You've defined purely functional programming, which seems to be the increasingly common meaning of FP. The original definitions only explicitly refer to constructing programs by combining functions:
A History of Lisp http://jmc.stanford.edu/articles/lisp/lisp.pdf
> LISP is characterized by [...] composition of functions as a tool for forming more complex functions.
Can programming be liberated from the von Neumann style? https://dl.acm.org/doi/pdf/10.1145/359576.359579
> informal description of a class of simple applicative programming systems called functional programming (FP) systems, in which "programs" are simply functions without variables.
However, Backus defines his functional programming system mathematically, which could reasonably be construed as referentially transparent.