Flow
Prof. COP4020
Programming
Languages
Control Robert van Engelen
Overview
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Structured and unstructured flow
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Goto's
Sequencing
Selection
Iteration and iterators
Recursion
Applicative- and normal-order evaluation
Expressions evaluation
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Evaluation order
Assignments
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Control Flow: Ordering the
Execution of a Program
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Constructs for specifying the execution order:
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2.
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Sequencing: the execution of statements and evaluation of expressions
is usually in the order in which they appear in a program text
Selection (or alternation): a run-time condition determines the choice
among two or more statements or expressions
Iteration: a statement is repeated a number of times or until a run-time
condition is met
Procedural abstraction: subroutines encapsulate collections of
statements and subroutine calls can be treated as single statements
Recursion: subroutines which call themselves directly or indirectly to
solve a problem, where the problem is typically defined in terms of
simpler versions of itself
Concurrency: two or more program fragments executed in parallel,
either on separate processors or interleaved on a single processor
Nondeterminacy: the execution order among alternative constructs is
deliberately left unspecified, indicating that any alternative will lead to a
correct result
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Structured and Unstructuted
Flow
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Unstructured flow: the use of goto statements and
statement labels to implement control flow
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Merit or evil?
Generally considered bad, but sometimes useful for jumping out
of nested loops and for coding the flow of exceptions (when a
language does not support exception handling)
Java has no goto statement (supports labeled loops and breaks)
Structured flow:
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Statement sequencing
Selection with if-then-else statements and switch statements
Iteration with for and while loop statements
Subroutine calls (including recursion)
All of which promotes structured programming
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Sequencing
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A list of statements in a program text is executed in topdown order
A compound statement is a delimited list of statements
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A compund statement is called a block when it includes variable
declarations
C, C++, and Java use { and } to delimit a block
Pascal and Modula use begin ... end
Ada uses declare ... begin ... end
Special cases: in C, C++, and Java expressions can be
inserted as statements
In pure functional languages sequencing is impossible
(and not desired!)
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Selection
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If-then-else selection statements in C and C++:
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if (<expr>) <stmt> [else <stmt>]
Condition is a bool, integer, or pointer
Grouping with { and } is required for statement sequences in the then
clause and else clause
Syntax ambiguity is resolved with an else matches the closest if rule
Conditional expressions, e.g. if and cond in Lisp and a?b:c in C
Java syntax is like C/C++, but condition must be Boolean
Ada syntax supports multiple elsif's to define nested conditions:
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if <cond> then
<statements>
elsif <cond> then
...
else
<statements>
end if
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Selection (contd)
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Case/switch statements are different from if-then-else statements in
that an expression can be tested against multiple constants to select
statement(s) in one of the arms of the case statement:
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C, C++, and Java:
switch (<expr>)
{ case <const>: <statements> break;
case <const>: <statements> break;
...
default: <statements>
}
A break is necessary to transfer control at the end of an arm to the end
of the switch statement
Most programming languages support a switch-like statement, but do
not require the use of a break in each arm
A switch statement is much more efficient compared to nested ifthen-else statements
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Iteration
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Enumeration-controlled loops repeat a collection of
statements a number of times, where in each iteration a
loop index variable takes the next value of a set of
values specified at the beginning of the loop
Logically-controlled loops repeat a collection of
statements until some Boolean condition changes value
in the loop
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Pretest loops test condition at the begin of each iteration
Posttest loops test condition at the end of each iteration
Midtest loops allow structured exits from within loop with exit
conditions
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Enumeration-Controlled Loops
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History of failures on design of enumeration-controlled loops
Fortran-IV:
20
DO 20 i = 1, 10, 2
...
