update this example

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function gen_sorted_list(size, lo, hi)

size == 0 && return DistNil(DistUInt32)

don't learn their probabilities (this is on purpose - we could).

all sizes to use the same probability.

over sizes.

don't learn their probabilities (this is on purpose - we could).

@dice_ite if flip_for(size)

DistNil(DistUInt32)

else

Try changing the parameter to flip_for to a constant, which would force

all sizes to use the same probability.

x = unif(lo, hi)

DistCons(x, gen_sorted_list(size-1, x, hi))

end

INIT_SIZE = 5

over sizes.

DATASET = [DistUInt32(x) for x in 0:INIT_SIZE]

list = gen_sorted_list(

INIT_SIZE,

DistUInt32(1),

DistUInt32(INIT_SIZE),

)

list_len = length(list)

display(pr(list_len))

println()

train_group_probs!(bools_to_maximize, 1000, 0.3) # epochs and lr

println("Learned flip probability for each size:")

display(get_group_probs())

println()

display(pr(list_len))

println()

for _ in 1:3

print_tree(sample(list))

println()

end

Distribution before training:

0 => 0.49999999999999994

1 => 0.24999999999999972

2 => 0.12499999999999986

3 => 0.062499999999999924

4 => 0.03124999999999996

5 => 0.03124999999999996

1 => 0.5

2 => 0.33333333333333337

3 => 0.25000000000000006

4 => 0.19999999999999996

5 => 0.16666666666666663

2 => 0.1666666666666666

3 => 0.1666666666666666

0 => 0.16666666666666646

1 => 0.16666666666666646

4 => 0.16666666666666646

5 => 0.16666666666666646

Cons

├── 1

└── Cons

├── 2

└── Cons

├── 3

└── Cons

├── 3

└── Cons

├── 4

└── Nil

├── 3

└── Cons

├── 3

└── Cons

├── 3

└── Cons

├── 3

└── Cons

├── 5

└── Nil

├── 3

└── Cons

├── 5

└── Nil

==#

https://github.com/Juice-jl/Dice.jl/blob/9176da7528b183a5c07240f801c1478ab1b3f000/examples/qc/examples/demo_sortednatlist.jl#L1

# TODO: update this example

# # Demo of using BDD MLE to learn flip probs for a sorted nat list of uniform length.

# using Dice

# # Return a List
# function gen_sorted_list(size, lo, hi)
#     size == 0 && return DistNil(DistUInt32)
    
#     # The flips used in the uniform aren't tracked via flip_for, so we
#     # don't learn their probabilities (this is on purpose - we could).
#     @dice_ite if flip_for(size)
#         DistNil(DistUInt32)
#     else
#         # Try changing the parameter to flip_for to a constant, which would force
#         # all sizes to use the same probability.
#         x = unif(lo, hi)
#         DistCons(x, gen_sorted_list(size-1, x, hi))
#     end

# end

# # Top-level size/fuel. For gen_list, this is the max length.
# INIT_SIZE = 5

# # Dataset over the desired property to match. Below is a uniform distribution
# # over sizes.
# DATASET = [DistUInt32(x) for x in 0:INIT_SIZE]

# # Use Dice to build computation graph
# list = gen_sorted_list(
#     INIT_SIZE,
#     DistUInt32(1),
#     DistUInt32(INIT_SIZE),
# )
# list_len = length(list)

# println("Distribution before training:")
# display(pr(list_len))
# println()

# bools_to_maximize = [prob_equals(list_len, x) for x in DATASET]
# train_group_probs!(bools_to_maximize, 1000, 0.3)  # epochs and lr

# # Done!
# println("Learned flip probability for each size:")
# display(get_group_probs())
# println()

# println("Distribution over lengths after training:")
# display(pr(list_len))
# println()

# println("A few sampled lists:")
# for _ in 1:3
#     print_tree(sample(list))
#     println()
# end

# #==
# Distribution before training:
#    0 => 0.49999999999999994
#    1 => 0.24999999999999972
#    2 => 0.12499999999999986
#    3 => 0.062499999999999924
#    4 => 0.03124999999999996
#    5 => 0.03124999999999996

# Learned flip probability for each size:
#    1 => 0.5
#    2 => 0.33333333333333337
#    3 => 0.25000000000000006
#    4 => 0.19999999999999996
#    5 => 0.16666666666666663

# Distribution over lengths after training:
#    2 => 0.1666666666666666
#    3 => 0.1666666666666666
#    0 => 0.16666666666666646
#    1 => 0.16666666666666646
#    4 => 0.16666666666666646
#    5 => 0.16666666666666646

# A few sampled lists:
# Cons
# ├── 1
# └── Cons
#     ├── 2
#     └── Cons
#         ├── 3
#         └── Cons
#             ├── 3
#             └── Cons
#                 ├── 4
#                 └── Nil

# Cons
# ├── 3
# └── Cons
#     ├── 3
#     └── Cons
#         ├── 3
#         └── Cons
#             ├── 3
#             └── Cons
#                 ├── 5
#                 └── Nil

# Cons
# ├── 3
# └── Cons
#     ├── 5
#     └── Nil
# ==#