The document discusses various aspects of data generation, particularly focusing on recursive data structures and polymorphic functions. It also covers agile methodologies in project management and software development, along with combinatorial techniques for generating different types of structures. Additionally, it mentions specific problems and strategies related to the generation of trees and partitions.

1. Eric Torreborre / FP-Syd
Data generation
The hard parts

4. NOT SO SIMPLE

6. Recursive data structures
Polymorphic functions
Constrained data

11. Recursive data structures

12. Agile Estimating and Planning
Agile Management
Agile Product Management with Scrum
Agile Product Planning and Analysis
Agile Project Management:
Creating Innovative Products
Agile Project Management For Dummies
Agile Software Development, Principles,
Patterns, and Practices
Agile Software Development with Scrum
Agile Software Development with Distributed Teams
Agile Testing
Agile Estimating and Planning
Agile Management
Agile Product Management with Scrum
Agile Product Planning and Analysis
Agile Project Management:
Creating Innovative Products
Agile Project Management For Dummies
Agile Software Development, Principles,
Patterns, and Practices
Agile Software Development with Scrum
Agile Software Development with Distributed Teams
Agile Testing

13. Agile
+ Estimating and Planning
+ Management
+ Product
+ Management with Scrum
+ Planning and Analysis
+ Project Management
+ Creating Innovative Products
+ For Dummies
+ Software Development
+ Principles, Patterns, and Practices
+ with Scrum
+ with Distributed Teams
+ Testing
Agile
+ Estimating and Planning
+ Management
+ Product
+ Management with Scrum
+ Planning and Analysis
+ Project Management
+ Creating Innovative Products
+ For Dummies
+ Software Development
+ Principles, Patterns, and Practices
+ with Scrum
+ with Distributed Teams
+ Testing

14. Generate trees

17. Generate treesDepth?
Width?
Balanced?
Coverage?
Composition?
Uniformity?
Constraints?
Performance?

18. programs
well-typed

19. Size and
dimension
Boltzmann
Model
Combinatorial
species

21. Same size bound

22. 505
values
on average for n=100

23. 18 constructors
P = 1 / 8
9

24. P=1/4
P = 1 / 9

26. generating function
System of equations
solution +
singularity
size in O(n)

27. Enumerate structures
Sample uniformly

29. Set of
labels
Family of
structures

31. 2
1
3
4
5
6
2
1
3
4
5
6
2
1
3
4
5
6

32. b
a
c
d
e
f
b
a
c
d
e
f
b
a
c
d
e
e

33. 2
1
3
4
5
6
2
1
3
4
5
6

34. Regular species

35. 0

36. 1

37. X
11

38. F
1
G
2
3
4
5
F
1
2
3
4
5
G
1
2
3
4
5

39. X
1
0
X
1

40. X
1
1
X
1

41. 1 1
1
1

42. n 11 1 …

43. n 11 1 …

44. n 11 1 …

45. F
1
G
2
3
4
5
F
1
2
3
4
5
G

46. X 0

47. X
1
1
X
1
1

48. X
1
X
X
1
X
1
2
2
X
2
X 1

49. X
1
X
X
1
X
2
2
3
X
X 3
X
1
X 3
X 2
X
2
X 1
X 3
X
3
X 2
X 1

51. L X1 L
L X1 L
L X
L X X
L X X X

52. L
1
2
3
4
1 2 3 4
2 1 3 4
3 2 1 4

53. L X1 L
L
X
1
1

54. 2 3 4
1
5
9
6 7 8
10
11
No symmetries

55. GF
1
2
3
4
5
1
2
3
4
5
G
F
G
G G

56. R LX R
2
1
3
4
5
6 7

57. F G

58. F '
1
2
3
4
5
F
1
2
3
4
5

59. F '
L L L
'
C L
'

60. F |n|
1 2
3
n
5
F
1
2
3
4
5
n
… …
… /
= n

61. Non regular speciesNon regular species

62. E
1 2
3
5
E
1
2
3
4
5
4

63. C
1 2
3
5
C
4
…

64. E
CEP

65. C
P CE
L
'C
L P

66. GF
1
2
3
4
5
F G
4
1
3
2
5 G
4
1
3
2
5
G
4
1
3
2
5

67. GF
EE |2|
EX|2|

68. in code?

74. Maths…

75. "seems it is doable
to find such a
function,
but needs work."
"we have a
noneasy
question"

76. My strategy

77. number of partitions having p sets
…

78. int partitions of 6
change of representation
3-int partitions of n

79. Given an index k

81. Proper notion
of size
Uniformity
Species combinators
for constraints

82. Eric Torreborre / FP-Syd
Data generation
The hard parts
Thanks!