Semantics(1)

2 Symantec(1)  To provide an authoritative definition of the meaning of all language constructs for: 1.Programmers 2.Compiler writers 3.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 Operational definition  Abstract Syntax  Interpreter

5 Approaches to define Semantics (2)  Axiomatic Semantics Ascertain about the relationships that remain the same each time the program executes The axiomatic formula: {P} c {Q}  c : command or control structure  P : pre-conditions  Q : post-conditions

6  Denotation Semantics Denotation definition  Abstract syntax  Semantic algebra defining a computational model  Valuation functions The valuation functions map the syntactic constructs to semantic algebra The meaning can be expressed as a collection of functions operating on a program state Approaches to define Semantics (3)

7 Expression Semantics  Expression Semantics includes Operators Operators associativity and precedence Role of different evaluation order Importance of precision

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

9 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

10 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*-

11 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

12 Example 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; } while (p !=null){ If (p.inf == key) break; 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  a is semantically undefined  a = 14 Increment i after the 2 nd referencing  a=19 Increment i before the 2 nd referencing  In many languages sub-expression in separate sub-trees may be evaluated in any order i = 2; b = 2; c=5; a = b * i++ + c * i

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 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.