> "the accounting spreadsheet abstracts away all of the calculus because all the numbers are written down exhaustively"
I'm not even sure what the meaning is supposed to be, because I would not expect to use a spreadsheet to do calculus. (Of course there are ways of forcing calculus into a spreadsheet, but I wonder if you just meant 'calculation'.) Here I would say that it is absolutely relevant to speak of a spreadsheet abstracting away the details of a computation: the logic of the spreadsheet will probably refer often to the contents of cells, without worrying about what the contents are, and that is very definitely a kind of abstraction.
I would certainly not call the process of entering numbers into a spreadsheet an abstraction; but it seems to be the opposite of what type theory does. For example, type theory allows general reasoning about families of types, without reasoning case by case for each individual one. This seems to be the very essence of abstraction (in which capacity it is, conceptually, not completely distinct from the formulas in a spreadsheet).
If you see no abstraction, only concreteness, in type-theory notation, I suspect that is more an indication that you have learned to see through the abstraction than that it isn't there.