1. Semantics (1)

2. Symantec (1)
To provide an authoritative definition of the meaning of all language constructs for:
Programmers
Compiler writers
Standards developers
A programming language is complete only when its syntax, type system, and semantics are well-defined

3. Symantec (2)
Semantics is a precise definition of the meaning of a syntactically and type-wise correct program

4. Approaches to define Semantics (1)
Operational Semantics
Whatever happened when the program compiled is compiled by a compiler C and run on a machine M
Axiomatic Semantics
Axiomatize the meaning of each statement of the language
Give the formal specification of what a program is supposed to do.

5. Approaches to define Semantics (2)
Denotation Semantics
Define the meaning of each type of statement that occurs in the abstract syntax as a state-transformation mathematical function.
The meaning can be expressed as a collection of functions operating on a program state

6. Expression Semantics Expression Semantics includes Operators
Operators associativity and precedence
Role of different evaluation order
Importance of precision

7. Infix Notation Binary operator is written between its operands
Ambiguous expression
Associativity and Precedence is one way to eliminate the ambiguity

8. Eliminating infix Expression Ambiguity (1)
Polish prefix notations
Binary operator is written in front of the two operands
Semantics is inherently unambiguous
Prefix can be generated by using a prefix walk (preorder traversal)
Limitation: some symbol cannot be used for an operation with deferent number of operands
- is cannot be used for both unary and binary minus
One solution using different symbols
Example:
the infix: a+b-c*d  the prefix: -+ab*cd

9. Eliminating infix Expression Ambiguity (2)
Polish postfix notations
Binary operator follows the two operands
Semantics is inherently unambiguous
postfix can be generated by using a postfix walk (postorder traversal)
Example:
the infix: a+b-c*d 
the postfix: ab+cd*-

10. Expression Sort-Circuit Evaluation (1)
Evaluating a Boolean expression from left to right and stop as soon as the truth of the expression can be determined.
The short-circuit definition of A and B
if A then B else false
The short-circuit definition of A or B
if A then true else B

11. Expression Sort-Circuit Evaluation (2)
Advantages:
shorter and clear code
Disadvantages:
A && B is not the same as B && A
A  false and B  undefined
A && B  false
B && A  undefined

12. Example while (p !=null){ If (p.inf == key) break; P=p.next; }
Node p = head;
while (p != null &&
p.info != key)
p = p.next;
if (p == null)
// not in list
...
else // found it
boolean found = false;
while (p != null &&
! found) {
if (p.info == key)
found = true;
else
p = p.next; }

13. The Meaning of an Expression
Meaning of expression should depend only on
the values of its sub-expressions and
the meaning of its operator
Fixed size representation of numbers in computer makes numbers have smallest and largest values
Mathematics has unlimited values

14. Example: (a+b)+c ≠ a+(b+c) for some values of a, b, c Assume:
a = largest possible integer
b = 3
c =-5
Left-hand side= error (integer overflow)
Right-hand side = largest integer -2

15. Example i = 2; b = 2; c=5; a = b * i++ + c * i
a is semantically undefined
a = 14
Increment i after the 2nd referencing
a=19
Increment i before the 2nd referencing
In many languages sub-expression in separate sub-trees may be evaluated in any order

16. Program State (1)
The state of a program is the collection of all active objects and their current values.
Maps:
The pairing of active objects with specific memory locations, and
the pairing of active memory locations with their current values

17. Program State (2)
The current statement (portion of an abstract syntax tree) to be executed in a program is interpreted relative to the current state.
The individual steps that occur during a program run can be viewed as a series of state transformations

18. Example
Suppose variables i and j have the values 13 and -1 at some time during the execution
i and j are associated with memory locations 154 and 155 at that time
The current state:
Environment {i,154, j,155}
Memory {0,undef, … 154,13, 155,-1, …}

19. Program State (3) The state of a program is a product of
its active objects,
Their memory locations, and
Associative values
Function composed of two maps environment and memory
State = environment x memory
State is like watch widow

20. Assignment Semantics The semantic is as follows
Assignment = Variable target; Expression source
The semantic is as follows
Source expression is evaluated in the current state, resulting in a value
The resulting value replaces the value of the target variable, resulting in a new state

21. Assignment Semantics (1) Assignment Statement vs. Expression
In most languages, assignment is a statement; cannot appear in an expression.
In C-like languages, assignment is an expression.
Example: if (a = 0) ... // an error
while (*p++ = *q++) ; // strcpy
while (ch = getc(fp)) ...

22. Assignment Semantics (2) Copy vs. Reference Semantics
Copy: a = b;
a, b have same value.
Changes to either have no effect on other.
Used in imperative languages.
Reference
a, b point to the same object.
A change in object state affects both
Used by many object-oriented languages.