in my work with explicit topological ordering under the presence of loops, i figured this out:
topological ordering is the same as partial ordering. so for two nodes `{a,b}`, when `a -> b`, then `a < b`.
with cyclical dependencies, this no longer makes sense under a linear partial order. if `a -> b, b -> a`, then `a < b < a`.
we need cyclic partial ordering, which is based on cyclic order (https://en.wikipedia.org/wiki/Cyclic_order). now we can express this after all, as `[a, b, a]`.
tarjan's SCC algo is typically used to construct a DAG from a cyclical graph, but its strongly connected components are soup.
as an example, the dependency graph below counts as a single SCC even though we can clearly see it has a substructure, which suggests that {2,5,6,7} should be iterated in a subloop.
the question now is whether ternary relation terms, or something similar, could allow us to describe subcycles.
LRDL presently solves the problem by requiring that the user picks explicit backedges (using `cue` for insertion rather than `then`), which turns the entire cyclical graph into a spanning DAG.
it also requires that we put edges connecting {2,5,6,7} in a dedicated `fold` block which guarantees evaluating this subgraph will reach a fixed point before the parent continues.
this makes execution order "reasonable", but is it the only good solution?
@yesbait been there done that, and it's insufficient. strongly connected components are soup.
the graph below counts as one single SCC even though we can clearly see it has a substructure. no SCC algorithm can catch this relationship.
LR
winden^capsule^batman.group
YesBait