9. Expressions and Assignment Statements
Polish Notation
An alternative method of constructing a well-formed formula that dispenses with parentheses in favor of the order of the signs.
Type Conversation
An explicit function call that takes a value of one type and computes a corresponding value of another type. can be widening or narrowing
Expressions
Are the fundamental means of specifying computations in a programming language. consist of constants, variables, parentheses, function calls, and operators
Essence of imperative languages
Dominant role of assignment statements
Side Effects
- A side effect of a function, called a functional side effect, occurs when the function changes either one of its parameters or a global variable. Operand evaluation order is important if functional side effects are possible - Ex: a + fun(a) If fun does not have the side effect of changing a, then the order of evaluation of the two operands, a and fun(a), has no effect on the value of the expression. However, if fun changes a, there is an effect. - Ex: Consider the following situation: fun returns 10 and changes its parameter to have the value 20, and: a = 10; b = a + fun(a); If the value of a is fetched first (in the expression evaluation process), its value is 10 and the value of the expression is 20 (a + fun(a)= 10 + 10). But if the second operand is evaluated first, then the value of the first operand is 20 and the value of the expression is 30 (a + fun(a)= 20 + 10). The following shows a C program which illustrate the same problem. int a = 5; int fun1() { a = 17; return 3;} /* end of fun1 */ void main() { a = a + fun1(); // C language a = 20; Java a = 8 } /* end of main */ The value computed for a in main depends on the order of evaluation of the operands in the expression a + fun1(). The value of a will be either 8 (if a is evaluated first) or 20 (if the function call is evaluated first).
Expressions in Lisp
- All arithmetic and logic operations are by explicitly called subprograms - Ex: to specify the c expression a + b * c in Lisp, one must write the following expression: (+ a (* b c)) // + and * are the names of functions
Errors in Expressions
- Caused by: Inherent limitations of arithmetic e.g., division by zero Limitations of computer arithmetic e.g., overflow or underflow - Floating-point overflow and underflow, and division by zero are examples of run-time errors, which are sometimes called exceptions.
Precedence
- The operator precedence rules for expression evaluation define the order in which the operators of different precedence levels are evaluated. - Many languages also include unary versions of addition and subtraction. - Unary addition (+) is called the identity operator because it usually has no associated operation and thus has no effect on its operand. - In Java and C#, unary minus also causes the implicit conversion of short and byte operands to int type.
Design issues for arithmetic expressions:
- What is the operator precedence rules? - What is the operator associativity rules? - What is the order of operand evaluation? - Are there restrictions on operand evaluation side effects? - Does the language allow user-defined operator overloading? - What mode mixing is allowed in expressions?
Example 15 7 1 1 +-/ 3 * 2 1 1 ++-
( ( (15 / (7 - (1 + 1) ) ) * 3) - (2 + (1 + 1) ) = (15/5)*3 - 4 = 3*3 - 4 = 9 - 4 = 5
value of the Boolean expression:
(a >= 0) && (b < 10) // is independent of the second expression if a < 0, because expression (FALSE && (b < 10)) is FALSE for all values of b- So when a < 0, there is no need to evaluate b, the constant 10, the second relational expression, or the && operation. - Unlike the case of arithmetic expressions, this shortcut can be easily discovered during execution. •Short-circuit evaluation exposes the potential problem of side effects in expressions (a > b) || (b++ / 3) // b is changed only when a <= b If the programmer assumed b would change every time this expression is evaluated during execution, the program will fail.
Operand evaluation order
1. Variables: fetch the value from memory 2. Constants: sometimes a fetch from memory; sometimes the constant is in the machine language instruction 3. Parenthesized expressions: evaluate all operands and operators first 4. The most interesting case is when an operand is a function call
Short-Circuit Evaluation
A complex conditional expression where the subsequent condition(s) might not be executed. A short-circuit evaluation of an expression is one in which the result is determined without evaluating all of the operands and/or operators. Ex: (13 * a) * (b/13 - 1) // is independent of the value of (b/13 - 1) if a = 0, because 0 * x = 0 for any x - So, when a = 0, there is no need to evaluate (b/13 - 1) or perform the second multiplication. - However, this shortcut is not easily detected during execution, so it is never taken. 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 |)
widening conversion
A conversion between one data type and another in which information is not lost. Is one in which an object is converted to a type that can include at least approximations to all of the values of the original type e.g., int to float.
narrowing conversion
A conversion from one data type into another in which information could be lost. Converting from "double" to an "int" is a narrowing conversion. Is one that converts an object to a type that cannot include all of the values of the original type e.g., double to float. Some narrowing conversions produce erroneous values
Boolean Expressions
Evaluates to either true or false; used in the conditional of an if-structure. Operands are Boolean and the result is Boolean Versions of C prior to C99 have 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 a > b > c - The left most operator is evaluated first because the relational operators of C are left associative, producing either 0 or 1 - Then, this result is compared with var c. There is never a comparison between b and c.
