That won't help fund the next season, or genre, or whatever you value enough to watch.
edit: I think "vote with your wallet" is the best influence for profit based entertainment, since they follow the money. Whoever is paying is who they will follow.
Ahh, well! That's a trickier problem! You need a bidirectional system that has unification for metavariables, and then some system for handling unsolved metavars. But to do that requires a more complicated set up. The goal of the post was to introduce the core ideas and show that it's relatively simple to do decent chunks of this stuff. :)
Indeed! Tho this is only half the problem, because `T` there includes metavariables, so it's not a type but rather a schema at the meta-level for types. What we'd like is something like `forall a b c. (b -> c) -> (a -> b) -> a -> c` so that composition can be used at arbitrary choices of the types. So like, while we can use this composition function at any particular place we need composition, we can't define `compose` to have this type because the first use site will force the metavars to have a particular value and then we get a nasty global monomorphism. We need to explicitly have metavariables in the language itself, rather than at the metalevel of doing the synthesis/checking.
mm.. perhaps I'm just not familiar enough with prolog, but I don't think it's possible to extract out a set of Prolog-level metavariables and compute over them? This is what's necesary to turn something like `_G947 -> _G947` into `forall a. a -> a`. but probably I just don't know enough. cool if you can, tho!
That extraction is what the term_variables/2 predicate does that I use in my code. It gives you a list of all unbound variables in the given term. To simulate the quantification, I then just add that list in front of the term with the ^ operator (which has no semantics, it is just the traditional constructor for these things).
So for `_G947 -> _G947` I get the variable list `[_G947]` and use it to represent the universally quantified term as `[_G947]^(_G947 -> _G947)`. If you want to display this with nicer variable names, just substitute names of your choice for the variables in the quantifier list.
Oh! Was Murray Shanahan's lab involved with this? Cool. I've chatted with Murray a very tiny bit on twitter about this all. That paper is part of what inspired me to write this blog post, because I was dissatisfied with the approach they propose.
It felt to me like they had found a way to restrict "symbolic" data to a very narrow domain where issues like hierarchical structure was totally absent, and vectorial representation was therefore quite straight forward, and I wanted to figure out an alternative. Instead of restricting the kinds of symbolic data involved, do the full spectrum. I had the symbolic vector idea in my head for about two years as an answer to the representation problem, but I hadn't seen what the right answer was to the other aspects, at least not clearly. But that paper motivated me to start thinking about it again, and this time I saw the answer. :)
Reading a graph back can't be done with any certainty, nor is it intended to be done. It's a representation that's intended to be used to build inputs to ML systems, not outputs. Building symbolic outputs should be done via the other techniques mentioned in the blog post (eg. structural editing), that way you can take advantage of notions of correctness inherent in the symbolic representation.
Regarding handling lossiness, it's not clear to what extent it needs to be handled, but the `k` mentioned in the definition of symbolic vectors is a parameter, and the larger `k` is, the less lossy the representation.
