1 / 125

Program Analysis via 3-Valued Logic

Program Analysis via 3-Valued Logic. Thomas Reps University of Wisconsin. Joint work with Mooly Sagiv and Reinhard Wilhelm. t. y. NULL. 1. 2. 3. NULL. x. Example: In-Situ List Reversal. typedef struct list_cell { int val; struct list_cell *next; } *List;.

petersont
Download Presentation

Program Analysis via 3-Valued Logic

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Program Analysisvia 3-Valued Logic Thomas Reps University of Wisconsin Joint work with Mooly Sagiv and Reinhard Wilhelm

  2. t y NULL 1 2 3 NULL x Example: In-Situ List Reversal typedef struct list_cell { int val; struct list_cell *next; } *List; List reverse (List x) { List y, t; y = NULL; while (x != NULL) { t = y; y = x; x = x  next; y  next = t; } return y; }

  3. t y NULL 1 2 3 NULL x Example: In-Situ List Reversal typedef struct list_cell { int val; struct list_cell *next; } *List; List reverse (List x) { List y, t; y = NULL; while (x != NULL) { t = y; y = x; x = x  next; y  next = t; } return y; }

  4. t y 1 2 3 NULL x Example: In-Situ List Reversal typedef struct list_cell { int val; struct list_cell *next; } *List; NULL List reverse (List x) { List y, t; y = NULL; while (x != NULL) { t = y; y = x; x = x  next; y  next = t; } return y; }

  5. Example: In-Situ List Reversal typedef struct list_cell { int val; struct list_cell *next; } *List; t y NULL 1 2 3 NULL List reverse (List x) { List y, t; y = NULL; while (x != NULL) { t = y; y = x; x = x  next; y  next = t; } return y; } x

  6. Example: In-Situ List Reversal typedef struct list_cell { int val; struct list_cell *next; } *List; t y NULL 1 2 3 NULL List reverse (List x) { List y, t; y = NULL; while (x != NULL) { t = y; y = x; x = x  next; y  next = t; } return y; } x

  7. Example: In-Situ List Reversal typedef struct list_cell { int val; struct list_cell *next; } *List; t y NULL 1 2 3 NULL List reverse (List x) { List y, t; y = NULL; while (x != NULL) { t = y; y = x; x = x  next; y  next = t; } return y; } x

  8. Example: In-Situ List Reversal typedef struct list_cell { int val; struct list_cell *next; } *List; t y NULL 1 2 3 NULL List reverse (List x) { List y, t; y = NULL; while (x != NULL) { t = y; y = x; x = x  next; y  next = t; } return y; } x

  9. Example: In-Situ List Reversal typedef struct list_cell { int val; struct list_cell *next; } *List; t y NULL 1 2 3 NULL List reverse (List x) { List y, t; y = NULL; while (x != NULL) { t = y; y = x; x = x  next; y  next = t; } return y; } x

  10. Example: In-Situ List Reversal typedef struct list_cell { int val; struct list_cell *next; } *List; t y NULL 1 2 3 NULL List reverse (List x) { List y, t; y = NULL; while (x != NULL) { t = y; y = x; x = x  next; y  next = t; } return y; } x

  11. Example: In-Situ List Reversal typedef struct list_cell { int val; struct list_cell *next; } *List; t y NULL 1 2 3 NULL List reverse (List x) { List y, t; y = NULL; while (x != NULL) { t = y; y = x; x = x  next; y  next = t; } return y; } x

  12. Example: In-Situ List Reversal typedef struct list_cell { int val; struct list_cell *next; } *List; t y NULL 1 2 3 NULL List reverse (List x) { List y, t; y = NULL; while (x != NULL) { t = y; y = x; x = x  next; y  next = t; } return y; } x

  13. Example: In-Situ List Reversal typedef struct list_cell { int val; struct list_cell *next; } *List; t y NULL 1 2 3 NULL List reverse (List x) { List y, t; y = NULL; while (x != NULL) { t = y; y = x; x = x  next; y  next = t; } return y; } x

  14. Example: In-Situ List Reversal typedef struct list_cell { int val; struct list_cell *next; } *List; t y NULL 1 2 3 NULL List reverse (List x) { List y, t; y = NULL; while (x != NULL) { t = y; y = x; x = x  next; y  next = t; } return y; } x

  15. Example: In-Situ List Reversal typedef struct list_cell { int val; struct list_cell *next; } *List; t y NULL 1 2 3 NULL List reverse (List x) { List y, t; y = NULL; while (x != NULL) { t = y; y = x; x = x  next; y  next = t; } return y; } x

