Gram-Schmidt

I needed a Gram-Schmidt orthogonalization that took an arbitrary
inner-product:

    gschmidt(lind, inprod) := block([iter, n],
      n: length(lind),
      iter(v, m) :=
      if m > n
      then v
      else
      iter(append(v, [lreduce(lambda([a, b], a - b),
            append([lind[m]], makelist(inprod(lind[m], v[i])
                  / abs(inprod(v[i], v[i])) * v[i],
                  i, 1, m - 1)))]),
        m + 1),
      iter([], 1));

For instance:

    (%i8) gschmidt([1, sin(x), cos(x)],
      lambda([f, g], integrate(f * g, x, a, b))),
    a = -%pi/2, b = %pi/2;
                                                     2
    (%o8)                      [1, sin(x), cos(x) - ---]
                                                    %pi

It works; but I'd rather employ the builtin `gramschmidt', if only I
could break the assumption that inner product = dot-product.

Eigen.mac seemed to imply that redefining `innerproduct' might work;
but no avail.

Any suggestions?