See Girard, The Blind Spot: Lectures on Logic (2011) for some attempts at tackling this question. (in particular, his "proof nets" attempt to have a canonical f

See Girard, The Blind Spot: Lectures on Logic (2011) for some attempts at tackling this question. (in particular, his "proof nets" attempt to have a canonical form, such that we can identify differently drawn concrete proof nets as representing the same abstract proof) https://en.wikipedia.org/wiki/Proof_net https://en.wikipedia.org/wiki/Proof_net