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introduction_to_using_msol_over_strings_to_verify_linked_lists [2007/05/09 22:45] vkuncak |
introduction_to_using_msol_over_strings_to_verify_linked_lists [2007/05/14 12:02] (current) vkuncak |
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====== Introduction to using MSOL over strings to verify linked data structures ====== | ====== Introduction to using MSOL over strings to verify linked data structures ====== | ||
- | The following is an example of a method and its annotation in the Jahob verification system. | + | Here is a [[simple linked list operation in Jahob]]. |
- | + | ||
- | <code java> | + | |
- | 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; | + | |
- | } | + | |
- | } | + | |
- | </code> | + | |
- | + | ||
- | 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 calculus|lambda expression]] for defining functions. | + | |
- | + | ||
- | Automated verification of properties that involve reachability is a very difficult problem in general. The reason why it is possible in our case is that we are requiring the invariant 'tree [Node.next]' whose meaning is: | + | |
- | * 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 can be generalized to trees, but we first examine the case of lists. | + | |
What do verification conditions look like? | What do verification conditions look like? |