The notion of the tree edit distance provides a unifying framework for measuring distance and finding approximate common patterns between two trees. A diversity of tree edit distance measures have been proposed to deal with tree related problems, such as minor containment, maximum common subtree isomorphism, maximum common embedded subtree, and alignment of trees. These classes of problems are characterized by the conditions of the tree mappings, which specify how to associate the nodes in one tree with the nodes in the other. In this paper, we study the declarative semantics of edit distance measures based on the tree mapping. In prior work, the edit distance measures have been not well-formalized. So the relationship among various algorithms based on the tree edit distance has hardly been studied. Our framework enables us to study the relationship. By using our framework, we reveal the declarative semantics of the alignment of trees, which has remained unknown in prior work.