I am trying to understand https://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/library/Sequents/Sequents/Sequents.html and https://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/library/Sequents/Sequents/ILL.html and I have problems with the understanding the meaning of the basic items, namely:
types o, seq'
nonterminals seq, seqobj, seqcont?
Do these types and nonterminals have some "real world" counterparts? Sequent is represented by function [o, seq']=>seq', so, maybe o and seq' do not have any real world counterparts?
I am reading "Isabelle's Logics" (http://isabelle.in.tum.de/dist/Isabelle2016-1/doc/logics.pdf especially chapter 4), LNCS 828, Isabelle/Isar reference manual (especially 8.2 and 8.5 about mixfix notations and syntax definition), but I can not grasp the meaning of those symbols and therefor I can not move forward. Any guidance would be very helpful!
I am trying to implement monoidal logic http://www.sciencedirect.com/science/article/pii/S1570868314000573 as a object logic in Isabelle/HOL, but everything is so detached from the "real world" (how the mathematics is being done on paper).