Why this simple makefile does not rebuild the source on changes?

Question

I wrote this simple makefile, which works fine until I want to do some changes and apply them into binary. Then I need to do 'make clean' and 'make' again, because obj. file will not be rebuilt. Althought it seems like a simple task so far I failed to modify it in order to make obj. file rebuild implicitly (So I can write only 'make' when I modify source).

COMPILER=g++-5.3
CXXFLAGS=-std=c++11 -O2 -pedantic

build : a.o
     $(COMPILER) a.o -o a

a.o:
     $(COMPILER) $(CXXFLAGS) -c a.cpp -o a.o

clean :
    rm -f *.o *~ a

Edit: I tried changes suggested by Omada (I tried the same myself before I wrote this question) and this is result:

me@pc: ~/mypath$ cat a.cpp
#include <iostream>
int main(int argc, char* argv[])
{
    if ( argc!=2 ){
        std::ceaaarr<<"Prrogram expects 1 argument\n";
        return 1;
    }
    return 0;
}me@pc: ~/mypath$ make
g++-5.3 a.o -o a
me@pc: ~/mypath$ cat Makefile
#init

COMPILER=g++-5.3
CXXFLAGS=-std=c++11 -O2 -pedantic

build: a.o
        $(COMPILER) a.o -o a

a.o: a.cpp
        $(COMPILER) $(CXXFLAGS) -c a.cpp -o a.o

clean:
        rm -f *.o *~ a

Answer 1

Since you never told the makefile that a.o depends on a.cpp, it won't be able to determine that when a.cpp changes, it should rebuild a.o.

To fix this change

a.o:
    $(COMPILER) $(CXXFLAGS) -c a.cpp -o a.o

to this

a.o: a.cpp
    $(COMPILER) $(CXXFLAGS) -c a.cpp -o a.o

Let me know if it doesn't work, I'm a bit rusty on my makefiles.