Proving conditional termination

1
Proving conditional termination Byron Cook,
Sumit Gulwani, Tal Lev-Ami, Andrey Rybalchenko
Mooly Sagiv

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2
Motivation

• Automatic termination/liveness proving is now a
  reality
• Modern tools support
• Concurrency,
• Pointers and heap,
• Recursion,
• Liveness properties (Omega-regular),
• Counterexample-generation.
• Tools
• Terminator (now being productized for the Windows
  SDV tool)
• ARMC (Andreys publicly available version)
• Polyrank (from Bradley, Manna Sipma, supports
  phase-change)
• T2 (in development for my book and CMU course)

3
Motivation

• Automatic termination/liveness proving is now a
  reality
• Modern tools support
• Concurrency,
• Pointers and heap,
• Recursion,
• Liveness properties (Omega-regular),
• Counterexample-generation.
• Tools
• Terminator (now being productized for the Windows
  SDV tool)
• ARMC (Andreys publicly available version)
• Polyrank (from Bradley, Manna Sipma, supports
  phase-change)
• T2 (in development for my book and CMU course)

4
Motivation

• Automatic termination/liveness proving is now a
  reality
• Advanced termination/liveness tools now
  supporting
• Concurrency,
• Pointers,
• Heap,
• Recursion,
• Omega-regular properties,
• Counterexample-generation,
• etc
• Tools
• Terminator (currently being transferred into
  Windows SDV product)
• ARMC (Andreys publicly available version)
• Polyrank (from Bradley, Manna, Sipma)
• T2 (in development for my book and CMU course)

5
Motivation

• Automatic termination/liveness proving is now a
  reality
• Advanced termination/liveness tools now
  supporting
• Concurrency,
• Pointers,
• Heap,
• Recursion,
• Omega-regular properties,
• Counterexample-generation,
• etc
• Tools
• Terminator (currently being transferred into
  Windows SDV product)
• ARMC (Andreys publicly available version)
• Polyrank (from Bradley, Manna, Sipma)
• T2 (in development for my book and CMU course)

6
Motivation

• Automatic termination/liveness proving is now a
  reality
• Advanced termination/liveness tools now
  supporting
• Concurrency,
• Pointers,
• Heap,
• Recursion,
• Omega-regular properties,
• Counterexample-generation,
• etc
• Tools
• Terminator (currently being transferred into
  Windows SDV product)
• ARMC (Andreys publicly available version)
• Polyrank (from Bradley, Manna, Sipma)
• T2 (in development for my book and CMU course)

7

• Automatic termination/liveness proving is now a
  reality
• Advanced termination/liveness tools now
  supporting
• Concurrency,
• Pointers,
• Heap,
• Recursion,
• Omega-regular properties,
• Counterexample-generation,
• etc
• Tools
• Terminator (currently being transferred into
  Windows SDV product)
• ARMC (Andreys publicly available version)
• Polyrank (from Bradley, Manna, Sipma)
• T2 (in development for my book and CMU course)

8

• Automatic termination/liveness proving is now a
  reality
• Advanced termination/liveness tools now
  supporting
• Concurrency,
• Pointers,
• Heap,
• Recursion,
• Omega-regular properties,
• Counterexample-generation,
• etc
• Tools
• Terminator (currently being transferred into
  Windows SDV product)
• ARMC (Andreys publicly available version)
• Polyrank (from Bradley, Manna, Sipma)
• T2 (in development for my book and CMU course)

9
Motivation

• Automatic termination/liveness proving is now a
  reality
• Advanced termination/liveness tools now
  supporting
• Concurrency,
• Pointers,
• Heap,
• Recursion,
• Omega-regular properties,
• Counterexample-generation,
• etc
• Tools
• Terminator (currently being transferred into
  Windows SDV product)
• ARMC (Andreys publicly available version)
• Polyrank (from Bradley, Manna, Sipma)
• T2 (in development for my book and CMU course)

10
Motivation

• Automatic termination/liveness proving is now a
  reality
• Advanced termination/liveness tools now
  supporting
• Concurrency,
• Pointers,
• Heap,
• Recursion,
• Omega-regular properties,
• Counterexample-generation,
• etc
• Tools
• Terminator (currently being transferred into
  Windows SDV product)
• ARMC (Andreys publicly available version)
• Polyrank (from Bradley, Manna, Sipma)
• T2 (in development for my book and CMU course)

11
Motivation

• Automatic termination/liveness proving is now a
  reality
• Advanced termination/liveness tools now
  supporting
• Concurrency,
• Pointers,
• Heap,
• Recursion,
• Omega-regular properties,
• Counterexample-generation,
• etc
• Tools
• Terminator (currently being transferred into
  Windows SDV product)
• ARMC (Andreys publicly available version)
• Polyrank (from Bradley, Manna, Sipma)
• T2 (in development for my book and CMU course)

12
Motivation

• Automatic termination/liveness proving is now a
  reality
• Advanced termination/liveness tools now
  supporting
• Concurrency,
• Pointers,
• Heap,
• Recursion,
• Omega-regular properties,
• Counterexample-generation,
• etc
• Tools
• Terminator (currently being transferred into
  Windows SDV product)
• ARMC (Andreys publicly available version)
• Polyrank (from Bradley, Manna, Sipma)
• T2 (in development for my book and CMU course)