Conditional Targets
Ex: Perl ($flag ? $count1 : $count2) = 0; ⇔if ($flag) { $count1 = 0; } else { $count2 = 0;
Conditional Expressions
The process of selection - examples are if-else statements where code is controlled by a condition that allows specific parts of an algorithm to be executed. - Sometimes if-then-else statements are used to perform a conditional expression assignment. - Ex: C-based languages if (count == 0) average = 0; else average = sum / count; - In the C-based languages, this can be specified more conveniently in an assignment statement using a conditional expression. Note that ? is used in conditional expression as a ternary operator (3 operands). expression_1 ? expression_2 : expression_3 - Ex: average = (count == 0) ? 0 : sum / count;
Overloaded Operators
Use of an operator for more than one purpose The use of an operator for more than one purpose is operator overloading. Some are common (e.g., + for int and float). Java uses + for addition and for string catenation. Some are potential trouble (e.g., & in C and C++) x = &y. // & as unary operator is the address of y // & as binary operator bitwise logical AND - Causes the address of y to be placed in x. - Some loss of readability to use the same symbol for two completely unrelated operations. - The simple keying error of leaving out the first operand for a bitwise AND operation can go undetected by the compiler "difficult to diagnose" C++, C#, and F# allow user-defined overloaded operators - When sensibly used, such operators can be an aid to readability (avoid method calls, expressions appear natural) - Potential problems: Users can define nonsense operations Readability may suffer, even when the operators make sense
Functional languages
Use variables of a different sort, such as the parameters of functions. These languages also have declaration statements that bind values to names. These declarations are similar to assignment statements, but do not have side effects.
Arithmetic Expressions
Was one of the motivations for the development of the first programming languages. •Most of the characteristics of arithmetic expressions in programming languages were inherited from conventions that had evolved in mathematics. •Arithmetic expressions consist of operators, operands, parentheses, and function calls. Is to specify an arithmetic computation.
Explicit Type Conversions
Where the developer uses a casting operator to direct the conversion - In the C-based languages, explicit type conversions are called casts - Ex: In Java, to specify a cast, the desired type is placed in parentheses just before the expression to be converted, as in (int)angle - In ML and F#, the casts have the syntax of function calls. For example, in F# we could have the following: float(sum)
Two possible solutions to the functional side effects problem:
Write the language definition to disallow functional side effects. Write the language definition to demand that operand evaluation order be fixed Java guarantees that operands are evaluated in left-to-right order, eliminating this problem
stack machine
a CPU architecture where a register stack is a central feature of the CPU. Operands may be taken from the stack and results pushed back on the stack.
Compound Assignment Operators
assignment operators other than the equal sign, which perform mathematical calculations on variables and literal values in an expression, and then assign a new value to the left operand. •A compound assignment operator is a shorthand method of specifying a commonly needed form of assignment •The form of assignment that can be abbreviated with this technique has the destination variable also appearing as the first operand in the expression on the right side, as in a = a + b •The syntax of assignment operators that is the catenation of the desired binary operator to the = operator sum += value; ⇔sum = sum + value;
operator
can be unary, meaning it has a single operand, binary, meaning it has two operands, or ternary, meaning it has three operands. - C-based languages include a ternary operator, which has three operands (conditional expression).
Unary Assignment Operators
combine increment and decrement operations with assignment •C-based languages include two special unary operators that are actually abbreviated assignments •The operators ++ and -- can be used either in expression or to form stand-alone single operator assignment statements. They can appear as prefix operators: sum = ++ count; ⇔count = count + 1; sum = count; •If the same operator is used as a postfix operator: sum = count ++; ⇔sum = count; count = count + 1;
Expression Evaluation
computing the value of an expression during program execution Need to be familiar with the orders of operator and operand evaluation.
associativity and precedence rules
for operators in the expressions of a language determine the order of operator evaluation in those expressions
Assignment Statements
initialize or change the value stored in a variable using the assignment operator =. Simple Assignments •The C-based languages use == as the equality relational operator to avoid confusion with their assignment operator •The operator symbol for assignment: 1. = Fortran, Basic, PL/I, C, C++, Java 2. := ALGOL, Pascal, Ada include target variables, assignments operators, and expressions
APL
is different; all operators have equal precedence, and all operators associate right to left. - Ex: APL A x B + C // A = 3, B = 4, C = 5 -> 27 - Precedence and associativity rules can be overridden with parentheses. - Programmers can alter the precedence and associativity rules by placing parentheses in expressions. - A parenthesized part of an expression has precedence over its adjacent Un parenthesized parts. - Ex:(A + B) * C // addition will be evaluated first
implementation of arithmetic computation
must cause two actions: •- Fetching the operands from memory •- Executing the arithmetic operations on those operands.
