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I have written a lot of XSL code which seems to be a pure functional language. (Can't change values once assigned, but you can do math an call functions etc.) I wonder how many other domain specific languages are functional?
I think Microsoft Excel would be the most common example.
If you do not use Macros. And spreadsheets are a cumbersome form of computation.
On the contrary, spreadsheets are a cool model of computation. They're live - you can update the value of any variable (cell) and all the other references update automatically. It's a dataflow model.

See, for example, the Cells project at http://common-lisp.net/project/cells/

Cool and cumbersome do not contradict each other.
Does make referential transparency a functional language?
Yes.
I disagree. Functions as first class values are more important.