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Synthesis, Analysis, and Verification Lecture 13

Synthesis, Analysis, and Verification Lecture 13. Dynamic Allocation. Linked List Example. class List { List next; } public static void main(){ // alloc ={}, next=  x.null List first = new List(); // alloc ={o1}, next=  x.null

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Synthesis, Analysis, and Verification Lecture 13

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  1. Synthesis, Analysis, and VerificationLecture 13 Dynamic Allocation

  2. Linked List Example class List{ List next; } public static void main(){ //alloc={}, next=x.null List first = new List(); //alloc={o1}, next=x.null List second = new List();//alloc={o1,o2}, next=x.null first.next = second; //alloc={o1,o2}, next=x.if(x==o1) o2 else null second.next = first; //alloc={o1,o2}, next=x.if(x==o2) o1 else if (x==o1) o2 else null } null next next o1 o2 o3 next ... AllObjects \ alloc

  3. Linked List Example class List{ List next; } public static void main(){ //alloc={}, next=x.null List first = new List(); //alloc={o1}, next=x.null List second = new List();//alloc={o1,o2}, next=x.null first.next = second; //alloc={o1,o2}, next=x.if(x==o1) o2 else null second.next = first; //alloc={o1,o2}, next=x.if(x==o2) o1 else if (x==o1) o2 else null } null next next next o1 o2 o3 ... AllObjects \ alloc first second

  4. Linked List Example class List{ List next; } public static void main(){ //alloc={}, next=x.null List first = new List(); //alloc={o1}, next=x.null List second = new List();//alloc={o1,o2}, next=x.null first.next = second; //alloc={o1,o2}, next=x.if(x==o1) o2 else null second.next = first; //alloc={o1,o2}, next=x.if(x==o2) o1 else if (x==o1) o2 else null } null next next o1 o2 o3 ... next AllObjects \ alloc first second

  5. Memory Allocation in Java x = new C(); y = new C(); assert(x != y); // fresh object references-distinct Why should this assertion hold? How to give meaning to ‘new’ so we can prove it?

  6. A View of the World Everything exists, and will always exist.(It is just waiting for its time to become allocated.) It will never die (but may become unreachable). alloc : Obj Boolean i.e. alloc : Set[Obj] x = new C();  ^defult constructor

  7. New Objects Point Nowhere class C { int f; C next; C prev; } this should work: x = new C(); assert(x.f==0 && x.next==null && x.prev==null) x = new C(); 

  8. If you are new, you are known by few class C { int f; C next; C prev; } Assume C is the only class in the program Lonely object: no other object points to it. Newly allocated objects are lonely! x = new C(); 

  9. Remember our Model of Java Arrays length : Array -> int data : Array -> (Int -> Int) or simply: Array x Int -> Int • assertassert data= data( (a,i):= x) class Array { int length; data : int[]} a[i] = x y = a[i]

  10. Allocating New Array of Objects class oArray{ int length; data : Object[]} x = new oArray[100] 

  11. D-Linked List assume P; if (first == null) { first = n; n.next = null; n.prev = null; } else { n.next = first; first.prev = n; n.prev = null; first = n; } assert Q;

  12. How to prove such verification conditions automatically?

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