The annihilating interaction between abstraction and application nodes is well-known in the area of interaction net research to ~correspond to β-reduction, as is also explained in the associated research paper [1].

α-conversion is not required in interaction nets. η-reduction is an additional rule not typically discussed, but see for example [2].

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

[2] https://www.sciencedirect.com/science/article/pii/S030439750...