Run-time Correctness Checking Is Algorithmically Undecidable for Pointer Data Structures

Programs routinely use complicated pointer (linked list-type) data structures such as linked lists, doubly linked lists, diierent types of trees, etc. These data structures are usually deened inductively: e.g., a tree can be deened as a structure that results from an empty tree by an arbitrary sequence of adding and deleting elements. When the program runs, these data structures take dynamically changing shapes. To test program correctness, it is important to check, at run-time, whether a current shape is a correct implementation of the corresponding structure. Algorithms are known for checking the \shape correctness" for basic pointer-based data structures such as linked list, binary tree, etc. In this paper, we show that the general problem { verifying that a given shape is an instance of an inductively deened data structure { is algorithmically undecidable.