Function of a function

Say, I have some function f[a_,b_,c开发者_如何学C_]=a+b+c. Now I need to define another function,g[f_,d_]=f+d, where the f here should be replaced by the definition of f, resulting in a+b+c+d.

How do I do this? I tried g[f_,d_]=f+d/.f->Definition[f], however that didn't work.

Well, your setup requires that g be a function of a, b, and c, since you explicitly made f a function thereof. Could instead do:

f[a_,b_,c_]=a+b+c;

g[f_,a_,b_,c_,d_] = f[a,b,c]+d

Out[2]= a + b + c + d

Daniel Lichtblau

Just an aside note.

The whole thing makes more sense when both functions share the same arguments, or the arguments for the second function are implicit in the first.

For example:

f[x_] := 1 + 1/x;

g[h_, x_] := h[x]^x;

Limit[g[f, x], x -> +Infinity]  
-> E

Or something like

f[x_] := EuclideanDistance[x, #] &

g[f_, x_] := If[f[2 x]@x < 3, x, 2 x]

g[f, 3]
->6

g[f,2]
->2

Daniel's answer is the right one - it answers what your question should have asked!

But just for fun here's something closer to what your question actually asked.

f[a_,b_,c_] := a + b + c

g[f_, d_] := Catch[Module[{dv},
  Check[dv = DownValues[f], Throw[$Failed], {DownValues::sym}];
  Switch[Length[dv],
         0, Print["No DownValues"]; $Failed,
         1, dv[[1, 2]] + d,
         _?(# > 1 &), Print["More than one DownValue - using the first!"]; 
                      dv[[1, 2]] + d,
         _, Print["huh?!"]; $Failed]]]

test it:

In[3]:= g[f, d]
Out[3]= a + b + c + d

Define another function:

ff[a_, b_, c_] := a b c

In[5]:= g[ff, d]
Out[5]= a b c + d

and give it a second definition:

In[6]:= ff[a_, b_] := a + b
In[7]:= DownValues[ff]
Out[7]= {HoldPattern[ff[a_,b_,c_]] :> a b c, HoldPattern[ff[a_,b_]] :> a+b}

In[8]:= g[ff, d]
During evaluation of In[8]:= More than one DownValue - using the first!
Out[8]= a b c + d

Of course, the fact that you don't pass any arguements to f in g[f_,d_] will (in most cases) make this type of thing pretty pointless...

In the definiton

 f[a_, b_, c_] := a+b+c

look at a, b and c as the first, second and third argument at the function call and NOT symbols a,b or c. Similar as in f := (#1 + #2 + #3)&, the call to f itself (without arguments) will not give desired results.

Perhaps you wanted to do something like this:

f := a+b+c

Now, the f is associated as a sum of a, b and c, which are global symbols and not function arguments. Then,

f+d

will give a + b + c + d and you can use ReplaceAll (or /.) for substitution:

f + d /. a->2x

gives b+c+d+2x. 2 f will give 2 (a+b+c), Sin[f] will give Sin[a+b+c], f-c will give a+b etc...

I also I find it difficult to discern your intent, but this is my interpretation:

f[a_, b_, c_] := a + b + c
g[f_, d_] := f[##] + d &;

g[f, 3]

  (* Out=  f[##1] + 3 &     *)

%[q, r, s]

  (* Out=  3 + q + r + s    *)

g[f, 5][1, 2, 3]

  (* Out=  11    *)

This way, g[f, x] returns a function which passes its arguments to f.