make does not rebuild target on header file modification - header

Question

I have a makefile of this kind:
program: \
a/a.o \
b/b.o
$(CXX) $(CXXFLAGS) -o program \
a/a.o \
b/b.o
a.o: \
a/a.cpp \
a/a.h
$(CXX) $(CXXFLAGS) -c a/a.cpp
b.o: \
b/b.cpp \
b/b.h
$(CXX) $(CXXFLAGS) -c b/b.cpp
So in the directory of the makefile I have two subdirectories a and b
that contain respectively a.h, a.cpp and b.h, b.cpp.
The problem is that if I modify a .cpp file, issuing a make rebuilds the target program
but if I modify an .h file make do not rebuilds anything but says
make: `program' is up to date.
I can't understand why, because the .h files are in the prerequisites line
along with the .cpp files.
Interestingly, if I issue a make on an object file target like
$ make a.o
instead, the modifications to a/a.h
are detected and the target a/a.o is rebuild.
Where is the problem?

Answer 1

The subdirectories that you added to the question later are causing the problem indeed. The target program depends on a/a.o and b/b.o, but there are no explicit rules to make those to .o files -- only the targets a.o and b.o are present but those are not in the subdirectories.
Therefore, make will look for implicit rules to build a/a.o and b/b.o. That rule does exist, you will see it being found when you run make -d. That implicit rule depends on a/file_a.cpp only, not on a/file_a.h. Therefore, changing a/file_a.cpp will make a/a.o out of date according to that implicit rule, whereas a/file_a.h will not.
For your reference, the make User's Manual has a section Catalogue of Implicit Rules. That also explains that you can use the argument --no-builtin-rules to avoid that implicit behavior. If you use that, you will see that make can not find any rules to make a/a.o and b/b.o.
Finally, running make a.o will run the recipe for the target a.o as defined in your makefile. That target does have a/a.h as its prerequisite so any change to that file will result in a recompile. But essentially, that has nothing to do with the target program, which has different prerequisites.