Associativity
specifies the order in which a sequence of operations with the same precedence are evaluated The operator associativity rules for expression evaluation define the order in which adjacent operators with the same precedence level are evaluated. An operator can be either left or right associative. - Typical associativity rules: Left to right, except **, which is right to left Sometimes unary operators associate right to left (e.g., Fortran) - Ex: Java a - b + c // left to right - Ex: Fortran A ** B ** C // right to left (A ** B) ** C // in Ada it must be parenthesized
Relational Expressions
use relational operators and operands of various types; evaluate to some Boolean representation A relational operator: an operator that compares the values of its two operands •Relational Expressions: two operands and one relational operator •The value of a relational expression is Boolean, unless it is not a type included in the language •- Use relational operators and operands of various types •- Operator symbols used vary somewhat among languages (!=, /=, .NE., <>, #) JavaScript and PHP have two additional relational operator, === and !== - Similar to their cousins, == and !=, except that they do not coerce their operands "7" == 7 // true in JavaScript "7" === 7 // false in JavaScript, because no coercion is done on the operand of this operator
Mixed-Mode Assignment
•Assignment statements can also be mixed mode •In Fortran, C, and C++, any numeric value can be assigned to any numeric scalar variable; whatever conversion is necessary is done. •In Java and C#, only widening assignment coercions are done. In Ada, there is no assignment coercion. •In all languages that allow mixed-mode assignment, the coercion takes place only after the right-side expression has been evaluated. For example, consider the following code: int a, b; float c; . . . c = a / b; - Because c is float, the values of a and b could be coerced to float before the division, which could produce a different value for c than if the coercion were delayed (for example, if a were 2 and b were 3).
Assignment in Functional Programming Languages
•Identifiers in functional languages are only names of values •Ex: in ML, names are bound to values with the val declaration, whose form is exemplified in the following: val cost = quantity * price; - If cost appears on the left side of a subsequent val declaration, that declaration creates a new version of the name cost, which has no relationship with the previous version, which is then hidden - F#'s let is like ML's val, except let also creates a new scope
Assignment as an Expression
•This design treats the assignment operator much like any other binary operator, except that it has the side effect of changing its left operand. •Ex: while ((ch = getchar()) != EOF) {. . .} // why ( ) around assignment? - The assignment statement must be parenthesized because the precedence of the assignment operator is lower than that of the relational operators. -Disadvantage: another kind of expression side effect which leads to expressions that are difficult to read and understand. For example a = b + (c = d / b) - 1 denotes the instructions Assign d / b to c Assign b + c to temp Assign temp - 1 to a •There is a loss of error detection in the C design of the assignment operation that frequently leads to program errors. if (x = y) . . . instead of if (x == y) . . .
Coercion in Expressions
Implicit type conversions, or coercions, in expressions are common, although they eliminate the error-detection benefit of type checking, thus lowing reliability - A mixed-mode expression is one that has operands of different types. - A coercion is an implicit type conversion. - Disadvantage of coercions: They decrease in the type error detection ability of the compiler - In most languages, all numeric types are coerced in expressions, using widening conversions - In ML and F#, there are no coercions in expressions - Language designers are not in agreement on the issue of coercions in arithmetic expressions Those against a broad range of coercions are concerned with the reliability problems that can result from such coercions, because they eliminate the benefits of type checking. Those who would rather include a wide range of coercions are more concerned with the loss in flexibility that results from restrictions. The issue is whether programmers should be concerned with this category of errors or whether the compiler should detect them.
unary minus operator
In all of the common imperative languages, the unary minus operator can appear in an expression either at the beginning or anywhere inside the expression, as long as it is parenthesized to prevent it from being next to another operator. For example, unary minus operator (-): A + (- B) * C // is legal A + - B * C // is illegal - Exponentiation has higher precedence that unary minus, so -A ** B Is equivalent to - (A ** B)
Binary operators
Infix •Prefix •Postfix (Reverse Polish Notation)
Ex:
Java int a; float b, c, d; . . . d = b * a; Assume that the second operand of the multiplication operator was supposed to be c, but because of a keying error it wat typed as a Because mixed-mode expressions are legal in Java, the compiler would not detect this as an error. Simply, a will be coerced to float.
Multiple Assignments
Perl, Ruby, and Lua provide multiple-target multiple-source assignments •Ex: Perl ($first, $second, $third) = (20, 30, 40); - The semantics is that 20 is assigned to $first, 30 is assigned to $second, and 40 is assigned to $third. - Also, the following is legal and performs an interchange: ($first, $second) = ($second, $first); - The correctly interchanges the values of $first and $second, 30 without the use of a temporary variable
