How to replace ~ with $HOME properly using sed inline?

The idea is to transform this ~/.local/bin let's say to this /home/user1/.local/bin

so I have a Makefile that basically a try to get it to work but it doesn't

system: 
	sed -i 's/~/$HOME/g' myapp.desktop
	

[Desktop Entry]
Version=0.4
Type=Application

Name=Desktop App

Exec=~/.local/bin/desktop_app
Terminal=false

Since your own code is generating the tilde-including pseudo-path, I guess you can be confident of the form. This is important, because in general, the shell's tilde expansion behavior is not wholly consistent with the simple translation you want to perform. The shell's tilde expansion differs in at least these ways:

• it applies only when the tilde is the first character of the word
• it affects a prefix of the subject word up to but excluding the first slash (/), if any
• it affects only a prefix such as described above, not any other tilde appearances in the subject word

A simple substitution such as your example sed command suggests will have the same effect as the shell's tilde expansion on some possible inputs, but different effects on others, so again, it's important that you are controlling the form of the input.

For your particular case, you seem to want the shell to expand $HOME, but single-quoting it suppresses that. On the other hand, you need make to not expand $H (to nothing, probably), so you need to escape the $ from make. The resulting rule might look like this:

system: 
        sed -i "s/~/$${HOME}/g" myapp.desktop

There are other problems with that, though, such as that the -i option is non-portable. Some seds don't have it at all, and behavior varies among those that do have it (BSD-style sed vs GNU sed, for example).

Since you're generating this desktop file via a code generator, however, the first question that comes to mind is why are you not generating it with the wanted Exec path in the first place?

The only answer that make sense to me is that you are generating the desktop file in a separate context from the one(s) in which the software will be installed. In that case, however, the next question is why are you not taking advantage of the standard tools for working with desktop files? In particular, it would be appropos to use desktop-file-install to both install the file into the user's .local/share/applications, and, simultaneously, to set the correct value of the Exec key within. Example:

INSTALL_BIN = "$${HOME}"/.local/bin
INSTALL_DESKTOP = "$${HOME}"/.local/share/applications
install:
        mkdir -p $(INSTALL_BIN)
        mkdir -p $(INSTALL_DESKTOP)
        install -m 0755 desktop-app $(INSTALL_BIN)
        desktop-file-install --dir=$(INSTALL_DESKTOP) --set-key=Exec --set-value=$(INSTALL_BIN)/desktop-app