[stack] Why is point-free form so interesting?

I have been struggling to formalize/rationalize my intuition that
point-free form is somehow better than a form with names from the
standpoint of tools (e.g. analyzers, compilers, translators,
optimizers, etc.). Note: this is completely separate from any
statements about the usability of point-free form for programmers.
That is a controversial idea that I would rather avoid debating (I
have nothing useful to add to that debate anyway)

Here are some bullet points that describe what I percieve to be the
main advantages of point-free form:

- less ambiguity (is foo a parameter or definition?)
- fewer evaluation rules (no alpha-conversion, no beta-conversion)
- flat structure versus tree
- maps more nicely to imperative programs: semi-colon (or in some
languages newline, and sometimes comma) is essentially a composition
operator
- syntactic analysis can be performed on tokens rather than parse tree
- fewer parantheses: all interesting computations are compositions,
rather than applications.
- ease of transformation
- rewriting rules are fundamentally easier (linear as opposed to trees)

Any other additions to this list, corrections, or clarifications would
be much appreciated!

One question is: can we reasonably claim with any formality that a
linear form is somehow easier to work with than a tree?

Cheers,
Christopher
http://cdiggins.com