If a word begins with an unquoted tilde character (‘~’), all of the characters up to the first unquoted slash (or all characters, if there is no unquoted slash) are considered a tilde-prefix. If none of the characters in the tilde-prefix are quoted, the characters in the tilde-prefix following the tilde are treated as a possible login name. If this login name is the null string, the tilde is replaced with the value of the HOME shell variable. If HOME is unset, the home directory of the user executing the shell is substituted instead. Otherwise, the tilde-prefix is replaced with the home directory associated with the specified login name.
If the tilde-prefix is ‘~+’, the value of the shell variable PWD replaces the tilde-prefix. If the tilde-prefix is ‘~-’, the value of the shell variable OLDPWD, if it is set, is substituted.
If the characters following the tilde in the tilde-prefix consist of a
number N, optionally prefixed by a ‘+’ or a ‘-’,
the tilde-prefix is replaced with the
corresponding element from the directory stack, as it would be displayed
dirs builtin invoked with the characters following tilde
in the tilde-prefix as an argument (see The Directory Stack).
If the tilde-prefix, sans the tilde, consists of a number without a
leading ‘+’ or ‘-’, ‘+’ is assumed.
If the login name is invalid, or the tilde expansion fails, the word is left unchanged.
Each variable assignment is checked for unquoted tilde-prefixes immediately following a ‘:’ or the first ‘=’. In these cases, tilde expansion is also performed. Consequently, one may use file names with tildes in assignments to PATH, MAILPATH, and CDPATH, and the shell assigns the expanded value.
The following table shows how Bash treats unquoted tilde-prefixes:
fooof the home directory of the user