POSIX defines “absolute pathname” as follows:
A pathname beginning with a single or more than two <slash> characters
and “relative pathname” as follows:
A pathname not beginning with a <slash> character.
That’s all there is to it for relative and absolute paths.
Canonical paths aren’t defined in POSIX, but the term usually refers to comparable paths, i.e. if you take two paths to a file system object, and convert them to canonical form, the result should be identical if and only if the two file system objects are identical. This involves removing “..” as you mention, but it also means resolving symbolic links; so a canonical path could be defined as
A pathname whose components are all real directories or files, excluding “.” and “..”, and whose slashes are not repeated
In POSIX terms, a canonical pathname is effectively a resolved pathname (as long as you accept that canonical pathnames can only be determined for file system objects which exist).
Note that this only works because hard-linked directories aren’t allowed...
So to answer your questions:
- an absolute path can contain
/../
;
- a canonical path can not contain
/../
, nor can it contain /./
, //
(except arguably in first position), or symbolic links;
foo
is a relative path.
(Pedantically, they are all pathnames, not just paths.)