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Chapter 7: Expressions

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- Expressions are the fundamental means of specifying computations in a programming language
- To understand expression evaluation, need to be familiar with the orders of operator and operand evaluation
- Essence of imperative languages is dominant role of assignment statements

- Design issues for arithmetic expressions:
1. What are the operator precedence rules?

2. What are the operator associativity rules?

3. What is the order of operand evaluation?

4. Are there restrictions on operand evaluation side effects?

5. Does the language allow user-defined operator overloading?

6. What mode mixing is allowed in expressions?

- Ordinary prefixFunction name precedes its arguments f(a,b,c)Example:(a+b)*(c/d) becomes *(+(a,b),/(c,d))
- A variant (Cambridge Polish or fully parenthesized) moved the left paren before the operand and deletes the commas Example: (a+b)*(c/d) becomes (*(+a b) (/c d)) - LISP
- Polish, allows parens to be dropped Parens are unnecessary if number of args is fixed and knownExample: *+ab/cd Named because the Polish mathematician Lukasiewiez invented the notation.Difficult to readWorks for any number of operands (unlike infix notation)Easy to decode mathematically.

- Postfix Notation (suffix or reverse Polish) notation Not used in programming languages, but frequently for execution time representationEasily evaluated using a stack - Easy code generation
- Infix Notation Suitable only for binary operationsCommon use in mathematics and programming languages

Problems with infix

- Since only works for binary operations, others must use prefix (or postfix) making translation worse
- ambiguity: parens, precedence
Comparison of notations

- Infix is a natural representation,but requires complex implicit rules and doesn't work for non-binary operatorsIn the absence of implicit rules, large number of parens are required
- prefix and Cambridge Polish require large number of parens
- Polish requires no parens, but requires you know the arity of each operatorHard to read

- Operand evaluation order
- The process:
1. Variables: just fetch the value

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. Function references: The case of most interest

- Order of evaluation is crucial

- The process:

- Functional side effects - when a function changes a parameter or a nonlocal variable
- The problem with functional side effects:
- When a function referenced in an expression alters another operand of the expression; e.g., for a parameter change:
a = 10;

b = a + fun(&a);

Does the first a get loaded before or after the second use?

- Same problem with global variables

- When a function referenced in an expression alters another operand of the expression; e.g., for a parameter change:

- Two Possible Solutions to the Problem:
1. Write the language definition to disallow functional side effects

- No two-way parameters in functions
- No non-local references in functions
- Advantage: it works!
- Disadvantage: Programmers want the flexibility of two-way parameters (what about C?) and non-local references

2. Write the language definition to demand that operand evaluation order be fixed

- Disadvantage: limits some compiler optimizations

- C++ and Ada allow user-defined overloaded operators
- Potential problems:
- Users can define nonsense operations
- Readability may suffer, even when the operators make sense

- Def: 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., float to int
- Def: A widening conversion 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

- Def: A mixed-mode expression is one that has operands of different types
- Def: A coercion is an implicit type conversion
- The 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 Ada, there are virtually no coercions in expressions

- Explicit Type Conversions
- Often called casts

Eager evaluation

- For each operation node in the expression tree, first evaluate (or generate code to do so) each operand, then apply the operation. Sounds good - but complications: Z+(y==0?x:x/y)If we evaluate the operands of condition first, we do what the condition was set up to avoid.
- Sometimes optimizations make use of the fact that association can be changed. Sometimes, reordering causes problems:
- adding large and small values together - lose small ones due to number of significant digits which can be stored
- can be confusing to reader - exception thrown or side effects seen to be out of order
Evaluation Order

- Bottom-up evaluation of syntax tree
- For function calls: all arguments evaluated before call.
- translator may rearrange the order of computation so it is more efficient.
- If order of evaluation is unspecified, not portable

- Suppose Java did not use short-circuit evaluation
- Problem: table look-up
index = 1;

while (index <= length) && (LIST[index] != value)

index++;

- Problem: divide by zero

- 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)
- Short-circuit evaluation exposes the potential problem of side effects in expressions e.g. (a > b) || (b++ / 3)

- Delayed order evaluation
- used in functional languages. Don't evaluate until actually needed.Example:
- function sq(x:integer):integer;
begin sq = x*x;

end;

sq(i++)

Becomes sq(i++) = (i++)*(i++) is evaluated twice.

- More complicated assignments
Unary assignment operators (C, C++, and Java)a++;

C, C++, and Java treat = as an arithmetic binary operatore.g. a = b * (c = d * 2 + 1) + 1

This is inherited from ALGOL 68

- Assignment as an Expression
- In C, C++, and Java, the assignment statement produces a result
- So, they can be used as operands in expressionswhile ((ch = getchar())!=EOF){…}
- Disadvantage
- Another kind of expression side effect

- In FORTRAN, C, and C++, any numeric value can be assigned to any numeric scalar variable; whatever conversion is necessary is done
- In Pascal, integers can be assigned to reals, but reals cannot be assigned to integers (the programmer must specify whether the conversion from real to integer is truncated or rounded)
- In Java, only widening assignment coercions are done
- In Ada, there is no assignment coercion