not full array
• Pointer arithmetic
– <Pointer, Integer> addition
int a[10];
int n;
n = *(a+3);
– <Pointer, Pointer> subtraction and comparison
int
int
int
int
a[10];
* x = a + 4;
* y = a + 7;
closer_to_front = x < y;
50
Dangling References
• dangling reference – a live pointer that
no longer points to a valid object
– to heap object: in explicit reclamation,
programmer reclaims an object to which a
pointer still refers
– to stack object: subroutine returns while some
pointer in wider scope still refers to local
object of subroutine
• How do we prevent them?
51
Dangling References
• Prevent pointer from pointing to objects
with shorter lifetimes (e.g. Algol 68, Ada
95). Difficult to enforce
• Tombstones
• Locks and Keys
52
Tombstones
• Idea
– Introduce another level of indirection: pointer contain the address of the
tombstone; tombstone contains address of object
– When object is reclaimed, mark tombstone (zeroed)
• Time overheads
– Create tombstone
– Check validity of access
– Double indirection
• Space overheads
– when to reclaim??
• Extra benefits
– easy to compact heap
– works for heap and stack
53
54
Locks and Keys
• Idea
– Every pointer is <address, key> tuple
– Every object starts with same lock as pointer’s key
– When object is reclaimed, object’s lock marked (zeroed)
• Advantages
– No need to keep tombstones around
• Disadvantages
– Objects need special key field (usually implemented only for
heap objects)
– Probabilistic protection
• Time overheads
– Lock to key comparison costly
55
56
Garbage Collection
• Language implementation notices when
objects are no longer useful and reclaims
them automatically
– essential for functional languages
– trend for imperative languages
• When is object no longer useful?
– Reference counts
– Mark and sweep
– “Conservative” collection
57
Reference Counts
• Idea
– Counter in each object that tracks number of
pointers that refer to object
– Recursively decrement counts for objects and
reclaim those objects with count of zero
• Must identify every pointer
– in every object (instance of type)
– in every stack frame (instance of method)
– use compiler-generated type descriptors
58
Type descriptors example
myFunc type descriptor at 0x104
public class MyProgram {
public void myFunc () {
Car c;
}
}
i
offset
address
0
0 (Car)
0x018
Car type descriptor at 0x018
public class Car {
char a, b, c;
Engine e;
Wheel w;
}
public class Engine {
char x, y;
Valve v;
}
i
offset
address
0
4 (Engine)
0x0A2
1
5 (Wheel)
0x005
Engine type descriptor at 0x0A2
i
offset
address
0
3 (Valve)
0xB05
public class Wheel {...}
public class Valve {...}
Wheel type descriptor at 0x005
Valve type descriptor at 0xB05
59
Mark-and-Sweep
•
Idea
… when space low
1. Mark every block “useless”
2. Beginning with pointers outside the heap,
recursively explore all linked data structures
and mark each traversed as useful
3. Return still marked blocks to freelist
•
Must identify pointers
– in every block
– use type descriptors
60
Garbage Collection Comparison
• Reference Count
– Will never reclaim
circular data structures
– Must record counts
• Mark-and-Sweep
– Lower overhead
during regular
operation
– Bursts of activity
(when collection
performed, usually
when space is low)
61
Conservative collection
• Idea
– Number of blocks in heap is much smaller than number of
possible addresses (232) – a word that could be a pointer into
heap is probably pointer into heap
– Scan all word-aligned quantities outside the heap; if any looks
like block address, mark block useful and recursively explore
words in block
• Advantages
– No need for type descriptors
– Usually safe, though could “hide” pointers
• Disadvantages
– Some garbage is unclaimed
– Can not compact (not sure what is pointer and what isn’t)
62