1. Dr. Muhammed Al-Mulhem 1ICS535-101 ICS 535 Design and Implementation of Programming Languages Part 1 Fundamentals (Chapter 4) Operational Semantics ICS 535 Design and Implementation of Programming Languages Part 1 Fundamentals (Chapter 4) Operational Semantics

2. Dr. Muhammed Al-Mulhem 2ICS535-101 Semantic Domains and State Transformation Semantic domain Semantic domain A semantic domain is any set whose properties and operations are independently well-understood and upon which the functions that define the semantics of a language are ultimately based, Examples: natural numbers, integers, booleans Examples: natural numbers, integers, booleans Useful semantic domains for programming languages are Useful semantic domains for programming languages are 1. Environment 2. Memory 3. Locations

3. Dr. Muhammed Al-Mulhem 3ICS535-101 Semantic Domains and State Transformation Suppose we have variables i and j with values 13 and -1 at memory locations 154 and 155. Suppose we have variables i and j with values 13 and -1 at memory locations 154 and 155. Environment Environment A set of pairs that unite specific variables with memory locations  = {, } Memory [static and dynamic] Memory [static and dynamic] A set of pairs that unite specific locations with values  = {, ….,, …} Locations Locations Locations are the natural numbers.

4. Dr. Muhammed Al-Mulhem 4ICS535-101 Semantic Domains and State Transformation State State The state of a program is the product of its environment and its memory Simplified form The state  of a program is a set of pairs that represents all the active variables and their currently assigned values at some stage during the execution of the program.  = {,, … }  = {,, … } NOTE: Value of each variable is undefined before the program begins execution.

5. Dr. Muhammed Al-Mulhem 5ICS535-101 Semantic Domains and State Transformation Example of a state Example of a state  = {,, }  = {,, } Value retrieval function  (var) Value retrieval function  (var)  (y) gives the value 12  (y) gives the value 12 State transformations represent the changes in state of a program due to the execution of program statements. State transformations represent the changes in state of a program due to the execution of program statements. State transformation can be represented mathematically by a special function called Overriding Union ( Ū ). State transformation can be represented mathematically by a special function called Overriding Union ( Ū ).

6. Dr. Muhammed Al-Mulhem 6ICS535-101 Semantic Domains and State Transformation Overriding union Ū between two sets of pairs Overriding union Ū between two sets of pairs X Ū Y = replace in X all pairs whose first member matches a pair from Y by and then add to X any remaining pairs in Y Ū is a formal and generalized model of assignment statement Example Example  1 = {,, } y = 2*w + 3; z = 14;  2 = {, }  =  1 Ū  2 = {,,, }

7. Dr. Muhammed Al-Mulhem 7ICS535-101 Operational Semantics Operational semantics of a program provides a definition of program meaning by simulating the program’s behavior on a machine model Operational semantics of a program provides a definition of program meaning by simulating the program’s behavior on a machine model Structured operational semantics model use Structured operational semantics model use Rule-based approach Rule-based approach We developed this kind of operational semantics for Jay language. We developed this kind of operational semantics for Jay language.

8. Dr. Muhammed Al-Mulhem 8ICS535-101 Operational Semantics Operational semantics model uses the following notations: Operational semantics model uses the following notations: 1. Expression computation  (e)  v The computation of a value v from the expression e in state  2. Execution rule: It has the form If the premise is true then the conclusion is true. premise Conclusion

9. Dr. Muhammed Al-Mulhem 9ICS535-101 Operational Semantics Execution rule for addition Execution rule for addition  (e 1 )  v 1  (e 2 )  v 2 :  (e 1 + e 2 )  v 1 + v 2 Execution rule for an assignment statement Execution rule for an assignment statement s.target = s.source  (s.source)  v :  (s.target = s.source;)   Ū { } Execution rule for statement sequences s 1, s 2 Execution rule for statement sequences s 1, s 2  (s 1 )   1  1 (s 2 )   2 :  (s 1, s 2 )   2

10. Dr. Muhammed Al-Mulhem 10ICS535-101 Operational Semantics Execution rule for conditional statement Execution rule for conditional statement s = if (s.test) s.thenpart else s.elsepart  (s.test)  true  (s.thenpart)   1 :  (if(s.test) s.thenpart else s.elsepart)   1  (s.test)  false  (s.elsepart)   1 :  (if(s.test) s.thenpart else s.elsepart)   1

11. Dr. Muhammed Al-Mulhem 11ICS535-101 Operational Semantics Execution rule for loops Execution rule for loops s = while (s.test) s.body;  (s.test)  true  (s.body)   1  (while(s.test) s.body)   2 :  (while(s.test) s.body)   2  (s.test)  false :  (while(s.test) s.body)  

12. Dr. Muhammed Al-Mulhem 12ICS535-101 Examples - addition Suppose we have x = x + 1; and a current state in which the value of x is 5. That is Suppose we have x = x + 1; and a current state in which the value of x is 5. That is  = { …,, …}  = { …,, …} The operational semantics computes a new state as follows: The operational semantics computes a new state as follows:  (x)  5  (1)  1  (x + 1)  6  (x = x + 1;)  { …,, …} Ū {…, …}  This transformed the state to  = { …,, …}

13. Dr. Muhammed Al-Mulhem 13ICS535-101 Example - conditional If we have the state  = { …,, …} If we have the state  = { …,, …} And the following Jay statement And the following Jay statement If ( x<0 ) x = x -1; else x = x + 1; We apply the false rule We apply the false rule The rule concludes that the result of executing the conditional is the same as the result of executing x = x + 1; in state  = { …,, …} leaving as final result the state  1 = { …,, …} The rule concludes that the result of executing the conditional is the same as the result of executing x = x + 1; in state  = { …,, …} leaving as final result the state  1 = { …,, …}