Nelson, G.: Verifying reachability invariants of linked structures. In: Symp. on Princ. of Prog. Lang. (1983) 38--47  Home/Search   Document Not in Database   Summary   Related Articles   Check

....analyzes the list reversal example fully automatically, in contrast to our use of user supplied approximation hints. However, we believe that it is possible to automate the heuristics we have used for identifying approximations, so that programs such as this are handled fully automatically. In [25, 27], wp for reachability is calculated, but no other shape predicates are considered. Predicate abstraction, combined with model checking, has been used in analyses of some heap properties: points to analysis [1] correctness of concurrent garbage collectors [10, 9] and loop invariants [13] These ....

G. Nelson. Verifying reachability invariants of linked structures. In POPL, 1983.

....about pointers, building on work of Morris. Here we describe a semantics that validates the approach, and use it to help devise axioms for operations that allocate and dispose of memory. 1. INTRODUCTION It is widely acknowledged that pointers cause problems for program proving formalisms (e.g. [8, 17, 13, 16, 9, 1, 14, 7]) but there is less agreement on precisely what the problems are. So, before describing our own work, we rst discuss where we believe the diculties lie. The rst issue that must be faced is aliasing , where distinct expressions can denote the same l value. The problem here can be seen by ....

Nelson, G. Verifying reachability invariants of linked structures. In Conference Record of the Tenth ACM Symposium on Principles of Programming Languages (1983), pp. 38-47.

....linked list type with a method that appends a list to another. Reasoning about a program with such a type requires reasoning about reachability among linked list nodes. To this end, we assume the underlying logic to contain a function symbol Reach (adapted from Greg Nelson s reachability predicate [14]) Informally, Reach(e 0 , e 1 , #, f, e 2 ) is true whenever it is possible to reach from object e 0 to object e 1 via applications of f in # , never going through object e 2 . The example in this section assumes that the underlying logic contains the following two axioms, which relate Reach ....

Greg Nelson. Verifying reachability invariants of linked structures. Conference Record of the Tenth Annual ACM Symposium on Principles of Programming Languages, pages 38--47, January 1983.

....about pointers, building on work of Morris. Here we describe a semantics that validates the approach, and use it to help devise axioms for operations that allocate and dispose of memory. 1 Introduction It is widely acknowledged that pointers cause problems for program proving formalisms (e.g. [10, 20, 16, 19, 11, 1, 17, 9]) but there is less agreement on precisely what the problems are. So, before describing our own work, we rst discuss where we believe the diculties lie. The rst issue that must be faced is aliasing , where distinct expressions can denote the same l value. The problem here can be seen by ....

Nelson, G. Verifying reachability invariants of linked structures. In Conference Record of the Tenth ACM Symposium on Principles of Programming Languages (1983), pp. 38-47.

....Other problems e.g. insertion sort, properties of finite sets, sequences, double ended queues, and natural numbers require induction. At the suggestion of Jim Saxe, we also tried proving properties of the reachability relation of linked linear lists based on an axiomatization proposed in [17] (see Appendix) 4 We also experimented with problems never tried, to our knowledge, using LP before. This included some well known and difficult first order problems including Bledsoe s Intermediate Value Theorem, 5 McCarthy s mutilated checkerboard problem, and a problem involving equalities ....

....Value problem, the same proof strategy used for the Intermediate Value problem was tried, and it worked. 7 Ganzinger s Saturate system, which supports implementation of special rules for transitive relations, for instance, solves this problem fairly easily. Reachability of Linked Lists In [17], Nelson formalized the reachability theory of linear lists, and then reported hand proofs of many properties useful for reasoning about linear lists in programs (see Appendix for the axiomatization and properties of interest) All the proofs are done using first order reasoning, and there is no ....

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Nelson, G., "Verifying Reachability Invariants of Linked Structures," Proc. Tenth ACM Symposium on Principles of Programming Languages, 1983, 38-47.

