Learning Loop Invariants for Program Verification Xujie Si*, Hanjun - - PowerPoint PPT Presentation

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Learning Loop Invariants for Program Verification Xujie Si*, Hanjun - - PowerPoint PPT Presentation

Aug 17, 2023 46 likes •390 views

Learning Loop Invariants for Program Verification Xujie Si*, Hanjun Dai*, Mukund Raghothaman, Mayur Naik, Le Song University of Pennsylvania Georgia Institute of Technology NeurIPS 2018 Code: https://github.com/PL-ML/code2inv * equal

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Learning Loop Invariants for Program Verification

Xujie Si*, Hanjun Dai*, Mukund Raghothaman, Mayur Naik, Le Song University of Pennsylvania Georgia Institute of Technology NeurIPS 2018 Code: https://github.com/PL-ML/code2inv

* equal contribution

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SLIDE 2

Program verification

  • Prove whether your code is bug-free
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SLIDE 3

Program verification

  • Prove whether your code is bug-free
  • - Some of rules can be automated:

sequence rule, conditional rule, ......

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SLIDE 4

Program verification

  • Prove whether your code is bug-free

Loop Invariant <> Halting Problem

  • - Some of rules can be automated:
  • - Except ‘while rule’

sequence rule, conditional rule, ......

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SLIDE 5

What is loop invariant?

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SLIDE 6

What is loop invariant?

Program

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SLIDE 7

What is loop invariant?

Program Loop Invariant

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SLIDE 8

What is loop invariant?

Program Loop Invariant Requirement:

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SLIDE 9

Loop Invariant Checker

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SLIDE 10

Loop Invariant Checker

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SLIDE 11

Loop Invariant Checker

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SLIDE 12

Difficulties of learning loop Invariant

  • 1. Highly sparse and non-smooth reward

code

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Difficulties of learning loop Invariant

  • 1. Highly sparse and non-smooth reward

Agent

code

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SLIDE 14

Difficulties of learning loop Invariant

  • 1. Highly sparse and non-smooth reward

Agent

code

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SLIDE 15

Difficulties of learning loop Invariant

  • 1. Highly sparse and non-smooth reward

Agent 0 / 1 (Correct or not)

code

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SLIDE 16

Difficulties of learning loop invariant

  • 2. Generalization ability

Agent 0 / 1 (Correct or not) code1

......

Agent 0 / 1 (Correct or not) codeN

! ≥ 1 ⋁ % = 0

Agent 0 / 1 (Correct or not) code2

() ≤ 2 ⋀ (- > 0

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SLIDE 17

Difficulties of learning loop invariant

  • 2. Generalization ability

Agent 0 / 1 (Correct or not) code1

......

Agent 0 / 1 (Correct or not) codeN

! ≥ 1 ⋁ % = 0

Agent 0 / 1 (Correct or not) code2

() ≤ 2 ⋀ (- > 0

Agent New code =>

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SLIDE 18

Solution to sparsity and non-smoothness

Agent 0 (not correct)

code

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SLIDE 19

Solution to sparsity and non-smoothness

Agent 0 (not correct)

code

Counter-example: why am I wrong?

! = 1, % = −10

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SLIDE 20

Solution to sparsity and non-smoothness

Agent 0 (not correct)

code

Counter-example: why am I wrong?

! = 1, % = −10

Collection of counter-examples:

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SLIDE 21

Solution to sparsity and non-smoothness

Agent 0 (not correct)

code

Counter-example: why am I wrong?

! = 1, % = −10

! = 1, % = −1 ! = 0, % = −1 ! = 0, % = −2 ! = 2, % = −1 ! = 2, % = −1 ! = 2, % = −2 ! = 3, % = −1 ! = 3, % = −1 ! = 3, % = −2 ! = 0, % = −3 ! = 0, % = −4

Pre Inv Post Collection of counter-examples:

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SLIDE 22

Solution to sparsity and non-smoothness

Agent 0 (not correct)

code

Counter-example: why am I wrong?

! = 1, % = −10

! = 1, % = −1 ! = 0, % = −1 ! = 0, % = −2 ! = 2, % = −1 ! = 2, % = −1 ! = 2, % = −2 ! = 3, % = −1 ! = 3, % = −1 ! = 3, % = −2 ! = 0, % = −3 ! = 0, % = −4

Pre Inv Post Collection of counter-examples:

  • Smoothed reward
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SLIDE 23

Solution to sparsity and non-smoothness

Agent 0 (not correct)

code

Counter-example: why am I wrong?

! = 1, % = −10

! = 1, % = −1 ! = 0, % = −1 ! = 0, % = −2 ! = 2, % = −1 ! = 2, % = −1 ! = 2, % = −2 ! = 3, % = −1 ! = 3, % = −1 ! = 3, % = −2 ! = 0, % = −3 ! = 0, % = −4

Pre Inv Post Collection of counter-examples:

  • Smoothed reward
  • Reduced Z3 calls
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SLIDE 24

Solution to generalization

  • Transferable graph representation of source code

=> =>

SSA Transformation

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Code2Inv: End-to-end learning framework

......

! ≥ 0 && ! < 4 ' ≥ 100

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SLIDE 26

Experimental evaluation of Code2Inv

  • We collect 133 benchmark programs

OOPSLA 2013, Dillig et al POPL 2016, Garag et al

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SLIDE 27

Experimental evaluation of Code2Inv

  • We collect 133 benchmark programs

OOPSLA 2013, Dillig et al POPL 2016, Garag et al

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Code2Inv as an

  • ut-of-the-box

solver

Solved more instances with same # Z3 calls

Ours

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Generalize to new programs

void main (int n) { int x = 0 int m = 0 while (x < n) { if (unknown()) { m = x } x = x + 1 } if (n > 0) { assert (m < n) } }

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Generalize to new programs

void main (int n) { int x = 0 int m = 0 while (x < n) { if (unknown()) { m = x } x = x + 1 } if (n > 0) { assert (m < n) } } int w = 0 int z = 0

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SLIDE 31

Generalize to new programs

void main (int n) { int x = 0 int m = 0 while (x < n) { if (unknown()) { m = x } x = x + 1 } if (n > 0) { assert (m < n) } } int w = 0 int z = 0 z = z + 1 w = m + x z = m + 1

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Generalize to new programs

void main (int n) { int x = 0 int m = 0 while (x < n) { if (unknown()) { m = x } x = x + 1 } if (n > 0) { assert (m < n) } } void main (int n) { int x = 0 int w = 0 int m = 0 int z = 0 while (x < n) { z = z + 1 if (unknown()) { m = x z = m + 1 } x = x + 1 w = m + x } if (n > 0) { assert (m < n) } } int w = 0 int z = 0 z = z + 1 w = m + x z = m + 1

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SLIDE 33

Generalization ability of Code2Inv

1 confounding variable 3 confounding variables 5 confounding variables

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Poster session: Room 210 & 230 AB #23 05:00 -- 07:00 PM