13
Motivation

• Automatic termination/liveness proving is now a
  reality
• Advanced termination/liveness tools now
  supporting
• Concurrency,
• Pointers,
• Heap,
• Recursion,
• Omega-regular properties,
• Counterexample-generation,
• etc
• Tools
• Terminator (currently being transferred into
  Windows SDV product)
• ARMC (Andreys publicly available version)
• Polyrank (from Bradley, Manna, Sipma)
• T2 (in development for my book and CMU course)

14
Motivation
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Underapproximating weakest preconditions

• Dream termination prover

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Underapproximating weakest preconditions

• Dream termination prover

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Underapproximating weakest preconditions

• Dream termination prover

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Underapproximating weakest preconditions

• Dream termination prover

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Underapproximating weakest preconditions

• Dream termination prover

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Underapproximating weakest preconditions

• Dream termination prover

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Underapproximating weakest preconditions

• Dream termination prover

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Outline

• Motivation
• Precondition synthesis
• Precondition synthesis for phase-change programs
• Examples
• Remarks

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PreSynth

• Automatic termination/liveness proving is now a
  reality
• Advanced termination/liveness tools now
  supporting
• Concurrency,
• Pointers,
• Heap,
• Recursion,
• Omega-regular properties,
• Counterexample-generation,
• etc
• Tools
• Terminator (currently being transferred into
  Windows SDV product)
• ARMC (Andreys publicly available version)
• Polyrank (from Bradley, Manna, Sipma)
• T2 (in development for my book and CMU course)

24
PreSynth

• Automatic termination/liveness proving is now a
  reality
• Advanced termination/liveness tools now
  supporting
• Concurrency,
• Pointers,
• Heap,
• Recursion,
• Omega-regular properties,
• Counterexample-generation,
• etc
• Tools
• Terminator (currently being transferred into
  Windows SDV product)
• ARMC (Andreys publicly available version)
• Polyrank (from Bradley, Manna, Sipma)
• T2 (in development for my book and CMU course)

25
PreSynth

• Automatic termination/liveness proving is now a
  reality
• Advanced termination/liveness tools now
  supporting
• Concurrency,
• Pointers,
• Heap,
• Recursion,
• Omega-regular properties,
• Counterexample-generation,
• etc
• Tools
• Terminator (currently being transferred into
  Windows SDV product)
• ARMC (Andreys publicly available version)
• Polyrank (from Bradley, Manna, Sipma)
• T2 (in development for my book and CMU course)

26
PreSynth

• Automatic termination/liveness proving is now a
  reality
• Advanced termination/liveness tools now
  supporting
• Concurrency,
• Pointers,
• Heap,
• Recursion,
• Omega-regular properties,
• Counterexample-generation,
• etc
• Tools
• Terminator (currently being transferred into
  Windows SDV product)
• ARMC (Andreys publicly available version)
• Polyrank (from Bradley, Manna, Sipma)
• T2 (in development for my book and CMU course)

27
PreSynth
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PreSynth

• Automatic termination/liveness proving is now a
  reality
• Advanced termination/liveness tools now
  supporting
• Concurrency,
• Pointers,
• Heap,
• Recursion,
• Omega-regular properties,
• Counterexample-generation,
• etc
• Tools
• Terminator (currently being transferred into
  Windows SDV product)
• ARMC (Andreys publicly available version)
• Polyrank (from Bradley, Manna, Sipma)
• T2 (in development for my book and CMU course)

29
PreSynth

• Automatic termination/liveness proving is now a
  reality
• Advanced termination/liveness tools now
  supporting
• Concurrency,
• Pointers,
• Heap,
• Recursion,
• Omega-regular properties,
• Counterexample-generation,
• etc
• Tools
• Terminator (currently being transferred into
  Windows SDV product)
• ARMC (Andreys publicly available version)
• Polyrank (from Bradley, Manna, Sipma)
• T2 (in development for my book and CMU course)

30
PreSynth
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PreSynth
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PreSynth
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PreSynth
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PreSynth
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PreSynth
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PreSynth
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PreSynth
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PreSynth
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PreSynth
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PreSynth
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PreSynth
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PreSynth
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PreSynth
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PreSynth
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PreSynth
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PreSynth
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Outline

• Motivation
• Precondition synthesis
• Precondition synthesis for phase-change programs
• Examples
• Remarks

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Phase-change programs
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Phase-change programs
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Phase-change programs
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Phase-change programs
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Phase-change programs
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Phase-change programs
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Phase-change programs
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Phase-change programs
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Phase-change programs
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Phase-change programs
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Phase-change programs
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Phase-change programs
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Phase-change programs
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Phase-change programs
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Outline

• Motivation
• Precondition synthesis
• Precondition synthesis for phase-change programs
• Examples
• Remarks

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Examples
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Examples
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Examples
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Examples
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Examples
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Examples
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Examples
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Examples
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Outline

• Motivation
• Precondition synthesis
• Precondition synthesis for phase-change programs
• Examples
• Remarks

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Remarks

• Are we generating the weakest linear
  precondition?
• Future work (though, its probably no)
• Concurrent programs
• Environment synthesis is more important
• Working on this problem now based on PLDI07
• Applications
• Interprocedural termination proving, disproving
  safety, library analysis, etc