structure of programming language statements. expression
TRANSCRIPT
What is an expression ?
• The notion of value is central to programming.
• Program variables get instantiated to values at run-time.
– Integer variables to integer values
– String variables to array of characters etc.
• With this perspective, we could define an expression
simply as:
An expression is a formal description of a value.
Expression Examples
• 2
• 2 * 5
• F(4) + 2*5 // Need to define function F
• A < B
• A < B \/ C = D // A,B,C,D are variables
• P(A, B) \/ Q(C, D) // P,Q are predicates
Prefix, Infix, Postfix
• Notation Position of Function Examples
• Prefix Left of argument(s) sqrt(16), f(3,4)
• Infix Between two arguments 3 f 4, 3 + 4
• Postfix Right of arguments 16 sqrt, 3 4 f
Postfix evaluation - Example
Expression Code Stack Contents
3 5 + 8 6 - * push 3 <3>
^ push 5 <3,5>
add <8>
3 5 + 8 6 - * push 8 <8,8>
^ push 6 <8,8,6>
sub <8, 2>
3 5 + 8 6 - * mul <16>
^
C, C++, and Java have over 50 operators and 17 different levels of precedence
Pascal: not, unary - *, /, div, mod, +, -
Ada: ** *, /, mod, rem unary -, not +, -, &and, or, xor
Operator Precedence
Arithmetic Expressions: Operator Associativity Rule
• The operator associativity rules for expression evaluation define the
order in which adjacent operators with the same precedence level are
evaluated
• Typical associativity rules
– Left to right, except **, which is right to left
– Sometimes unary operators associate right to left (e.g., in FORTRAN)
• APL is different; all operators have equal precedence and all operators
associate right to left
- Use relational operators and operands of various
types
- Evaluate to some boolean representation
- Operator symbols used vary somewhat among
languages (!=, /=, .NE., <>, #)
Relational Expressions
- Operands are boolean and the result is boolean
- Operators:
FORTRAN 77 FORTRAN 90 C Ada
.AND. and && and
.OR. or || or
.NOT. not ! not
xor
- C has no boolean type--it uses int type with 0
for false and nonzero for true
-
Boolean Expressions
Relational and Boolean Expressions: No Boolean Type in C
• C has no Boolean type--it uses int type with 0 for false and nonzero
for true
• One odd characteristic of C’s expressions:
a < b < c is a legal expression, but the result is not what you might
expect:
– Left operator is evaluated, producing 0 or 1
– The evaluation result is then compared with the third operand (i.e.,
c)
Evaluating an expression without evaluating all the
operands.
e.g. (a > b) and (c > 5)
If we know that a > b is false, then there is no need
To determine whether (c > 5) is true.
Short Circuit Evaluation
Pascal: does not use short-circuit evaluation index := 1; while (index <= length) and (LIST[index] <> value) do index := index + 1
If value is not in LIST, then ???
Short Circuit Evaluation
C, C++, and Java: use short-circuit evaluation for the usual Boolean operators (&& and ||), but also provide bitwise Boolean operators that are not short circuit (& and |)
Ada: programmer can specify either (short-circuit is specified with and then and or else)
FORTRAN 77: short circuit, but any side-affected place must be set to undefined
Short-circuit evaluation exposes the potential problem of side effects in expressions e.g. (a > b) || (b++ / 3)
Short circuit evaluation
Conditional Expressions
• Conditional Expressions
– C-based languages (e.g., C, C++)
– An example:
average = (count == 0)? 0 : sum / count
– Evaluates as if written like
if (count == 0) average = 0
else average = sum /count
Let expressions
• Example: let square(x) = x*x in square(square(2))
• Of the form: let function_definition in
sub_expression
• The function definition defines a function f in
equational form.
• The sub-expression contains function applications of f
• We assume that definition of f is non-recursive.
Let expressions
• Evaluation proceeds by replacing applications of f
in sub-expression with the definition of f
• Example: let square(x) = x*x in
square(square(2))
• square(2) * square(2)
• 2 * 2 * 2 * 2 = 16
• Let expressions allow for function definitions.
• Their evaluation is same as macro-expansion.
Assignment Statements
• The general syntax
<target_var> <assign_operator> <expression>
• The assignment operator
= FORTRAN, BASIC, PL/I, C, C++, Java
:= ALGOLs, Pascal, Ada
Assignment Statements: Compound Operators
• A shorthand method of specifying a commonly needed form of assignment
• Introduced in ALGOL; adopted by C• Example
a = a + b
is written as
a += b
Mixed-Mode Assignment
• Assignment statements can also be mixed-mode, for exampleint a, b;
float c;
c = a / b;• In Pascal, integer variables can be assigned
to real variables, but real variables cannot be assigned to integers
• In Java, only widening assignment coercions are done
• In Ada, there is no assignment coercion
Selection Statements
• A selection statement provides the means of
choosing between two or more paths of
execution
• Two general categories:
– Two-way selectors
– Multiple-way selectors
Two-Way Selection Statements
• General form:if control_expression
then clauseelse clause
• Design Issues:
– In C, Python, and C++, the control
expression can be arithmetic
– In languages such as Ada, Java, Ruby, and
C#, the control expression must be Boolean
Two-Way Selection: Examples
• FORTRAN: IF (boolean_expr) statement
• Problem: can select only a single statement; to select
more, a GOTO must be used, as in the following example
IF (.NOT. condition) GOTO 20
...
