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# Simple linked list operation in Jahob

The following is an example of a method and its annotation in the Jahob verification system.

```class Node {
public /*: claimedby List */ Node next;
}
class List
{
private static Node first;
/*:
public static specvar content :: objset;
vardefs "content == {x. x ~= null & (first,x) : {(v,w). v..Node.next=w}^*}";

public static specvar pointed :: "obj => bool";
public vardefs "pointed == (% n. EX x. x ~= null & x..Node.next = n)";

invariant firstUnaliased: "first ~= null --> ~ pointed first";
invariant isTree: "tree [Node.next]";
*/

/*: requires "n ~: content & n ~= null & n..Node.next = null & ~ pointed n"
modifies content, pointed
ensures "comment ''post'' (content = old content Un {n})"
*/
{
n.next = first;
first = n;
}
}```

It is an ordinary Java code with some annotations written in comments. The code manipulates a singly linked list of 'Node' elements. The specification variable 'content' stores all non-null objects reachable from the static variable 'first'. The definition of 'content' uses set comprehension notation '{(v,w). …}' and transitive closure notation 'r^*' to define the set of non-null nodes reachable from the first element.

The 'pointed' shorthand is a predicate that is true for a node 'n' if another node 'x' points to it. The 'pointed' predicate is defined using lambda expression for defining functions.

The invariant 'tree [Node.next]' means that

• there are never two objects that point to the same object along Node.next field
• there are no cycles of 'Node.next' fields

Such invariants apply to trees in general, but also to lists as a special case.