CONTINUE
which is defined to be equivalent to
20
i=1
...
i=i+2
IF i.LE.10 GOTO 20
Problems:
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Requires positive constant loop bounds (1 and 10) and step size (2)
If loop index variable i is modified in the loop body, the number of
iterations is changed compared to the iterations set by the loop bounds
GOTOs can jump out of the loop and also from outside into the loop
The value of counter i after the loop is implementation dependent
The body of the loop will be executed at least once (no empty bounds)
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Enumeration-Controlled Loops
(contd)
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Fortran-77:
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Same syntax as in Fortran-IV, but many dialects support ENDDO instead
of CONTINUE statements
Can jump out of the loop, but cannot jump from outside into the loop
Assignments to counter i in loop body are not allowed
Number of iterations is determined by
max(!(H-L+S)/S", 0)
for lower bound L, upper bound H, step size S
Body is not executed when (H-L+S)/S < 0
Either integer-valued or real-valued expressions for loop bounds and
step sizes
Changes to the variables used in the bounds do not affect the number
of iterations executed
Terminal value of loop index variable is the most recent value assigned,
which is
L + S*max(!(H-L+S)/S", 0)
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Enumeration-Controlled Loops
(contd)
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Algol-60 combines logical conditions in combination
loops:
for <id> := <forlist> do <stmt>
where the syntax of <forlist> is
<forlist>
::= <enumerator> [, enumerator]*
<enumerator> ::= <expr>
| <expr> step <expr> until <expr>
| <expr> while <cond>
Not orthogonal: many forms that behave the same:
for i := 1, 3, 5, 7, 9 do ...
for i := 1 step 2 until 10 do ...
for i := 1, i+2 while i < 10 do ...
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Enumeration-Controlled Loops
(contd)
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Pascals enumeration-controlled loops have simple and
elegant design with two forms for up and down:
for <id> := <expr> to <expr> do <stmt>
and
for <id> := <expr> downto <expr> do <stmt>
Can iterate over any discrete type, e.g. integers, chars,
elements of a set
Lower and upper bound expressions are evaluated once
to determine the iteration range
Counter variable cannot be assigned in the loop body
Final value of loop counter after the loop is undefined
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Enumeration-Controlled Loops
(contd)
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!
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Adas for loop is much like Pascal's:
for <id> in <expr> .. <expr> loop
<statements>
end loop
and
for <id> in reverse <expr> .. <expr> loop
<statements>
end loop
Lower and upper bound expressions are evaluated once
to determine the iteration range
Counter variable has a local scope in the loop body
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Not accessible outside of the loop
Counter variable cannot be assigned in the loop body
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Enumeration-Controlled Loops
(contd)
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C, C++, and Java do not have true enumeration-controlled loops
A for loop is essentially a logically-controlled loop
for (i = 1; i <= n; i++) ...
which iterates i from 1 to n by testing i <= n before the start of
each iteration and updating i by 1 in each iteration
Why is this not enumeration controlled?
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Assignments to counter i and variables in the bounds are allowed, thus
it is the programmer's responsibility to structure the loop to mimic
enumeration loops
Use continue to jump to next iteration
Use break to exit loop
C++ and Java also support local scoping for counter variable
for (int i = 1; i <= n; i++) ...
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Enumeration-Controlled Loops
(contd)
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Other problems with C/C++ for loops to emulate enumerationcontrolled loops are related to the mishandling of bounds and limits
of value representations
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This C program never terminates (do you see why?)
#include <limits.h> // INT_MAX is max int value
main()
{ int i;
for (i = 0; i <= INT_MAX; i++)
printf(Iteration %d\n, i);
}
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This C program does not count from 0.0 to 10.0, why?
main()
{ float n;
for (n = 0.0; n <= 10; n += 0.01)
printf(Iteration %g\n, n);
}
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Enumeration-Controlled Loops
(contd)
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How is loop iteration counter overflow handled?
