Can non-canonicalized forms of filesystem paths be significant? (eg. "foo//bar", "foo/./bar", and "foo/../bar")

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http://unix.stackexchange.com – I have a script for building a particular flavor of GCC cross-compiler. Throughout the script there are many paths that are not in canonical form, such as duplicate path separators (/xxx/foo//bar/yyy) and intervening "this" directories (/xxx/foo/./bar/yyy). I was about to canonicalize all of them, but I wonder if these forms are significant rather than just a case of the script not being cleaned up. In addition to the forms just mentioned, I am also curious whether including an "up directory" in a path can also be significant in any particular situation (ie. "/xxx/foo/../bar/yyy instead of /x (HowTos)