Generalize incremental hom search to work for nonmonic matches and rules #72
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The key computational challenge here is enumerating all epimorphisms.
The gist of this idea is that you work in an arrow schema, where the codom copy of the schema represents a set of equivalence classes for each part (but there are also morphisms between these sets equivalence classes - this is important for naturality!). We want to work up to isomorphism of the codomain but not the domain, so we add an attribute
_Fix :: Int
that bakes in the id of everything in the domain as real data.We initialize the tree search with the most refined partition, where the data in codom portion is identical to the data in the dom portion. The data in the domain portion never changes throughout the search, but we iteratively take pairs of equivalence classes and quotient them until we arrive at the terminal object.
Important for this complexity to not blow up is using the nauty hash, as pushouts are unique only up to isomorphism.