  16. Example: In-Situ List Reversal typedef struct list_cell { int val; struct list_cell *next; } *List; t y NULL 1 2 3 NULL List reverse (List x) { List y, t; y = NULL; while (x != NULL) { t = y; y = x; x = x  next; y  next = t; } return y; } x

  17. t y x Example: In-Situ List Reversal typedef struct list_cell { int val; struct list_cell *next; } *List; List reverse (List x) { List y, t; y = NULL; while (x != NULL) { t = y; y = x; x = x  next; y  next = t; } return y; }

  18. t y NULL x Example: In-Situ List Reversal typedef struct list_cell { int val; struct list_cell *next; } *List; List reverse (List x) { List y, t; y = NULL; while (x != NULL) { t = y; y = x; x = x  next; y  next = t; } return y; }

  19. NULL Example: In-Situ List Reversal typedef struct list_cell { int val; struct list_cell *next; } *List; t y List reverse (List x) { List y, t; y = NULL; while (x != NULL) { t = y; y = x; x = x  next; y  next = t; } return y; } x

  20. Example: In-Situ List Reversal typedef struct list_cell { int val; struct list_cell *next; } *List; t y NULL List reverse (List x) { List y, t; y = NULL; while (x != NULL) { t = y; y = x; x = x  next; y  next = t; } return y; } x

  21. Example: In-Situ List Reversal typedef struct list_cell { int val; struct list_cell *next; } *List; t y NULL List reverse (List x) { List y, t; y = NULL; while (x != NULL) { t = y; y = x; x = x  next; y  next = t; } return y; } x Materialization

  22. Example: In-Situ List Reversal typedef struct list_cell { int val; struct list_cell *next; } *List; t y NULL List reverse (List x) { List y, t; y = NULL; while (x != NULL) { t = y; y = x; x = x  next; y  next = t; } return y; } x

  23. Example: In-Situ List Reversal typedef struct list_cell { int val; struct list_cell *next; } *List; t y NULL List reverse (List x) { List y, t; y = NULL; while (x != NULL) { t = y; y = x; x = x  next; y  next = t; } return y; } x

  24. Example: In-Situ List Reversal typedef struct list_cell { int val; struct list_cell *next; } *List; t y NULL List reverse (List x) { List y, t; y = NULL; while (x != NULL) { t = y; y = x; x = x  next; y  next = t; } return y; } x

  25. Example: In-Situ List Reversal typedef struct list_cell { int val; struct list_cell *next; } *List; t y NULL List reverse (List x) { List y, t; y = NULL; while (x != NULL) { t = y; y = x; x = x  next; y  next = t; } return y; } x

  26. Example: In-Situ List Reversal typedef struct list_cell { int val; struct list_cell *next; } *List; t y NULL List reverse (List x) { List y, t; y = NULL; while (x != NULL) { t = y; y = x; x = x  next; y  next = t; } return y; } x

  27. Example: In-Situ List Reversal typedef struct list_cell { int val; struct list_cell *next; } *List; t y NULL List reverse (List x) { List y, t; y = NULL; while (x != NULL) { t = y; y = x; x = x  next; y  next = t; } return y; } x

  28. Example: In-Situ List Reversal typedef struct list_cell { int val; struct list_cell *next; } *List; t y List reverse (List x) { List y, t; y = NULL; while (x != NULL) { t = y; y = x; x = x  next; y  next = t; } return y; } x

  29. Example: In-Situ List Reversal typedef struct list_cell { int val; struct list_cell *next; } *List; t y List reverse (List x) { List y, t; y = NULL; while (x != NULL) { t = y; y = x; x = x  next; y  next = t; } return y; } x

  30. Example: In-Situ List Reversal typedef struct list_cell { int val; struct list_cell *next; } *List; t y List reverse (List x) { List y, t; y = NULL; while (x != NULL) { t = y; y = x; x = x  next; y  next = t; } return y; } x

  31. Example: In-Situ List Reversal typedef struct list_cell { int val; struct list_cell *next; } *List; t y List reverse (List x) { List y, t; y = NULL; while (x != NULL) { t = y; y = x; x = x  next; y  next = t; } return y; } x

  32. Example: In-Situ List Reversal typedef struct list_cell { int val; struct list_cell *next; } *List; t y List reverse (List x) { List y, t; y = NULL; while (x != NULL) { t = y; y = x; x = x  next; y  next = t; } return y; } x

