Basic if else statement in Makefile

Change your make target to this (adding semicolons):

check:
    if [ -z "$(APP_NAME)" ]; then \
        echo "Empty"; \
    else \
        echo "Not empty"; \
    fi

For evaluating a statement in a shell without newlines (newlines get eaten by the backslash \) you need to properly end it with a semicolon. You cannot use real newlines in a Makefile for conditional shell-script code (see Make-specific background)

[ -z "$(APP_NAME)" ],
echo "Empty",
echo "Not empty" are all statements that need to be evaluated (similar to pressing enter in terminal after you typed in a command).

Make-specific background

make spawns a new shell for each command on a line, so you cannot use true multi line shell code as you would e.g. in a script-file.

Taking it to an extreme, the following would be possible in a shell script file, because the newline acts as command-evaluation (like in a terminal hitting enter is a newline-feed that evaluates the entered command):

if
[ 0 ]
then
echo "Foo"
fi

Listing 1

If you would write this in a Makefile though, if would be evaluated in its own shell (changing the shell-state to if) after which technically the condition [ 0 ] would be evaluated in its own shell again, without any connection to the previous if.
However, make will not even get past the first if, because it expects an exit code to go on with the next statement, which it will not get from just changing the shell’s state to if.

In other words, if two commands in a make-target are completely independent of each other (no conditions what so ever), you could just perfectly fine separate them solely by a normal newline and let them execute each in its own shell.

So, in order to make make evaluate multi line conditional shell scripts correctly, you need to evaluate the whole shell script code in one line (so it all is evaluated in the same shell).

Hence, for evaluating the code in Listing 1 inside a Makefile, it needs to be translated to:

if \
[ 0 ]; \
then \
echo "Foo"; \
fi

The last command fi does not need the backslash because that’s where we don’t need to keep the spawned shell open anymore.