Treating same inputs on duplicate functions also arises in the treatment of counterfactuals (since one duplicates the causal graph across worlds of interest). The treatment I am familiar with is systematic merges of portions of the counterfactual graph which can be proved to be the same. I don't really understand why this issue is about logic (rather than about duplication).

What was confusing me, however, was the remark that it is possible to create causal graphs of mathematical facts (presumably with entailment functioning as a causal relationship between facts). I really don't see how this can be done. In particular the result is highly cyclic, infinite for most interesting theories, and it is not clear how to define interventions on such graphs in a satisfactory way.