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# Lab for Automated Reasoning and Analysis LARA

# 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]"; */ public static void add(Node n) /*: 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.