R help - Jun 2010 - The curious special case of "~ (a + b)/c"

This isn't at all an urgent practical question, but recently while
exploring the details of how R formulas are interpreted, I learned of
this funny special case for how / interacts with +. In all of the
following cases, the multiplication-like operator simply distributes
over addition:
  (a + b):c = a:c + a:c
  a:(b + c) = a:b + a:c
  (a + b)*c = a*c + b*c
  a*(b + c) = a*b + a*c
  a/(b + c) = a/b + a/c

But:
  (a + b)/c = a + b + a:b:c, not a/c + b/c = a + a:c + b + b:c

Chambers and Hastie mention this, but give no explanation (page 29/30,
"Slightly more subtle is...").

So for my own edification, does anyone know/care to speculate about
why (a + b)/c works this way?

-- Nathaniel

The "/" is used for nesting and is defined by
A/B == A + (B %in% A)

thus
(a+b)/c == (a+b) + c %in% (a+b) == a + b + a:b:c

Rich

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