C, C++, and Java: nope
Fortran-77
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Calculate the number of iterations in advance
For REAL typed index variables an exception is raised when
overflow occurs
Pascal and Ada
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Only specify step size 1 and -1 and detection of the end of the
iterations is safe
Pascals final counter value is undefined (may have wrapped)
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Iterators
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Iterators are used to iterate over elements of containers such as
sets and data structures such as lists and trees
Iterator objects are also called enumerators or generators
C++ iterators are associated with a container object and used in
loops similar to pointers and pointer arithmetic:
vector<int> V;
for (vector<int>::iterator it = V.begin(); it != V.end(); ++it)
cout << *n << endl;
An in-order tree traversal:
tree_node<int> T;
for (tree_node<int>::iterator it = T.begin(); it != T.end(); ++it)
cout << *n << endl;
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Iterators (contd)
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Java supports generics similar to C++ templates
Iterators are similar to C++, but do not have the usual C++
overloaded iterator operators:
TreeNode<Integer> T;
for (Integer i : T)
System.out.println(i);
Note that Java has the above special for-loop for iterators that is
essentially syntactic sugar for:
for (Iterator<Integer> it = T.iterator(); it.hasNext(); )
{
Integer i = it.next();
System.out.println(i);
}
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Iterators (contd)
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Iterators typically need special loops to produce
elements one by one, e.g. in Clu:
for i in int$from_to_by(first, last, step) do
end
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While Java and C++ use iterator objects that hold the
state of the iterator, Clu, Python, Ruby, and C# use
generators (=true iterators) which are functions that run
in parallel to the loop code to produce elements
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The yield operation in Clu returns control to the loop body
The loop returns control to the generators last yield operation to
allow it to compute the value for the next iteration
The loop terminates when the generator function returns
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Logically-Controlled Pretest
loops
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Logically-controlled pretest loops check the exit condition before the
next loop iteration
Not available Fortran-77
Ada has only one kind of logically-controlled loops: midtest loops
Pascal:
while <cond> do <stmt>
where the condition is a Boolean-typed expression
C, C++:
while (<expr>) <stmt>
where loop the terminates when the condition evaluates to 0, NULL,
or false
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Use continue and break to jump to next iteration or exit the loop
Java is similar C++, but condition is restricted to Boolean
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Logically-Controlled Posttest
Loops
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Logically-controlled posttest loops check the exit condition after
each loop iteration
Not available in Fortran-77
Ada has only one kind of logically-controlled loops: midtest loops
Pascal:
repeat <stmt> [; <stmt>]* until <cond>
where the condition is a Boolean-typed expression and the loop
terminates when the condition is true
C, C++:
do <stmt> while (<expr>)
where the loop terminates when the expression evaluates to 0,
NULL, or false
Java is similar to C++, but condition is restricted to Boolean
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Logically-Controlled Midtest
Loops
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Ada supports logically-controlled midtest loops check exit conditions
anywhere within the loop:
loop
<statements>
exit when <cond>;
<statements>
exit when <cond>;
...
end loop
!
Ada also supports labels, allowing exit of outer loops without gotos:
outer: loop
...
for i in 1..n loop
...
exit outer when a[i]>0;
...