....linked list type with a method that appends a list to another. Reasoning about a program with such a type requires reasoning about reachability among linked list nodes. To this end, we assume the underlying logic to contain a function symbol Reach (adapted from Greg Nelson s reachability predicate [16]) Informally, Reach(e 0 , e 1 , #, f, e 2 ) is true whenever it is possible to reach from object e 0 to object e 1 via applications of f in # , never going through object e 2 . The example in this section assumes that the underlying logic contains the following two axioms, which relate Reach to ....

Greg Nelson. Verifying reachability invariants of linked structures. Conference Record of the Tenth Annual ACM Symposium on Principles of Programming Languages, pages 38--47, January 1983.

....discussion of copy , but also by linked lists, by defining to be the operation of advancing to the next node in the list using the address stored in a link field of the node. Our axioms about iterator ranges generalize some of the reachability properties of linked structures discussed in [11], but they do not have the complexity of other axioms of that paper that are specific to linked structures. 3 Axioms and inference rules for imperative programs We adopt a notation and set of axioms and inference rules similar in spirit to Hoare s or Dijkstra s axiomatic systems [3, 1] but ....

G. Nelson, "Verifying Reachability Invariants of Linked Structures," Tenth Annual ACM Symposium on Principles of Programming Languages, Austin, Texas, Jan. 2426, 1983, pp. 38--47.

....linked list type with a method that appends a list to another. Reasoning about a program with such a type requires reasoning about reachability among linked list nodes. To this end, we assume the underlying logic to contain a function symbol Reach (adapted from Greg Nelson s reachability predicate [Nelson 1983]) Informally, Reach(e 0 ; e 1 ; oe; f; e 2 ) is true whenever it is possible to reach object e 1 from object e 0 via applications of f in oe, never going through object e 2 . The example in this section assumes that the underlying logic contains the following two axioms, which relate Reach to ....

Nelson, Greg 1983. Verifying Reachability Invariants of Linked Structures. In Conference Record of the Tenth Annual ACM Symposium on Principles of Programming Languages, 38--47.

....rewrite them into modification constraints. The license to modify a[b # [t] gives rise to the postcondition contribution # # s : a[s] a # [s] # t b # nil s # where the notation t b # x s , read t reaches s via (applications of) b , not going through x , is defined by Nelson [42]. Similarly, the license to modify a[b # [t] gives rise to the postcondition contribution # # s : a[s] a # [s] # s b # nil t # 57 The second change to our proof system is to the pointwise axiom for any abstract variable involved in a cycle of dependencies. We will describe the ....

Greg Nelson. Verifying reachability invariants of linked structures. Conference Record of the Tenth Annual ACM Symposium on Principles of Programming Languages, pages 38--47, January 1983.

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Nelson, G.: Verifying reachability invariants of linked structures. In: Symp. on Princ. of Prog. Lang. (1983) 38--47

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G. Nelson. Verifying reachability invariants of linked structures. In Proceedings of the 10th ACM SIGACT-SIGPLAN symposium on Principles of programming languages, pages 38--47. ACM Press, 1983.

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G. Nelson. Verifying reachability invariants of linked structures. In: POPL, pp. 38--47. ACM Press, 1983.

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G. Nelson. Verifying reachability invariants of linked structures. In Symp. on Principles of Programming Languages (POPL), pages 38--47, 1983.

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G. Nelson. Verifying reachability invariants of linked structures. In Symp. on Principles of Programming Languages (POPL), pages 38--47, 1983.

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G. Nelson. Verifying reachability invariants of linked structures. In POPL, 1983.

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G. Nelson. Verifying reachability invariants of linked structures. In: POPL, pp. 38--47. ACM Press, 1983.

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G. Nelson. Verifying Reachability Invariants of Linked Structures. In Proc. of the 10th ACM Symp. on Principles of Programming Languages (POPL'83), pages 38--47, 1983.

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Greg Nelson. Verifying reachability invariants of linked structures. In Conference Record of the Tenth ACM Symposium on Principles of Programming Languages, pages 38--47, 1983.

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G. Nelson, Verifying reachability invariants of linked structures. Proceedings of POPL (1983), ACM Press, 38-47.

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Greg Nelson. Verifying reachability invariants of linked structures. In POPL

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