1738 is insufficiently formal, and AFAIK is superseded by 2616 and 3986. 3986 (URI Generic Syntax) says that the host component is required, but one of the alternatives for it is “reg-name” which may be zero-length, but:

If the URI scheme defines a default for host, then that default applies when the host subcomponent is undefined or when the registered name is empty (zero length). For example, the "file" URI scheme is defined so that no authority, an empty host, and "localhost" all mean the end-user's machine, whereas the "http" scheme considers a missing authority or empty host invalid.

RFC 2616 (HTTP/1.1) specifies the host as being non-optional and using the grammar from RFC 2396, which defines it such that the empty string is not included. Therefore my previous claim was incorrect per specifications.

Safari 4.0.4 Mac implements http:// and http:///foo as equivalent to http://localhost/ and http://localhost/foo/, possibly by analogy to file:///foo/.