end loop;
end outer loop;
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Recursion
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Recursion: subroutines that call themselves directly or indirectly
(mutual recursion)
Typically used to solve a problem that is defined in terms of simpler
versions, for example:
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Iteration and recursion are equally powerful in theoretical sense
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To compute the length of a list, remove the first element, calculate the
length of the remaining list in n, and return n+1
Termination condition: if the list is empty, return 0
Iteration can be expressed by recursion and vice versa
Recursion is more elegant to use to solve a problem that is naturally
recursively defined, such as a tree traversal algorithm
Recursion can be less efficient, but most compilers for functional
languages are often able to replace it with iterations
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Tail-Recursive Functions
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Tail-recursive functions are functions in which no operations follow
the recursive call(s) in the function, thus the function returns
immediately after the recursive call:
tail-recursive
not tail-recursive
int trfun()
{
return trfun();
}
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A tail-recursive call could reuse the subroutine's frame on the runtime stack, since the current subroutine state is no longer needed
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int rfun()
{
return rfun()+1;
}
Simply eliminating the push (and pop) of the next frame will do
In addition, we can do more for tail-recursion optimization: the
compiler replaces tail-recursive calls by jumps to the beginning of
the function
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Tail-Recursion Optimization
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Consider the GCD function:
int gcd(int a, int b)
{ if (a==b) return a;
else if (a>b) return gcd(a-b, b);
else return gcd(a, b-a);
}
a good compiler will optimize the function into:
int gcd(int a, int b)
{ start:
if (a==b) return a;
else if (a>b) { a = a-b; goto start; }
else { b = b-a; goto start; }
}
which is just as efficient as the iterative version:
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int gcd(int a, int b)
{ while (a!=b)
if (a>b) a = a-b;
else b = b-a;
return a;
}
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Converting Recursive Functions
to Tail-Recursive Functions
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Remove the work after the recursive call and include it in some other
form as a computation that is passed to the recursive call
For example, the non-tail-recursive function
(define summation (lambda (f low high)
(if (= low high)
(f low)
(+ (f low) (summation f (+ low 1) high)))))
can be rewritten into a tail-recursive function:
(define summation (lambda (f low high subtotal)
(if (=low high)
(+ subtotal (f low))
(summation f (+ low 1) high (+ subtotal (f low))))))
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Example
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Here is the same example in C:
typedef int (*int_func)(int);
int summation(int_func f, int low, int high)
{ if (low == high)
return f(low)
else
return f(low) + summation(f, low+1, high);
}
rewritten into the tail-recursive form:
int summation(int_func f, int low, int high, int
subtotal)
{ if (low == high)
return subtotal+f(low)
else
return summation(f, low+1, high, subtotal+f(low));
}
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When Recursion is Bad
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The Fibonacci function implemented as a recursive function is very
inefficient as it takes exponential time to compute:
(define fib (lambda (n)
(cond ((= n 0) 1)
((= n 1) 1)
(else (+ (fib (- n 1)) (fib (- n 2)))))))
with a tail-recursive helper function, we can run it in O(n) time:
(define fib (lambda (n)
(letrec ((fib-helper (lambda (f1 f2 i)
(if (= i n)
f2
(fib-helper f2 (+ f1 f2) (+ i 1))))))
(fib-helper 0 1 0))))
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Applicative- and Normal-Order
Evaluation
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Lazy evaluation
Topic skipped
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Expression Syntax and Effect
on Evaluation Order
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An expression consists of
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Common syntactic forms for operators:
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An atomic object, e.g. number or variable
An operator applied to a collection of operands (or arguments)
that are expressions
Function call notation, e.g. somefunc(A, B, C)
Infix notation for binary operators, e.g. A + B
Prefix notation for unary operators, e.g. -A
Postfix notation for unary operators, e.g. i++
Cambridge Polish notation, e.g. (* (+ 1 3) 2) in Lisp
"Multi-word" infix, e.g. a>b?a:b in C and
myBox displayOn: myScreen at: 100@50
in Smalltalk, where displayOn: and at: are written infix with
arguments mybox, myScreen, and 100@50
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Operator Precedence and
Associativity
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The use of infix, prefix, and postfix notation sometimes lead to
ambiguity as to what is an operand of what
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Fortran example: a+b*c**d**e/f
Operator precedence: higher operator precedence means that a
(collection of) operator(s) group more tightly in an expression than
operators of lower precedence
Operator associativity: determines grouping of operators of the
same precedence
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Left associative: operators are grouped left-to-right (most common)
Right associative: operators are grouped right-to-left (Fortran power
operator **, C assignment operator = and unary minus)
Non-associative: requires parenthesis when composed (Ada power
operator **)
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Operator Precedence and
Associativity
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Pascal's flat precedence levels is a design mistake
if A<B and C<D then
is grouped as follows
if A<(B and C)<D then
!
Note: levels of operator precedence and associativity are
easily captured in a grammar as we saw earlier
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Evaluation Order of Expressions
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Precedence and associativity state the rules for grouping operators
in expressions, but do not determine the operand evaluation order!
