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

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

5. Excel Help-forums

6. 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 1.Number Transformation Language 2.Synthesis Algorithm 3.String & Number Language Combination 4.Synthesis Algorithm for Combination 5.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

15. Number Format 123.4567123.46 123.4123.40 Exactly 2 decimal places

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

17. GenerateStr 123.4567123.46 123.4123.40

18. Intersect

19. Extension to Integer parts 12.4567012.46 123.4123.40

21. Round Format 1145 4695 =Min(Roundup(A1/45, 0)*45, Roundup(A1/95,0)*95) Round off to upper 45

22. GenerateStr

23. Intersect

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 1)(-5, -4) 2)(-5, dot -1) 3)(-5, dot 2) 4)(-5, 7) 5)(6, -4) 6)…. Program P 1 to extract 7 in input (P 1, 7 -> 7)

37. Synthesis Algorithm 2004.07.08  7/8/2004 (P 1, 7 -> 7) Program P 2 to extract 07 in input 1)(dot 1, dot 2) 2)(dot 1, dot -1) 3)(-6, -4) 4)(-6, dot -1) 5)(-6, dot 2) 6)…. (P 2, 07 -> 7)

38. GenerateStr 2004.07.08  7/8/2004 (P 1, 7 -> 7) (P 2, 07 -> 7)

39. GenerateStr 2004.07.08  7/8/2004 (P 3, 8 -> 8) (P 4, 08 -> 8)

40. Constructing the DAG 071/283/425060748071/283/425060748 01234567 (P 1, 7 -> 7) (P 2, 07 -> 7) 8

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! End-Users Algorithm Designers Software Developers CAV Large potential

49. Questions & Comments

50. Backup slides

51. Number Format 123.4567123.46 123.4

52. Number Format 123.4567123.46 123.4123.4_

53. ab cd ef gh ij kl

54. Help-forums

55. Number Format 123.4567123.46 123.4 At most 2 decimal places

56. Number Format 123.4567123.46 123.4123.4_ Exactly 2 decimal places with space