Standard: http://www.w3.org/TR/xpath#function-local-name

string local-name (node-set?)

Standard excerpt:

The local-name function returns the local part of the expanded-name of the node in the argument node-set that is first in document order. If the argument node-set is empty or the first node has no expanded-name, an empty string is returned. If the argument is omitted, it defaults to a node-set with the context node as its only member.