Having written both a PDF and PS interpreter, I can tell you that PDF command streams (the stuff that tells the viewer how to draw the page) has no loops or variables. You can't do calculations, the closest being PostScript functions, but you can't directly use the output of such a function (it's used to calculate colors).
Now, to be fully PDF compliant, you must support a limited subset of PostScript commands. There at least you can do math, but loops need not be implemented, just a few math related operators.
In theory, Type1 fonts is just PostScript code, but PDF viewers never actually execute that code.
TrueType fonts have executable code that is executed, but I don't know if it's Turing-complete.