Eric Torreborre / FP-Syd

Data generation

The hard parts

NOT SO SIMPLE

Recursive data structuresPolymorphic functions

Constrained data

Recursive data structures

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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

Generate trees

Generate treesDepth?

Width?

Balanced?

Coverage?

Composition?

Uniformity?

Constraints?

Performance?

programs

well-typed

Size and dimension

BoltzmannModel

Combinatorialspecies

Same size bound

505 valueson average for n=100

18 constructors

P = 1 / 89

P=1/4

P = 1 / 9

generating function

System of equations

solution + singularity

size in O(n)

Enumerate structures

Sample uniformly

Set of labels

Family ofstructures

2

1

3

4

5

6

2

1

3

4

5

6

2

1

3

4

5

6

b

a

c

d

e

f

b

a

c

d

e

f

b

a

c

d

e

e

2

1

3

4

5

6

2

1

3

4

5

6

Regular species

0

1

X

11

F

1

G

23

45

F1

23 4

5

G1

23 4

5

X

1

0

X1

X

1

1

X1

1 1

1

1

n 11 1 …

n 11 1 …

n 11 1 …

F

1

G

23

45

F

1

2

3

4

5

G

X 0

X

1

1

X1

1

X

1

X

X1

X

1

2

2

X2

X1

X

1

XX

1X

2

2

3

XX

3

X1

X3

X2

X2

X1

X3

X3

X2

X1

L X1 L

L X1 L

L X

L X X

L X X X

L

12

3

4

1 2 3 4

2 1 3 4

3 2 1 4

L X1 L

LX

1

1

2 3 4

1

5

9

6 7 8

10 11

No symmetries

GF

12

3

45

1

2

3

4

5

G

F

G

G G

R LX R

2

1

3

4

5

6 7

F G

F '

12

3

45

F

1

2

34

5

F '

L L L'

C L'

F |n|

1 23

n5

F

1

23

4

5 n

… …

… /= n

Non regular species

E

1 23

5

E

1

23

4

54

C

1 23

5

C

4…

E

CEP

C

P CE

L 'C

L P

GF

12

3

45

F G

4

1 3

25 G

4

1 3

25

G

4

1 3

25

GF

EE |2|

EX |2|

in code?

Maths…

"seems it is doable

to find such a function, but needs

work."

"we have a noneasy

question"

My strategy

number of partitions having p sets

…

int partitions of 6

change of representation

3-int partitions of n

Given an index k

Proper notion of size

Uniformity

Species combinators for constraints

Eric Torreborre / FP-Syd

Data generation

The hard partsThanks!