I've always wondered if there's more to FP than (more or less) point-free style with an associated algebra. TFA seems to stop just when it might get interesting. Did Backus ever develop (or aim for) a notion of semantic completeness, e.g. Cartesian closure or whatever works [0] for Hughes's Arrows? The last has the interesting property of being foundationally point-free but also supporting a syntax with variables (with non-standard scoping rules). Which perhaps refutes Backus's original concerns.

[0] https://en.wikipedia.org/wiki/Arrow_(computer_science)

Author here. This is work-in-progress, not linked from top level. I'll keep working.

TFA contains a great number of links to downloadable interesting research papers.