In case it wasn't obvious, PDF *is* Postscript!
It's *portable*
postscript.
Actually, significantly less portable in someways; for example, a PDF
is far more likely to be a binary file rather than a text file (as
compared to a PostScript file).
While I haven't looked into it in enough detail to be sure, I suspect
that PDF is a rather emasculated subset of PostScript - that it's PS
subsetted down to the point where it's no longer a general-purpose
programming language with a heavy page-description slant, but rather a
page-description language that cannot be used for general-purpose
programming.
Indeed, it would almost have to be for random access to the pages of a
document to be possible. Deciding whether a given piece of PostScript
code (such as the "showpage" that prints a page) is executed is, except
for interpreter limits, equivalent to the halting problem - and in
particular can, in principle, depend on everything earlier in the file.
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