No, and there's at least one reason why it would complicate matters to allow it. Nested functions are typically expected to have access to the enclosing scope. This makes it so the "stack" can no longer be represented with a stack data structure. Instead a full tree is needed.
Consider the following code that does actually compile in gcc as KennyTM suggests.
#include <stdio.h>
typedef double (*retdouble)();
retdouble wrapper(double a) {
double square() { return a * a; }
return square;
}
int use_stack_frame(double b) {
return (int)b;
}
int main(int argc, char** argv) {
retdouble square = wrapper(3);
printf("expect 9 actual %f\n", square());
printf("expect 3 actual %d\n", use_stack_frame(3));
printf("expect 16 actual %f\n", wrapper(4)());
printf("expect 9 actual %f\n", square());
return 0;
}
I've placed what most people would expect to be printed, but in fact, this gets printed:
expect 9 actual 9.000000
expect 3 actual 3
expect 16 actual 16.000000
expect 9 actual 16.000000
Notice that the last line calls the "square" function, but the "a" value it accesses was modified during the wrapper(4) call. This is because a separate "stack" frame is not created for every invocation of "wrapper".
Note that these kinds of nested functions are actually quite common in other languages that support them like lisp and python (and even recent versions of Matlab). They lead to some very powerful functional programming capabilities, but they preclude the use of a stack for holding local scope frames.