"
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Expression
a-f(b)-b*c
is structured as
(a-f(b))-(b*c)
but either (a-f(b)) or (b*c) can be evaluated first
The evaluation order of arguments in function and subroutine calls
may differ, e.g. arguments evaluated from left to right or right to left
Knowing the operand evaluation order is important
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Side effects: suppose f(b) above modifies the value of b (f(b) has a
side effect) then the value will depend on the operand evaluation order
Code improvement: compilers rearrange expressions to maximize
efficiency, e.g. a compiler can improve memory load efficiency by
moving loads up in the instruction stream
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Expression Operand Reordering
Issues
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Rearranging expressions may lead to arithmetic overflow or different
floating point results
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Assume b, d, and c are very large positive integers, then if b-c+d is
rearranged into (b+d)-c arithmetic overflow occurs
Floating point value of b-c+d may differ from b+d-c
Most programming languages will not rearrange expressions when
parenthesis are used, e.g. write (b-c)+d to avoid problems
Design choices:
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Java: expressions evaluation is always left to right in the order operands
are provided in the source text and overflow is always detected
Pascal: expression evaluation is unspecified and overflows are always
detected
C anc C++: expression evaluation is unspecified and overflow detection
is implementation dependent
Lisp: no limit on number representation
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Short-Circuit Evaluation
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!
Short-circuit evaluation of Boolean expressions: the result of an
operator can be determined from the evaluation of just one operand
Pascal does not use short-circuit evaluation
"
!
The program fragment below has the problem that element a[11] is
read resulting in a dynamic semantic error:
var a:array [1..10] of integer;
...
i := 1;
while i<=10 and a[i]<>0 do
i := i+1
C, C++, and Java use short-circuit conditional and/or operators
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If a in a&&b evaluates to false, b is not evaluated
If a in a||b evaluates to true, b is not evaluated
Avoids the Pascal problem, e.g.
while (i <= 10 && a[i] != 0) ...
Ada uses and then and or else, e.g. cond1 and then cond2
Ada, C, and C++ also have regular bit-wise Boolean operators
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Assignments and Expressions
!
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Fundamental difference between imperative and
functional languages
Imperative: "computing by means of side effects
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Computation is an ordered series of changes to values of
variables in memory (state) and statement ordering is influenced
by run-time testing values of variables
Expressions in functional language are referentially
transparent:
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All values used and produced depend on the local referencing
environment of the expression
A function is idempotent in a functional language: it always
returns the same value given the same arguments because of
the absence of side-effects
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L-Values vs. R-Values and Value
Model vs. Reference Model
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Consider the assignment of the form: a := b
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The left-hand side a of the assignment is an l-value which is an
expression that should denote a location, e.g. array element a[2] or a
variable foo or a dereferenced pointer *p
The right-hand side b of the assignment is an r-value which can be any
syntactically valid expression with a type that is compatible to the lefthand side
Languages that adopt the value model of variables copy the value of
b into the location of a (e.g. Ada, Pascal, C)
Languages that adopt the reference model of variables copy
references, resulting in shared data values via multiple references
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Clu copies the reference of b into a so that a and b refer to the same
object
Java is a mix: it uses the value model for built-in types and the
reference model for class instances
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Special Cases of Assignments
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Assignment by variable initialization
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Combinations of assignment operators
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Use of uninitialized variable is source of many problems, sometimes
compilers are able to detect this but with programmer involvement e.g.
definite assignment requirement in Java
Implicit initialization, e.g. 0 or NaN (not a number) is assigned by default
when variable is declared
In C/C++ a+=b is equivalent to a=a+b (but a[i++]+=b is different from
a[i++]=a[i++]+b, ouch!)
Compiler produces better code, because the address of a variable is
only calculated once
Multiway assignments in Clu, ML, and Perl
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a,b := c,d assigns c to a and d to b simultaneously, e.g. a,b :=
b,a swaps a with b
a,b := 1 assigns 1 to both a and b
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