Strict patterns and uniqueness

[Zolmeister]

This is perhaps more of a question than a feature.

My initial implementation of SetReplace treated pattern members as unique, and treated the resulting set as a unique set.

e.g. Given
{{1, 2}} -> {{2, 1}, {1, 3}}

These members would match
{1, 2}, {2, 3}, {3, 1}

However these would not
{1, 1}, {2, 2}, {3, 3}

Additionally I deduplicated set members, such that {{1, 1}, {1, 1}} collapses to {{1, 1}}.

I'd like to understand the rationale behind the looseness of the pattern matching and plurality of set members.

[maxitg]

There is no real justification for either of these. It's just a question of simplicity, and which kind of systems can emulate one another easily.

The pattern members are treated here the same way as the pattern members in Replace, i.e., {1, 1} matches {a_, b_}, similarly, {{1, 2}} -> {{2, 1}, {1, 3}}, which corresponds to {{a_, b_}} :> Module[{c}, {{b, a}, {a, c}}] matches {{1, 1}}.

This also makes it easier to find good initial conditions, as multiple copies of the same self-loop are more likely to match repeatedly than, i.e., the left-hand side of the rule.

As for deduplication, this is related to the question of whether the history of an edge should be used to identify it, see also #146. If we do deduplicate edges, however, it would mean that a single edge could have multiple creator events, which in turn would introduce timelike loops in the causal graph.

I think it could be useful to add options to WolframModel to allow this kind of evolution (i.e., "AllowDuplicateVertices" and "MergeIdenticalEdges"), however, this issue should be split in two, and these are independent features of the evolution.