notes: clarified note about parameter expansion in here doc

Still need to see if we have to implement that..

NOTES.md

@@ -459,15 +459,56 @@ source until a line containing only word (with no trailing blanks) is seen. All
 of the lines read up to that point are then used as the standard input for a
 command.
 
-TODO: The following paragraph may not apply fully to our project, check it again!
-
 No parameter and variable expansion, command substitution, arithmetic expansion,
-or filename expansion is performed on word. If any part of word is quoted, the
-delimiter is the result of quote removal on word, and the lines in the
-here-document are not expanded. If word is unquoted, all lines of the
-here-document are subjected to parameter expansion, command substitution, and
-arithmetic expansion, the character sequence \newline is ignored, and ‘\’ must
-be used to quote the characters ‘\’, ‘$’, and ‘`’.
+or filename expansion is performed on word. 
+
+If any part of word is quoted, the delimiter is the result of quote removal on
+word, and the lines in the here-document are not expanded. If word is unquoted,
+all lines of the here-document are subjected to parameter expansion, and the
+character sequence \\newline is ignored.
+
+This is the correct behaviour for quoting and parameter expansion:
+```shell
+bash-5.2$ cat << EOF
+> hello
+> $$
+> EOF
+hello
+1491742
+bash-5.2$ cat << "EOF"
+> hello
+> $$
+> EOF
+hello
+$$
+bash-5.2$ cat << 'E'OF
+> hello
+> $$
+> EOF
+hello
+$$
+bash-5.2$ cat << $USER
+> hello
+> khais
+> $USER
+hello
+khais
+bash-5.2$ echo $USER
+khais
+bash-5.2$ cat << "$USER"
+> $USER
+```
+
+TODO: do we need to ignore \\newline? subject says \\ is not required..
+
+If we have to implement it, this is the correct behaviour:
+```shell
+bash-5.2$ cat << EOF
+> hello \
+world
+> EOF
+hello world
+```
 
 ## Definitions
 cf. [Bash Reference Manual](https://www.gnu.org/savannah-checkouts/gnu/bash/manual/bash.html#Definitions)