1. 1 Termination and shape-shifting heaps Byron Cook bycook@microsoft.com Microsoft Research, Cambridge Joint work with Josh Berdine, Dino Distefano, and Peter O’Hearn

2. 2 Lines of code (x1000) Cut-point set size Experimental results with Terminator [CAV’06,PLDI’06,SAS’05]

3. 3 Lines of code (x1000) Cut-point set size Experimental results with Terminator [CAV’06,PLDI’06,SAS’05]

4. 4 Lines of code (x1000) Cut-point set size Experimental results with Terminator [CAV’06,PLDI’06,SAS’05]

5. 5 Lines of code (x1000) Cut-point set size Experimental results with Terminator [CAV’06,PLDI’06,SAS’05]

6. 6 Lines of code (x1000) Cut-point set size

7. 7 Outline Introduction TERMINATOR’s proof rule MUTANT/TERMINATOR Experimental results Conclusion & Discussion

8. 8 Outline Introduction TERMINATOR’s proof rule MUTANT/TERMINATOR Experimental results Conclusion & Discussion

9. 9 TERMINATOR’s proof rule

10. 10 TERMINATOR’s proof rule

11. 11 TERMINATOR’s proof rule

12. 12 TERMINATOR’s proof rule

13. 13 TERMINATOR’s proof rule

14. 14 TERMINATOR’s proof rule Ø

15. 15 TERMINATOR’s proof rule Ø

16. 16 TERMINATOR’s proof rule

17. 17 TERMINATOR’s proof rule

18. 18 TERMINATOR’s proof rule

19. 19 TERMINATOR’s proof rule

20. 20 TERMINATOR’s proof rule

21. 21 TERMINATOR’s proof rule

22. 22 TERMINATOR’s proof rule

23. 23 TERMINATOR’s proof rule

24. 24 Outline Introduction TERMINATOR’s proof rule MUTANT/TERMINATOR Experimental results Conclusion & Discussion

25. 25 Outline Introduction TERMINATOR’s proof rule MUTANT/TERMINATOR Experimental results Conclusion & Discussion

26. 26 Reversing the strategy

27. 27 Reversing the strategy

28. 28 Reversing the strategy

29. 29 Reversing the strategy

30. 30 Reversing the strategy

31. 31 Reversing the strategy

32. 32 Mutant

33. 33 Mutant

34. 34 Mutant example

35. 35 Mutant example

36. 36 Mutant example

37. 37 Mutant example

38. 38 Mutant example

39. 39 Mutant example

40. 40 Outline Introduction TERMINATOR’s proof rule MUTANT/TERMINATOR Experimental results Conclusion & Discussion

41. 41 Outline Introduction TERMINATOR’s proof rule MUTANT/TERMINATOR Experimental results Conclusion & Discussion

42. 42 Experimental results Revisiting loops falsely accused with TERMINATOR:

43. 43 Introduction

44. 44 Introduction

45. 45 Introduction

46. 46 Introduction

47. 47 Introduction

48. 48 Introduction

49. 49 Introduction

50. 50 Introduction

51. 51 Introduction

52. 52 Introduction

53. 53 Introduction

54. 54 Introduction

55. 55 Introduction

56. 56 Introduction

57. 57 Introduction

58. 58 Introduction

59. 59 Introduction

60. 60 Outline Introduction TERMINATOR’s proof rule MUTANT/TERMINATOR Experimental results Conclusion & Discussion

61. 61 Outline Introduction TERMINATOR’s proof rule MUTANT/TERMINATOR Experimental results Conclusion & Discussion

62. 62 Conclusion & Discussion Constructing automatic termination provers out of abstract interpreters:  Over-approximate binary reachability using encoding into states  Prove each state (partitioning of over-approximation) well-founded MUTANT/TERMINATOR:  Application using separation logic based abstract interpretation

63. 63 Conclusion & Discussion What’s next: combining termination analysis engines:  Integer linear programs (TERMINATOR, roughly speaking)  Mutating heaps (MUTANT)  Non-linear programs (ZIGZAG)

64. 64 Conclusion & Discussion What’s next: combining termination analysis engines:  Integer linear programs (TERMINATOR, roughly speaking)  Mutating heaps (MUTANT)  Non-linear programs (ZIGZAG)

65. 65 Conclusion & Discussion What’s next: combining termination analysis engines:  Integer linear programs (TERMINATOR, roughly speaking)  Mutating heaps (MUTANT)  Non-linear programs (ZIGZAG)

66. 66 Conclusion & Discussion What’s next: combining termination analysis engines:  Integer linear programs (TERMINATOR, roughly speaking)  Mutating heaps (MUTANT)  Non-linear programs (ZIGZAG)

67. 67 Conclusion & Discussion See http://research.microsoft.com/TERMINATORhttp://research.microsoft.com/TERMINATOR  Not-quite-camera-ready copy of CAV’06 paper about MUTANT  Papers about TERMINATOR (PLDI’06, SAS’06, CAV’06) Questions?