Algorithms as objects?

[Kreso]

I am writing an application that essentially calculates set of numbers,
say N1, N2, ..., where they can be calculated by several different 
algorithms. (One should be able to choose the algorithm at run time.) 
In each algorithm one starts from a set of functions, say f1, f2, ...,
which are then transformed into some other functions g1(f1, f2, ..),
g2(f1, f2, ...), ... , then maybe transformed once more and result is 
obtained by evaluating final functions. 
  I can naturally think about this as a collection of transformation
blocks, which have functions as input and output, and which can be
put together to get the final results. However, I am not sure
how to program this, especially since one cannot subclass function
type. To be clear let me give simplified example of what is needed:

f(x) has unknown shape, so one would like to try, say

f1(x) = ax - b x**2   or    f2(x) = a sin(b*x),

where a and b are variable parameters.

Then, one would like to create, with known k(x,y), function g(x) 
in one of two ways:
 
g1(x) = k(x, x)*f(x)  or   g2(x) = integrate(k(x, y) * f(y), y=0..1),

and finally evaluate N=g(1) as result. In this simple example 
there are 4 different algorithms  for f(x) -> g(x) -> N, and one
should be able to simply choose between them, e.g. by calling
N(g1, f2, (a,b)).

In practice algorithm is not necessary so linear,  but is
generally tree-lika:

(a,b) -> f1(x) --->g1(x)---+
                           |--> h(x) --> N
(c,d) ---+--> g2(x)--------+
         |
 f2(x) --+


It would be nice to have some class of function-objects,
that f1(x), .., g1(x), ... could be members/instances of so that common
operations on these functions could be possible (checking
that they satisfy some necessary properties, plotting them, ...),
and then second "class" of transformations/methods operating on
these objects.
I seem to be confused by the fact that I would like to somehow treat
algorithms as objects (so that one can experiment with different
algorithm systems) but I don't have clear picture how to do it.
I am just brainstorming for ideas. Any advice is welcome.