Are name, strict and internal, and structural equivalences defined in PostScript?
How is type equivalence defined in PostScript for each data type?
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I have no idea what you are asking here really. Names in PostScript are exactly that, name objects, they aren't 'equivalent' to anything else. You can use 'cvn' to convert other types of object into names, but that doesn't mean they are 'equivalent'.
Names are quite clearly defined in the PLRM, syntactically they are a '/' character followed by non-white space characters, the first white space (or certain other tokens, such as '{') terminates the name definition. The internal representation in the language the interpreter is written in is opaque, you can't see what it is and you have no need to.
There is no 'strict' or 'internal' keyword in PostScript, and PostScript doesn't support structures. Perhaps you could post an example PostScript program to clarify your question.