Implement renderer from SPN to SPML

[probsys]

Implement renderer from SPN to SPML

[fsaad]

Progress in https://github.com/probcomp/sum-product-dsl/compare/20200417-fsaad-render-imp

[fsaad]

#wont-fix

[fsaad]

Reopening---in the past I was trying render a Command from the Python AST (interpreter.py) to an SPML program, which turns out to be rather hard.

However, what I really meant to render is an SPN into SPML program, which is much easier.

The main issue is that we need to expose the branching variables while still ensuring SPN consistency (children of sum nodes have identical scope). But this situation can be an issue since different components of a sum may not have the same branching topology, and so latent variables that "exist" in one branch may not exist in another branch, for example:

The blue letter "b" indicates each location where a new branching variable is introduced in the scope. It is now obvious that the SPN is not consistent, since the left-subtree has variables b2, b3 that do not exist in the right subtree.

One solution is to define give all branching variables unique and define them at the top of the program. Not so bad. The resulting SPN is:

which now easy to render in SPML:

b1 ~ ...
b2 ~ ...
b3 ~ ...
if (b1 == 1):
    if (b2 == 2):
        x
    else
        x '
    if (b3 == 1):
        y
    else
        y '
else:
    x
    y

It may be a bit confusing that we sample branch variables for all sum nodes, even though they are effectively unused in program executions. In the example above, if we go down the right subtree, it's a bit strange to have sampled (b2, b3), but there is no harm in doing so other than a bit of confusion, and more verbose queries for constraining a path---i.e., to constrain the SPN for b2 == 1, we need to in practice constrain the whole path (b1==0 and b2==1).

[fsaad]

• render conditioned reals
• render environments for reals