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> there's an easy way to translate LC to IN

While easy, it sadly doesn't preserve semantics. Specifically, when you duplicate a term that ends up duplicating itself, results will diverge.

There exist more involved semantics preserving translations, using so-called croissants and brackets, or with the recent rephrased approach of [1].

[1] https://arxiv.org/abs/2505.20314





> While easy, it sadly doesn't preserve semantics.

There is actually an easy way that does preserve semantics at least to WHNF - it's called closed reduction. Mackie has worked on it a bunch (see some resources [1]).

An even simpler implementation is Sinot's token passing.

The problem with both of these approaches is the decreased amount of sharing and potential for parallelism, which is typically the reason for using interaction nets in the first place.

[1] https://github.com/marvinborner/interaction-net-resources?ta...




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