20 CONTINUE
• This problem was solved in FORTRAN 77
Two-Way Selection: Examples
• ALGOL 60:
if (boolean_expr)
then statement (then clause)
else statement (else clause)
• The statements could be single or compound
Nesting Selectors
• Java example
if (sum == 0)
if (count == 0)
result = 0;
else result = 1;
• Which if gets the else?
• Java's static semantics rule: else matches with
the nearest if
Nesting Selectors (continued)
• To force an alternative semantics, compound
statements may be used:
if (sum == 0) {
if (count == 0)
result = 0;
}
else result = 1;
• The above solution is used in C, C++, and C#
• Perl requires that all then and else clauses to be
compound
Multiple-Way Selection
• Early multiple selectors:
– FORTRAN arithmetic IF (a three-way selector)
IF (arithmetic expression) N1, N2, N3
– Segments require GOTOs
Multiple-Way Selection
• Modern multiple selectors
– C’s switch statement
switch (expression) {
case const_expr_1: stmt_1;
…
case const_expr_n: stmt_n;
[default: stmt_n+1]
}
31
Switch in C, C++, Jave
switch (x)
default:
if (prime(x))
case 2: case 3: case 5: case 7:
process_prime(x);
else
case 4: case 6: case 8:
case 9: case 10:
process_composite(x);
Multiple-Way Selection in C#
• It has a static semantics rule that disallows the implicit execution of
more than one segment
– Each selectable segment must end with an unconditional branch
(goto or break)
• The control expression and the case constants can be strings
switch (value) {
case -1: Negatives++;break;
case 0: Zeros++; goto case 1;
case 1: Positives++;break;
default: Console.WriteLine(“!!!\n”); }
Multiple-Way Selection: Examples
• Design choices for C’s switch statement
1. Control expression can be only an integer type
2. Selectable segments can be statement
sequences, blocks, or compound statements
3. default clause is for unrepresented values (if
there is no default, the whole statement does
nothing)
The Ada case statement
case Next_Char is
when ‘I’ => Val := 1;
when ‘V’ => Val := 5;
when ‘X’ => Val := 10;
when ‘C’ => Val := 100;
when ‘D’ => Val := 500;
when ‘M’ => Val := 1000;
when others => raise Illegal_Numeral;
end case;
Iterative Statements
• The repeated execution of a statement or
compound statement is accomplished either by
iteration or recursion
Counter-Controlled Loops
• A counting iterative statement has a loop variable, and a means of specifying the initial and terminal, and stepsize values
• Design Issues:1. What are the type and scope of the loop variable?2. What is the value of the loop variable at loop
termination?3. Should it be legal for the loop variable or loop
parameters to be changed in the loop body, and if so, does the change affect loop control?
4. Should the loop parameters be evaluated only once, or once for every iteration?
Iterative Statements: Examples
• FORTRAN 90 syntax
DO label var = start, finish [, stepsize]
• Stepsize can be any value but zero
• Design choices:
1. Loop variable must be INTEGER
3. The loop variable cannot be changed in the loop;
because they are evaluated only once, it does not
affect loop control
Iterative Statements
• Pascal’s for statement
for variable := initial (to|downto) final do
statement
• Design choices:
1. Loop variable must be an ordinal type of usual scope
2. After normal termination, loop variable is undefined
3. The loop variable cannot be changed in the loop but
they are evaluated just once, so it does not affect
loop control
Iterative Statements: Examples
• Adafor var in [reverse] discrete_range loop
...
end loop
• A discrete range is a sub-range of an integer or enumeration type
• Scope of the loop variable is the range of the loop
• Loop variable is implicitly undeclared after loop termination
Iterative Statements: Examples
• C’s for statementfor ([expr_1] ; [expr_2] ; [expr_3]) statement
• The expressions can be whole statements, or even statement sequences, with the statements separated by commas
– The value of a multiple-statement expression is the value of the last statement in the expression
• Everything can be changed in the loop
• The first expression is evaluated once, but the other two are evaluated with each iteration
Iterative Statements: Examples
• C++ differs from C in two ways:
The initial expression can include variable
definitions (scope is from the definition to the
end of the loop body)
• Java and C#
–Differs from C++ in that the control
expression must be Boolean
Iterative Statements: Logically-Controlled Loops
• Repetition control is based on a Boolean
• Design issues:
– Pre-test or post-test?
– Should the logically controlled loop be a special case of the counting loop statement ?
• General forms:
while (ctrl_expr) do
loop body loop body
while (ctrl_expr)
Iterative Statements: Logically-Controlled Loops: Examples
• Pascal has separate pre-test and post-test logical
loop statements (while-do and repeat-until)
• C and C++ also have both, but the control
expression for the post-test version is treated just
like in the pre-test case (while-do and do- while)
• Java is like C, except the control expression must
be Boolean (and the body can only be entered at
the beginning -- Java has no goto
Iterative Statements: Logically-Controlled Loops: Examples
• Ada has a pretest version, but no post-test
• FORTRAN 77 and 90 have neither
• Perl has two pre-test logical loops, while and
until, but no post-test logical loop
Iterative Statements: User-Located Loop Control Mechanisms break and continue
• C , C++, Java, Python, Ruby, C# : break statement
Unconditional; for any loop or switch; one level only
• Java and C# have a labeled break statement:
control transfers to the label
• An alternative: continue statement; it skips the
remainder of this iteration, but does not exit the
loop
Unconditional Branching
• Transfers execution control to a specified place in the program
• Represented one of the most heated debates in 1960’s and 1970’s
• Well-known mechanism: goto statement
• Major concern: Readability
• Some languages do not support goto statement (e.g., Module-2 and Java)
• C# offers goto statement (can be used in switch statements)