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Synthesizing Number Transformations from Input-Output Examples

Synthesizing Number Transformations from Input-Output Examples. Rishabh Singh and Sumit Gulwani. Number. One of the most commonly used data type Number Formatting Every language has its own format #.00? (C#, Excel), 05.2f (Python, C) End-users. Help-forums. Help-forums.

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Synthesizing Number Transformations from Input-Output Examples

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  1. Synthesizing Number Transformations from Input-Output Examples Rishabh Singh and SumitGulwani

  2. Number • One of the most commonly used data type • Number Formatting • Every language has its own format #.00? (C#, Excel), 05.2f (Python, C) • End-users

  3. Help-forums

  4. Help-forums

  5. Excel Help-forums

  6. Excel Help-forums upper 45 or 95

  7. Observations from Help-forums • Input-Output Examples • Specification mechanism • Additional inputs for removing ambiguity Excel add-in with same interface

  8. Talk Outline • Number Transformation Language • Synthesis Algorithm • String & Number Language Combination • Synthesis Algorithm for Combination • Experiments

  9. Generic Framework • Expression Language L • Expressive and succinct • Efficient Data structures for set of expressions • Version-space algebra • GenerateStr • All sets of expressions from I-O example • Intersect • Intersect two sets of expressions

  10. Number Transformations

  11. Number Transformation Language

  12. Number Transformation Language

  13. Number Transformation Language

  14. Format String • : minimum number of significant digits • : maximum number of significant digits • : number of whitespaces at end

  15. Number Format Exactly 2 decimal places .NET :

  16. Semantics Exactly 2 decimal places 24.589  24.59 24.2  24.20

  17. GenerateStr • Interval domains for invariant

  18. Intersect

  19. Extension to Integer parts Dec(u) ( Int(u), Frac(u)) GenerateStr(Frac(u1), Frac(u2)) GenerateStr(Int(u1)R, Int(u2)R)

  20. Rounding Numbers • zero of interval • size of interval • nearest, upper, lower

  21. Round Format Round off to upper 45 =Min(Roundup(A1/45, 0)*45, Roundup(A1/95,0)*95)

  22. GenerateStr Not enough info. to learn precise

  23. Intersect • Intersect((n1,n’1),(n2,n’2))

  24. Intersect • Intersect((31,45),(86,95))

  25. Intersect • Intersect((31,45),(86,95))

  26. Intersect • Intersect((31,45),(86,95))

  27. Intersect • Intersect((31,45),(86,95))

  28. Intersect • Intersect((31,45),(86,95))

  29. Intersect • Intersect((31,45),(86,95))

  30. GenerateStr Only need to maintain greatest value

  31. Intersect

  32. Combining String and Number Transformations

  33. String Language [GulwaniPOPL11]

  34. Combined Language

  35. Combination Examples

  36. Synthesis Algorithm 2004.07.08  7/8/2004 Program P1 to extract 7 in input (-5, -4) (-5, dot -1) (-5, dot 2) (-5, 7) (6, -4) …. (P1, 7 -> 7)

  37. Synthesis Algorithm 2004.07.08  7/8/2004 Program P2 to extract 07 in input (dot 1, dot 2) (dot 1, dot -1) (-6, -4) (-6, dot -1) (-6, dot 2) …. (P1, 7 -> 7) (P2, 07 -> 7)

  38. GenerateStr 2004.07.08  7/8/2004 (P1, 7 -> 7) (P2, 07 -> 7)

  39. GenerateStr 2004.07.08  7/8/2004 (P3, 8 -> 8) (P4, 08 -> 8)

  40. Constructing the DAG 071/283/425060748 (P1, 7 -> 7) 4 3 2 0 1 (P2, 07 -> 7) 5 6 8 7

  41. Intersection • DAG intersection • Edge-wise program intersection

  42. Experiments

  43. Benchmarks • 50 benchmark problems • Help forums • Excel product team

  44. Number of I/O examples

  45. Performance

  46. Related work • String Transformations [Gulwani POPL11] • Table Transformations [Singh,Gulwani VLDB12] • Spreadsheet Data Manipulation using Examples[Gulwani, Harris, Singh CACM 2012]

  47. Conclusion • Number Transformation Language • Synthesis algorithm • String + Number Transformations • Combined Synthesis algorithm

  48. Thanks! CAV Algorithm Designers Software Developers End-Users Large potential

  49. Questions & Comments

  50. Backup slides

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