Why does this work? (overloads)

["Jerry" <lanceboyle@qwest.net>]

(1) Why does the following work?
(2) Have I done something stupid or dangerous?

I have written some overloads to +, -, * / to make doing some vector-
matrix
calculations look more algebraic. I have also made some overloads to
allow
some element-by-element operations so that I can do Matlab-like
things,
such as "multiplying" two vectors of the same length and getting a
vector
back.

So here are a few lines of code with a couple declarations from the
G.3 Annex of Ada 2005. Note that the line that I originally wrote to
test
some of these overloads was this, involving some complex entities
  H := Two_Pi / (Two_Pi + j * Two_Pi * f * x);
(j = sqrt(-1.0)) but I think the simplified line for H below captures
the
essence of my question.


Here are a few lines of code.


-- From a-ngrear.ads (Ada 2005, Generic Real Arrays
-- instanciated with Long_Float)...
type Real_Vector is array (Integer range <>) of Real'Base; -- Vectors
function "*" (Left, Right : Real_Vector) return Real'Base; -- Inner
product


-- From some of my own overloads...
function "*" (x, y : Real_Vector) return Real_Vector; -- element-by-
element
function "+" (a : Long_Float; x : Real_Vector) return Real_Vector;


-- Some declarations...
f, x, H : Real_Vector(0 .. NN - 1);
a : Long_Float;


-- And finally, two lines of calculation...
H := 1.0 + f * x; -- Adds scalar, 1.0, to a vector using my overload
above.
a := 1.0 + f * x; -- Adds scalar, 1.0, to another scalar, an inner
product.


I get the results that I expected but I feel a little lucky.

Why when calculating H doesn't the compiler interpret f * x as an
inner
product then generate an error, after adding 1.0, when trying to make
the
assignment to H which is a vector?

Obviously the compiler figures out which of the * operators to use
depending on the assigned-to variable. Is this reliable for more
complicated
calculations? I wonder if it is possible to create an ambiguity that
would
be resolved "in the wrong way" and I would get incorrect results.

Regards,
Jerry

 ___
/o|o\
 (o)