  33. Example: In-Situ List Reversal typedef struct list_cell { int val; struct list_cell *next; } *List; t y List reverse (List x) { List y, t; y = NULL; while (x != NULL) { t = y; y = x; x = x  next; y  next = t; } return y; } x

  34. Example: In-Situ List Reversal typedef struct list_cell { int val; struct list_cell *next; } *List; t y List reverse (List x) { List y, t; y = NULL; while (x != NULL) { t = y; y = x; x = x  next; y  next = t; } return y; } x

  35. Example: In-Situ List Reversal typedef struct list_cell { int val; struct list_cell *next; } *List; t y List reverse (List x) { List y, t; y = NULL; while (x != NULL) { t = y; y = x; x = x  next; y  next = t; } return y; } x

  36. Example: In-Situ List Reversal typedef struct list_cell { int val; struct list_cell *next; } *List; t y List reverse (List x) { List y, t; y = NULL; while (x != NULL) { t = y; y = x; x = x  next; y  next = t; } return y; } x

  37. Example: In-Situ List Reversal typedef struct list_cell { int val; struct list_cell *next; } *List; t y List reverse (List x) { List y, t; y = NULL; while (x != NULL) { t = y; y = x; x = x  next; y  next = t; } return y; } x

  38. Example: In-Situ List Reversal typedef struct list_cell { int val; struct list_cell *next; } *List; t y List reverse (List x) { List y, t; y = NULL; while (x != NULL) { t = y; y = x; x = x  next; y  next = t; } return y; } x

  39. Example: In-Situ List Reversal typedef struct list_cell { int val; struct list_cell *next; } *List; t y List reverse (List x) { List y, t; y = NULL; while (x != NULL) { t = y; y = x; x = x  next; y  next = t; } return y; } x

  40. Example: In-Situ List Reversal typedef struct list_cell { int val; struct list_cell *next; } *List; t y NULL List reverse (List x) { List y, t; y = NULL; while (x != NULL) { t = y; y = x; x = x  next; y  next = t; } return y; } x

  41. Example: In-Situ List Reversal typedef struct list_cell { int val; struct list_cell *next; } *List; t y NULL List reverse (List x) { List y, t; y = NULL; while (x != NULL) { t = y; y = x; x = x  next; y  next = t; } return y; } x

  42. Example: In-Situ List Reversal typedef struct list_cell { int val; struct list_cell *next; } *List; t y NULL List reverse (List x) { List y, t; y = NULL; while (x != NULL) { t = y; y = x; x = x  next; y  next = t; } return y; } x

  43. Example: In-Situ List Reversal typedef struct list_cell { int val; struct list_cell *next; } *List; t y NULL List reverse (List x) { List y, t; y = NULL; while (x != NULL) { t = y; y = x; x = x  next; y  next = t; } return y; } x

  44. Original Problem: Shape Analysis • Characterize dynamically allocated data • x points to an acyclic list, cyclic list, tree, dag, etc. • data-structure invariants • Identify may-alias relationships • Establish “disjointedness” properties • x and y point to structures that do not share cells

  45. Formal: x Formalizing “. . .” Informal: x Summary node

  46. Why is Shape Analysis Difficult? • Destructive updating through pointers • pnext = q • Produces complicated aliasing relationships • Dynamic storage allocation • No bound on the size of run-time data structures • Data-structure invariants typically only hold at the beginning and end of operations • Need to verify that data-structure invariants are re-established

  47. Applications: Code Optimization • Machine-independent optimizations • constant propagation • loop-invariant code motion • common subexpression elimination • Machine-dependent optimizations • register allocation • parallelization • software prefetching • Insert storage-reclamation operations • Eliminate or move “checking code”

  48. Applications: Software Tools • Static detection of memory errors (cleanness) • dereferencing NULL pointers • dereferencing dangling pointers • memory leaks • Static detection of logical errors • Is a shape invariant restored? • What is in the heap? • list? doubly-linked list? tree? DAG? • disjoint? intertwined?

  49. Properties of reverse(x) • On entry: x points to an acyclic list • On exit: y points to an acyclic list • On exit: x == NULL • On each iteration, x and y point to disjoint acyclic lists • All the pointer dereferences are safe • No memory leaks

  50. A ‘Yacc’ for Shape Analysis: TVLA • Parametric framework • Some instantiations  known analyses • Other instantiations new analyses

More Related