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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

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

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

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

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

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

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

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

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9 TERMINATOR’s proof rule

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10 TERMINATOR’s proof rule

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11 TERMINATOR’s proof rule

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12 TERMINATOR’s proof rule

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13 TERMINATOR’s proof rule

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14 TERMINATOR’s proof rule Ø

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15 TERMINATOR’s proof rule Ø

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16 TERMINATOR’s proof rule

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17 TERMINATOR’s proof rule

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18 TERMINATOR’s proof rule

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19 TERMINATOR’s proof rule

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20 TERMINATOR’s proof rule

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21 TERMINATOR’s proof rule

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22 TERMINATOR’s proof rule

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23 TERMINATOR’s proof rule

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

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

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26 Reversing the strategy

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27 Reversing the strategy

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28 Reversing the strategy

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29 Reversing the strategy

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30 Reversing the strategy

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31 Reversing the strategy

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32 Mutant

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33 Mutant

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34 Mutant example

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35 Mutant example

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36 Mutant example

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37 Mutant example

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38 Mutant example

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39 Mutant example

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

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

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42 Experimental results Revisiting loops falsely accused with TERMINATOR:

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43 Introduction

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44 Introduction

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45 Introduction

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46 Introduction

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47 Introduction

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48 Introduction

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49 Introduction

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50 Introduction

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51 Introduction

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52 Introduction

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53 Introduction

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54 Introduction

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55 Introduction

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56 Introduction

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57 Introduction

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58 Introduction

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59 Introduction

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

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

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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

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

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

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

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

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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?

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