See https://arxiv.org/abs/0903.0340 for a basic introduction to the issues, and https://arxiv.org/abs/0908.3347 for a slightly more extensive treatment, also mentioning proof nets. This does not explicitly say that these diagrams can be understood as the equivalent to sequences in something FORTH-like, but this is in fact what the papers are pointing out in a general sense, so I see it as a rather trivial remark.
