Isabelle / HOL sequences: value of types o, seq ', value of nonterminals seq, seqobj, seqcont

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 understanding the meaning of the main elements, namely:

types o, seq '

nonterminals seq, seqobj, seqcont?

Do these types and nonterminals have any "real" analogs? Sequent is represented by the function [o, seq '] => seq', so maybe o and seq 'do not have real copies of the real world?

I read Isabelle's Logic (especially Chapter 4), LNCS 828, the Isabelle / Isar reference manual (especially 8.2 and 8.5 on mixfix substitutions and syntax definitions), but I cannot understand the meaning of these characters, and therefore I cannot understand move forward. Any guidance would be very helpful!

I am trying to implement the monoidal logic http://www.sciencedirect.com/science/article/pii/S1570868314000573 as object logic in Isabelle / HOL, but everything is so separated from the "real world" (as mathematics is done on paper).

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